Daily Papers

The rapid progress of foundation models has led to the prosperity of autonomous agents, which leverage the universal capabilities of foundation models to conduct reasoning, decision-making, and environmental interaction. However, the efficacy of agents remains limited when operating in intricate, realistic environments. In this work, we introduce the principles of Unified Alignment for Agents (UA^2), which advocate for the simultaneous alignment of agents with human intentions, environmental dynamics, and self-constraints such as the limitation of monetary budgets. From the perspective of UA^2, we review the current agent research and highlight the neglected factors in existing agent benchmarks and method candidates. We also conduct proof-of-concept studies by introducing realistic features to WebShop, including user profiles to demonstrate intentions, personalized reranking for complex environmental dynamics, and runtime cost statistics to reflect self-constraints. We then follow the principles of UA^2 to propose an initial design of our agent, and benchmark its performance with several candidate baselines in the retrofitted WebShop. The extensive experimental results further prove the importance of the principles of UA^2. Our research sheds light on the next steps of autonomous agent research with improved general problem-solving abilities.

Significant focus has been placed on integrating large language models (LLMs) with various tools in developing general-purpose agents. This poses a challenge to LLMs' tool-use capabilities. However, there are evident gaps between existing tool-use evaluations and real-world scenarios. Current evaluations often use AI-generated queries, single-step tasks, dummy tools, and text-only interactions, failing to reveal the agents' real-world problem-solving abilities effectively. To address this, we propose GTA, a benchmark for General Tool Agents, featuring three main aspects: (i) Real user queries: human-written queries with simple real-world objectives but implicit tool-use, requiring the LLM to reason the suitable tools and plan the solution steps. (ii) Real deployed tools: an evaluation platform equipped with tools across perception, operation, logic, and creativity categories to evaluate the agents' actual task execution performance. (iii) Real multimodal inputs: authentic image files, such as spatial scenes, web page screenshots, tables, code snippets, and printed/handwritten materials, used as the query contexts to align with real-world scenarios closely. We design 229 real-world tasks and executable tool chains to evaluate mainstream LLMs. Our findings show that real-world user queries are challenging for existing LLMs, with GPT-4 completing less than 50% of the tasks and most LLMs achieving below 25%. This evaluation reveals the bottlenecks in the tool-use capabilities of current LLMs in real-world scenarios, which provides future direction for advancing general-purpose tool agents. The code and dataset are available at https://github.com/open-compass/GTA.

The Massive Multitask Language Understanding (MMLU) benchmark has been widely used to evaluate language models across various domains. However, existing MMLU datasets primarily focus on high-resource languages such as English, which leaves low-resource languages like Bengali underrepresented. In this paper, we introduce BnMMLU, a benchmark to evaluate the multitask language understanding capabilities of Bengali in language models. The dataset spans 23 domains, including science, humanities, mathematics and general knowledge and is structured in a multiple-choice format to assess factual knowledge, application-based problem-solving and reasoning abilities of language models. It consists of 138,949 question-option pairs. We benchmark several proprietary and open-source large language models (LLMs) on the BnMMLU test set. Additionally, we annotate the test set with three cognitive categories-factual knowledge, procedural application and reasoning-to gain deeper insights into model strengths and weaknesses across various cognitive tasks. The results reveal significant performance gaps, highlighting the need for improved pre-training and fine-tuning strategies tailored to Bengali data. We release the dataset and benchmark results to facilitate further research in this area.

Despite the existence of various benchmarks for evaluating natural language processing models, we argue that human exams are a more suitable means of evaluating general intelligence for large language models (LLMs), as they inherently demand a much wider range of abilities such as language understanding, domain knowledge, and problem-solving skills. To this end, we introduce M3Exam, a novel benchmark sourced from real and official human exam questions for evaluating LLMs in a multilingual, multimodal, and multilevel context. M3Exam exhibits three unique characteristics: (1) multilingualism, encompassing questions from multiple countries that require strong multilingual proficiency and cultural knowledge; (2) multimodality, accounting for the multimodal nature of many exam questions to test the model's multimodal understanding capability; and (3) multilevel structure, featuring exams from three critical educational periods to comprehensively assess a model's proficiency at different levels. In total, M3Exam contains 12,317 questions in 9 diverse languages with three educational levels, where about 23\% of the questions require processing images for successful solving. We assess the performance of top-performing LLMs on M3Exam and find that current models, including GPT-4, still struggle with multilingual text, particularly in low-resource and non-Latin script languages. Multimodal LLMs also perform poorly with complex multimodal questions. We believe that M3Exam can be a valuable resource for comprehensively evaluating LLMs by examining their multilingual and multimodal abilities and tracking their development. Data and evaluation code is available at https://github.com/DAMO-NLP-SG/M3Exam.

While advancements in the reasoning abilities of LLMs have significantly enhanced their performance in solving mathematical problems, coding tasks, and general puzzles, their effectiveness in accurately adhering to instructions remains inconsistent, particularly with more complex directives. Our investigation identifies lazy reasoning during the thinking stage as the primary factor contributing to poor instruction adherence. To mitigate this issue, we propose a comprehensive framework designed to enable rigorous reasoning processes involving preview and self-checking, essential for satisfying strict instruction constraints. Specifically, we first generate instructions with complex constraints and apply a filtering process to obtain valid prompts, resulting in three distinct prompt datasets categorized as hard, easy, and pass. Then, we employ rejection sampling on the pass prompts to curate a small yet high-quality dataset, enabling a cold-start initialization of the model and facilitating its adaptation to effective reasoning patterns. Subsequently, we employ an entropy-preserving supervised fine-tuning (Entropy-SFT) strategy coupled with token-wise entropy-adaptive (TEA-RL) reinforcement learning guided by rule-based dense rewards. This approach encourages the model to transform its reasoning mechanism, ultimately fostering generalizable reasoning abilities that encompass preview and self-checking. Extensive experiments conducted on instruction-following benchmarks demonstrate remarkable performance improvements across various model scales. Notably, our Light-IF-32B model surpasses both larger open-source models such as DeepSeek-R1 and closed-source models like Doubao-1.6.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

Recent methods have demonstrated that Large Language Models (LLMs) can solve reasoning tasks better when they are encouraged to solve subtasks of the main task first. In this paper we devise a similar strategy that breaks down reasoning tasks into a problem decomposition phase and a problem solving phase and show that the strategy is able to outperform a single stage solution. Further, we hypothesize that the decomposition should be easier to distill into a smaller model compared to the problem solving because the latter requires large amounts of domain knowledge while the former only requires learning general problem solving strategies. We propose methods to distill these two capabilities and evaluate their impact on reasoning outcomes and inference cost. We find that we can distill the problem decomposition phase and at the same time achieve good generalization across tasks, datasets, and models. However, it is harder to distill the problem solving capability without losing performance and the resulting distilled model struggles with generalization. These results indicate that by using smaller, distilled problem decomposition models in combination with problem solving LLMs we can achieve reasoning with cost-efficient inference and local adaptation.

We consider the problem of eliciting compositional generalization capabilities in large language models (LLMs) with a novel type of prompting strategy. Compositional generalization empowers the LLMs to solve problems that are harder than the ones they have seen (i.e., easy-to-hard generalization), which is a critical reasoning capability of human-like intelligence. However, even the current state-of-the-art LLMs still struggle with this form of reasoning. To bridge this gap, we propose skills-in-context (SKiC) prompting, which instructs LLMs how to compose basic skills to resolve more complex problems. We find that it is crucial to demonstrate both the skills and the compositional examples within the same prompting context. With as few as two examplars, our SKiC prompting initiates strong synergies between skills and their composition capabilities. Notably, it empowers LLMs to solve unseen problems that require innovative skill compositions, achieving near-perfect generalization on a broad range of challenging compositionality tasks. Intriguingly, SKiC prompting unlocks the latent potential of LLMs, enabling them to leverage pre-existing internal skills acquired during earlier pre-training stages, even when these skills are not explicitly presented in the prompting context. This results in the capability of LLMs to solve unseen complex problems by activating and composing internal competencies. With such prominent features, SKiC prompting is able to achieve state-of-the-art performance on challenging mathematical reasoning benchmarks (e.g., MATH).

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

The capabilities and limitations of Large Language Models have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.

The recent advent of large language models has reinvigorated debate over whether human cognitive capacities might emerge in such generic models given sufficient training data. Of particular interest is the ability of these models to reason about novel problems zero-shot, without any direct training. In human cognition, this capacity is closely tied to an ability to reason by analogy. Here, we performed a direct comparison between human reasoners and a large language model (the text-davinci-003 variant of GPT-3) on a range of analogical tasks, including a non-visual matrix reasoning task based on the rule structure of Raven's Standard Progressive Matrices. We found that GPT-3 displayed a surprisingly strong capacity for abstract pattern induction, matching or even surpassing human capabilities in most settings; preliminary tests of GPT-4 indicated even better performance. Our results indicate that large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

The concept of Artificial Intelligence has gained a lot of attention over the last decade. In particular, AI-based tools have been employed in several scenarios and are, by now, pervading our everyday life. Nonetheless, most of these systems lack many capabilities that we would naturally consider to be included in a notion of "intelligence". In this work, we present an architecture that, inspired by the cognitive theory known as Thinking Fast and Slow by D. Kahneman, is tasked with solving planning problems in different settings, specifically: classical and multi-agent epistemic. The system proposed is an instance of a more general AI paradigm, referred to as SOFAI (for Slow and Fast AI). SOFAI exploits multiple solving approaches, with different capabilities that characterize them as either fast or slow, and a metacognitive module to regulate them. This combination of components, which roughly reflects the human reasoning process according to D. Kahneman, allowed us to enhance the reasoning process that, in this case, is concerned with planning in two different settings. The behavior of this system is then compared to state-of-the-art solvers, showing that the newly introduced system presents better results in terms of generality, solving a wider set of problems with an acceptable trade-off between solving times and solution accuracy.

In this perspective paper, we introduce the concept of Specialized Generalist Artificial Intelligence (SGAI or simply SGI) as a crucial milestone toward Artificial General Intelligence (AGI). Compared to directly scaling general abilities, SGI is defined as AI that specializes in at least one task, surpassing human experts, while also retaining general abilities. This fusion path enables SGI to rapidly achieve high-value areas. We categorize SGI into three stages based on the level of mastery over professional skills and generality performance. Additionally, we discuss the necessity of SGI in addressing issues associated with large language models, such as their insufficient generality, specialized capabilities, uncertainty in innovation, and practical applications. Furthermore, we propose a conceptual framework for developing SGI that integrates the strengths of Systems 1 and 2 cognitive processing. This framework comprises three layers and four key components, which focus on enhancing individual abilities and facilitating collaborative evolution. We conclude by summarizing the potential challenges and suggesting future directions. We hope that the proposed SGI will provide insights into further research and applications towards achieving AGI.

The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during pretraining? To disentangle these effects, we propose an evaluation framework based on "counterfactual" task variants that deviate from the default assumptions underlying standard tasks. Across a suite of 11 tasks, we observe nontrivial performance on the counterfactual variants, but nevertheless find that performance substantially and consistently degrades compared to the default conditions. This suggests that while current LMs may possess abstract task-solving skills to a degree, they often also rely on narrow, non-transferable procedures for task-solving. These results motivate a more careful interpretation of language model performance that teases apart these aspects of behavior.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

LLMs are typically trained to answer user questions or follow instructions similarly to how human experts respond. However, in the standard alignment framework they lack the basic ability of explicit thinking before answering. Thinking is important for complex questions that require reasoning and planning -- but can be applied to any task. We propose a training method for equipping existing LLMs with such thinking abilities for general instruction following without use of additional human data. We achieve this by an iterative search and optimization procedure that explores the space of possible thought generations, allowing the model to learn how to think without direct supervision. For each instruction, the thought candidates are scored using a judge model to evaluate their responses only, and then optimized via preference optimization. We show that this procedure leads to superior performance on AlpacaEval and Arena-Hard, and shows gains from thinking on non-reasoning categories such as marketing, health and general knowledge, in addition to more traditional reasoning & problem-solving tasks.

We developed a benchmark set to assess the generalization of state-of-the-art large language models on problems beyond linguistic tasks and evaluate it on a systematic progression of GPT models (GPT-3.5, GPT-4, GPT-4o, GPT-4o-mini). Using simple games like Tic-Tac-Toe, Connect Four, Battleship, and a Shape Recognition Game, all encoded in ASCII, we test strategic capabilities and spatial reasoning, core abilities any artificial intelligence would need to master for solving problems in chemistry. To probe generalization, we introduce two new games for spatial logic: LEGO Connect Language (LCL) and Guess-the-SMILES (GtS), a operationally simple chemistry benchmark. Our results show that GPT models provide meaningful responses for several tasks but, generally, perform poorly. A systematic performance progression with increased model capabilities (GPT-3.5, GPT-4, GPT-4o) is only observed for 4 out of the 7 benchmark tasks. All models consistently struggle with Battleship, LCL, and GtS. This suggests that while GPT models can emulate conversational proficiency and basic rule comprehension, they have limited generalization with respect to strategy and spatial reasoning. Particularly poor performance is observed for interpreting molecular graphs when encoded in ASCII. The results provided by our open-source benchmark suite (https://github.com/BlueVelvetSackOfGoldPotatoes/child-play{ChildPlay GitHub Repository}) caution against claims of emergent intelligence in GPT models, which appear more specialized than general.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

The potential of large language models (LLMs) to simultaneously perform a wide range of natural language processing (NLP) tasks has been the subject of extensive research. Although instruction tuning has proven to be a data-efficient method for transforming LLMs into such generalist models, their performance still lags behind specialist models trained exclusively for specific tasks. In this paper, we investigate whether incorporating broad-coverage generalist instruction tuning can contribute to building a specialist model. We hypothesize that its efficacy depends on task specificity and skill requirements. Our experiments assess four target tasks with distinct coverage levels, revealing that integrating generalist instruction tuning consistently enhances model performance when the task coverage is broad. The effect is particularly pronounced when the amount of task-specific training data is limited. Further investigation into three target tasks focusing on different capabilities demonstrates that generalist instruction tuning improves understanding and reasoning abilities. However, for tasks requiring factual knowledge, generalist data containing hallucinatory information may negatively affect the model's performance. Overall, our work provides a systematic guide for developing specialist models with general instruction tuning. Our code and other related resources can be found at https://github.com/DavidFanzz/Generalist_or_Specialist.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

The ability to solve problems is a hallmark of intelligence and has been an enduring goal in AI. AI systems that can create programs as solutions to problems or assist developers in writing programs can increase productivity and make programming more accessible. Recently, pre-trained large language models have shown impressive abilities in generating new codes from natural language descriptions, repairing buggy codes, translating codes between languages, and retrieving relevant code segments. However, the evaluation of these models has often been performed in a scattered way on only one or two specific tasks, in a few languages, at a partial granularity (e.g., function) level and in many cases without proper training data. Even more concerning is that in most cases the evaluation of generated codes has been done in terms of mere lexical overlap rather than actual execution whereas semantic similarity (or equivalence) of two code segments depends only on their ``execution similarity'', i.e., being able to get the same output for a given input.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Large language models (LLMs) such as ChatGPT and GPT-4 have made significant progress in NLP. However, their ability to memorize, represent, and leverage commonsense knowledge has been a well-known pain point for LLMs. It remains unclear that: (1) Can GPTs effectively answer commonsense questions? (2) Are GPTs knowledgeable in commonsense? (3) Are GPTs aware of the underlying commonsense knowledge for answering a specific question? (4) Can GPTs effectively leverage commonsense for answering questions? To evaluate the above commonsense problems, we conduct a series of experiments to evaluate ChatGPT's commonsense abilities, and the experimental results show that: (1) GPTs can achieve good QA accuracy in commonsense tasks, while they still struggle with certain types of knowledge. (2) ChatGPT is knowledgeable, and can accurately generate most of the commonsense knowledge using knowledge prompts. (3) Despite its knowledge, ChatGPT is an inexperienced commonsense problem solver, which cannot precisely identify the needed commonsense knowledge for answering a specific question, i.e., ChatGPT does not precisely know what commonsense knowledge is required to answer a question. The above findings raise the need to investigate better mechanisms for utilizing commonsense knowledge in LLMs, such as instruction following, better commonsense guidance, etc.

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified mathematical reasoning benchmark consisting of 23 diverse tasks along four dimensions: (i) mathematical abilities e.g., arithmetic, calculus (ii) language format e.g., question-answering, fill-in-the-blanks (iii) language diversity e.g., no language, simple language (iv) external knowledge e.g., commonsense, physics. We construct our benchmark by extending 20 datasets benchmark by collecting task instructions and solutions in the form of Python programs, thereby obtaining explainable solutions in addition to the correct answer. We additionally introduce two evaluation datasets to measure out-of-distribution performance and robustness to language perturbation. Finally, we introduce BHASKARA, a general-purpose mathematical reasoning model trained on LILA. Importantly, we find that multi-tasking leads to significant improvements (average relative improvement of 21.83% F1 score vs. single-task models), while the best performing model only obtains 60.40%, indicating the room for improvement in general mathematical reasoning and understanding.

While visual question-answering (VQA) benchmarks have catalyzed the development of reasoning techniques, they have focused on vertical thinking. Effective problem-solving also necessitates lateral thinking, which remains understudied in AI and has not been used to test visual perception systems. To bridge this gap, we formulate visual lateral thinking as a multiple-choice question-answering task and describe a three-step taxonomy-driven methodology for instantiating task examples. Then, we develop COLUMBUS, a synthetic benchmark that applies the task pipeline to create QA sets with text and icon rebus puzzles based on publicly available collections of compounds and common phrases. COLUMBUS comprises over 1,000 puzzles, each with four answer candidates. While the SotA vision-language models (VLMs) achieve decent performance, our evaluation demonstrates a substantial gap between humans and models. VLMs benefit from human-curated descriptions but struggle to self-generate such representations at the right level of abstraction.

As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization -- the capacity to combine learned skills in novel ways not encountered during training -- has garnered significant attention. This type of generalization, particularly in scenarios beyond training data, is also of great interest in the study of AI safety and alignment. A recent study introduced the SKILL-MIX evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified k-tuple of language skills. While small models struggled with composing even with k=3, larger models like GPT-4 performed reasonably well with k=5 and 6. In this paper, we employ a setup akin to SKILL-MIX to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills -- including rhetorical, literary, reasoning, theory of mind, and common sense -- GPT-4 was used to generate text samples that exhibit random subsets of k skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of k, revealed the following findings: (1) Training on combinations of k=2 and 3 skills results in noticeable improvements in the ability to compose texts with k=4 and 5 skills, despite models never having seen such examples during training. (2) When skill categories are split into training and held-out groups, models significantly improve at composing texts with held-out skills during testing despite having only seen training skills during fine-tuning, illustrating the efficacy of the training approach even with previously unseen skills. This study also suggests that incorporating skill-rich (potentially synthetic) text into training can substantially enhance the compositional capabilities of models.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

We study the depth of grade-school math (GSM) problem-solving capabilities of LLMs. To this end, we evaluate their performance on pairs of existing math word problems together so that the answer to the second problem depends on correctly answering the first problem. Our findings reveal a significant reasoning gap in most LLMs, that is performance difference between solving the compositional pairs and solving each question independently. This gap is more pronounced in smaller, more cost-efficient, and math-specialized models. Moreover, instruction-tuning recipes and code generation have varying effects across LLM sizes, while finetuning on GSM can lead to task overfitting. Our analysis indicates that large reasoning gaps are not because of test-set leakage, but due to distraction from additional context and poor second-hop reasoning. Overall, LLMs exhibit systematic differences in their reasoning abilities, despite what their performance on standard benchmarks indicates.

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

Large multimodal models extend the impressive capabilities of large language models by integrating multimodal understanding abilities. However, it is not clear how they can emulate the general intelligence and reasoning ability of humans. As recognizing patterns and abstracting concepts are key to general intelligence, we introduce PuzzleVQA, a collection of puzzles based on abstract patterns. With this dataset, we evaluate large multimodal models with abstract patterns based on fundamental concepts, including colors, numbers, sizes, and shapes. Through our experiments on state-of-the-art large multimodal models, we find that they are not able to generalize well to simple abstract patterns. Notably, even GPT-4V cannot solve more than half of the puzzles. To diagnose the reasoning challenges in large multimodal models, we progressively guide the models with our ground truth reasoning explanations for visual perception, inductive reasoning, and deductive reasoning. Our systematic analysis finds that the main bottlenecks of GPT-4V are weaker visual perception and inductive reasoning abilities. Through this work, we hope to shed light on the limitations of large multimodal models and how they can better emulate human cognitive processes in the future (Our data and code will be released publicly at https://github.com/declare-lab/LLM-PuzzleTest).

In this paper, we present a novel approach for distilling math word problem solving capabilities from large language models (LLMs) into smaller, more efficient student models. Our approach is designed to consider the student model's weaknesses and foster a tailored learning experience by generating targeted exercises aligned with educational science principles, such as knowledge tracing and personalized learning. Concretely, we let GPT-3 be a math tutor and run two steps iteratively: 1) assessing the student model's current learning status on a GPT-generated exercise book, and 2) improving the student model by training it with tailored exercise samples generated by GPT-3. Experimental results reveal that our approach outperforms LLMs (e.g., GPT-3 and PaLM) in accuracy across three distinct benchmarks while employing significantly fewer parameters. Furthermore, we provide a comprehensive analysis of the various components within our methodology to substantiate their efficacy.

This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

We study whether transformers can learn to implicitly reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we consistently find that transformers can learn implicit reasoning, but only through grokking, i.e., extended training far beyond overfitting. The levels of generalization also vary across reasoning types: when faced with out-of-distribution examples, transformers fail to systematically generalize for composition but succeed for comparison. We delve into the model's internals throughout training, conducting analytical experiments that reveal: 1) the mechanism behind grokking, such as the formation of the generalizing circuit and its relation to the relative efficiency of generalizing and memorizing circuits, and 2) the connection between systematicity and the configuration of the generalizing circuit. Our findings guide data and training setup to better induce implicit reasoning and suggest potential improvements to the transformer architecture, such as encouraging cross-layer knowledge sharing. Furthermore, we demonstrate that for a challenging reasoning task with a large search space, GPT-4-Turbo and Gemini-1.5-Pro based on non-parametric memory fail badly regardless of prompting styles or retrieval augmentation, while a fully grokked transformer can achieve near-perfect accuracy, showcasing the power of parametric memory for complex reasoning.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

Achieving generalizability in solving out-of-distribution tasks is one of the ultimate goals of learning robotic manipulation. Recent progress of Vision-Language Models (VLMs) has shown that VLM-based task planners can alleviate the difficulty of solving novel tasks, by decomposing the compounded tasks as a plan of sequentially executing primitive-level skills that have been already mastered. It is also promising for robotic manipulation to adapt such composable generalization ability, in the form of composable generalization agents (CGAs). However, the community lacks of reliable design of primitive skills and a sufficient amount of primitive-level data annotations. Therefore, we propose RH20T-P, a primitive-level robotic manipulation dataset, which contains about 38k video clips covering 67 diverse manipulation tasks in real-world scenarios. Each clip is manually annotated according to a set of meticulously designed primitive skills that are common in robotic manipulation. Furthermore, we standardize a plan-execute CGA paradigm and implement an exemplar baseline called RA-P on our RH20T-P, whose positive performance on solving unseen tasks validates that the proposed dataset can offer composable generalization ability to robotic manipulation agents.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

Advancements in LLMs have significantly expanded their capabilities across various domains. However, mathematical reasoning remains a challenging area, prompting the development of math-specific LLMs. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for SFT. Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for hard multi-step problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called JiuZhang-8B.

How cost-effectively can we elicit strong reasoning in language models by leveraging their underlying representations? We answer this question with Resa, a family of 1.5B reasoning models trained via a novel and efficient sparse autoencoder tuning (SAE-Tuning) procedure. This method first trains an SAE to capture reasoning abilities from a source model, and then uses the trained SAE to guide a standard supervised fine-tuning process to elicit such abilities in a target model, all using verified question-answer data without any reasoning traces. Notably, when applied to certain base models before further RL post-training, SAE-Tuning retains >97% of its RL-trained counterpart's reasoning performance while reducing training costs by >2000x to roughly \1 and training time by >450x to around 20 minutes. Furthermore, when applied to lightly RL-trained models (e.g., within 1 hour on 2 GPUs), it enables reasoning performance such as 43.33% Pass@1 on AIME24 and 90% Pass@1 on AMC23 for only around 1 additional cost. Surprisingly, the reasoning abilities extracted via SAEs are potentially both generalizable and modular. Generality means abilities extracted from one dataset still elevate performance on a larger and overlapping corpus. Modularity means abilities extracted from Qwen or Qwen-Math can be attached to the R1-Distill model at test time, without any retraining, and yield comparable gains. Extensive ablations validate these findings and all artifacts are fully open-sourced.

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Eleven Large Language Models (LLMs) were assessed using a custom-made battery of false-belief tasks, considered a gold standard in testing Theory of Mind (ToM) in humans. The battery included 640 prompts spread across 40 diverse tasks, each one including a false-belief scenario, three closely matched true-belief control scenarios, and the reversed versions of all four. To solve a single task, a model needed to correctly answer 16 prompts across all eight scenarios. Smaller and older models solved no tasks; GPT-3-davinci-003 (from November 2022) and ChatGPT-3.5-turbo (from March 2023) solved 20% of the tasks; ChatGPT-4 (from June 2023) solved 75% of the tasks, matching the performance of six-year-old children observed in past studies. We explore the potential interpretation of these findings, including the intriguing possibility that ToM, previously considered exclusive to humans, may have spontaneously emerged as a byproduct of LLMs' improving language skills.

Recent reasoning-oriented LLMs have demonstrated strong performance on challenging tasks such as mathematics and science examinations. However, core cognitive faculties of human intelligence, such as abstract reasoning and generalization, remain underexplored. To address this, we evaluate recent reasoning-oriented LLMs on the Abstraction and Reasoning Corpus (ARC) benchmark, which explicitly demands both faculties. We formulate ARC as a program synthesis task and propose nine candidate solvers. Experimental results show that repeated-sampling planning-aided code generation (RSPC) achieves the highest test accuracy and demonstrates consistent generalization across most LLMs. To further improve performance, we introduce an ARC solver, Knowledge Augmentation for Abstract Reasoning (KAAR), which encodes core knowledge priors within an ontology that classifies priors into three hierarchical levels based on their dependencies. KAAR progressively expands LLM reasoning capacity by gradually augmenting priors at each level, and invokes RSPC to generate candidate solutions after each augmentation stage. This stage-wise reasoning reduces interference from irrelevant priors and improves LLM performance. Empirical results show that KAAR maintains strong generalization and consistently outperforms non-augmented RSPC across all evaluated LLMs, achieving around 5% absolute gains and up to 64.52% relative improvement. Despite these achievements, ARC remains a challenging benchmark for reasoning-oriented LLMs, highlighting future avenues of progress in LLMs.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

In current NLP research, large-scale language models and their abilities are widely being discussed. Some recent works have also found notable failures of these models. Often these failure examples involve complex reasoning abilities. This work focuses on a simple commonsense ability, reasoning about when an action (or its effect) is feasible. To this end, we introduce FeasibilityQA, a question-answering dataset involving binary classification (BCQ) and multi-choice multi-correct questions (MCQ) that test understanding of feasibility. We show that even state-of-the-art models such as GPT-3, GPT-2, and T5 struggle to answer the feasibility questions correctly. Specifically, on MCQ and BCQ questions, GPT-3 achieves an accuracy of just (19%, 62%) and (25%, 64%) in zero-shot and few-shot settings, respectively. We also evaluate models by providing relevant knowledge statements required to answer the question. We find that the additional knowledge leads to a 7% gain in performance, but the overall performance still remains low. These results make one wonder how much commonsense knowledge about action feasibility is encoded in state-of-the-art models and how well they can reason about it.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Human intelligence excels at combining basic skills to solve complex tasks. This capability is vital for Artificial Intelligence (AI) and should be embedded in comprehensive intelligent models, enabling them to harness expert models for complex task-solving towards Artificial General Intelligence (AGI). Large Language Models (LLMs) show promising learning and reasoning abilities, and can effectively use external models, tools or APIs to tackle complex problems. In this work, we introduce OpenAGI, an open-source AGI research platform designed for multi-step, real-world tasks. Specifically, OpenAGI uses a dual strategy, integrating standard benchmark tasks for benchmarking and evaluation, and open-ended tasks including more expandable models, tools or APIs for creative problem-solving. Tasks are presented as natural language queries to the LLM, which then selects and executes appropriate models. We also propose a Reinforcement Learning from Task Feedback (RLTF) mechanism that uses task results to improve the LLM's ability, which creates a self-improving AI feedback loop. While we acknowledge that AGI is a broad and multifaceted research challenge with no singularly defined solution path, the integration of LLMs with domain-specific expert models, inspired by mirroring the blend of general and specialized intelligence in humans, offers a promising approach towards AGI. We are open-sourcing the OpenAGI project's code, dataset, benchmarks, evaluation methods, and demo to foster community involvement in AGI advancement: https://github.com/agiresearch/OpenAGI.

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These include theorem proving, solving quantitative mathematics problems, and reading/summarizing novels. In this paper, we run careful empirical studies exploring the length generalization capabilities of transformer-based language models. We first establish that naively finetuning transformers on length generalization tasks shows significant generalization deficiencies independent of model scale. We then show that combining pretrained large language models' in-context learning abilities with scratchpad prompting (asking the model to output solution steps before producing an answer) results in a dramatic improvement in length generalization. We run careful failure analyses on each of the learning modalities and identify common sources of mistakes that highlight opportunities in equipping language models with the ability to generalize to longer problems.

Generalist foundation models such as GPT-4 have displayed surprising capabilities in a wide variety of domains and tasks. Yet, there is a prevalent assumption that they cannot match specialist capabilities of fine-tuned models. For example, most explorations to date on medical competency benchmarks have leveraged domain-specific training, as exemplified by efforts on BioGPT and Med-PaLM. We build on a prior study of GPT-4's capabilities on medical challenge benchmarks in the absence of special training. Rather than using simple prompting to highlight the model's out-of-the-box capabilities, we perform a systematic exploration of prompt engineering. We find that prompting innovation can unlock deeper specialist capabilities and show that GPT-4 easily tops prior leading results for medical benchmarks. The prompting methods we explore are general purpose, and make no specific use of domain expertise, removing the need for expert-curated content. Our experimental design carefully controls for overfitting during the prompt engineering process. We introduce Medprompt, based on a composition of several prompting strategies. With Medprompt, GPT-4 achieves state-of-the-art results on all nine of the benchmark datasets in the MultiMedQA suite. The method outperforms leading specialist models such as Med-PaLM 2 by a significant margin with an order of magnitude fewer calls to the model. Steering GPT-4 with Medprompt achieves a 27% reduction in error rate on the MedQA dataset over the best methods to date achieved with specialist models and surpasses a score of 90% for the first time. Beyond medical problems, we show the power of Medprompt to generalize to other domains and provide evidence for the broad applicability of the approach via studies of the strategy on exams in electrical engineering, machine learning, philosophy, accounting, law, nursing, and clinical psychology.

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, which presents a substantial risk of model overfitting and fails to accurately represent genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly and readily applied across a diverse array of tasks. Motivated by this, we introduce MATHCHECK, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MATHCHECK includes multiple mathematical reasoning tasks and robustness test types to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MATHCHECK, we develop MATHCHECK-GSM and MATHCHECK-GEO to assess mathematical textual reasoning and multi-modal reasoning capabilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MATHCHECK-GSM and MATHCHECK-GEO to evaluate over 20 LLMs and 11 MLLMs, assessing their comprehensive mathematical reasoning abilities. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MATHCHECK better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. On our MATHCHECK, we can easily conduct detailed behavior analysis to deeply investigate models.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

We introduce Seed1.5-Thinking, capable of reasoning through thinking before responding, resulting in improved performance on a wide range of benchmarks. Seed1.5-Thinking achieves 86.7 on AIME 2024, 55.0 on Codeforces and 77.3 on GPQA, demonstrating excellent reasoning abilities in STEM and coding. Beyond reasoning tasks, the method demonstrates notable generalization across diverse domains. For instance, it surpasses DeepSeek R1 by 8% in win rate on non-reasoning tasks, indicating its broader applicability. Compared to other state-of-the-art reasoning models, Seed1.5-Thinking is a Mixture-of-Experts (MoE) model with a relatively small size, featuring 20B activated and 200B total parameters. As part of our effort to assess generalized reasoning, we develop two internal benchmarks, BeyondAIME and Codeforces, both of which will be publicly released to support future research. Model trial link: https://www.volcengine.com/experience/ark.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

The rapid advancement of artificial intelligence, particularly with the development of Large Language Models (LLMs) built on the transformer architecture, has redefined the capabilities of natural language processing. These models now exhibit remarkable performance across various language-related tasks, such as text generation, question answering, translation, and summarization, often rivaling human-like comprehension. More intriguingly, LLMs have demonstrated emergent abilities extending beyond their core functions, showing proficiency in tasks like commonsense reasoning, code generation, and arithmetic. This survey paper explores the foundational components, scaling mechanisms, and architectural strategies that drive these capabilities. Emphasizing models like GPT and LLaMA, we analyze the impact of exponential data and computational growth on LLM performance, while also addressing the trade-offs associated with scaling. We also examine LLM applications across sectors, such as healthcare, finance, education, and law, highlighting their adaptability and potential to solve domain-specific challenges. Central to this work are the questions of how LLMs generalize across diverse tasks, exhibit planning, and reasoning abilities, and whether these emergent abilities can be systematically elicited or enhanced. In particular, we provide some insights into the CoT (Chain of Thought) and PoT (Plan of Thought) abilities within LLMs, focusing on how pre-training data influences their emergence. Additionally, we investigate LLM-modulo frameworks that integrate external systems, allowing LLMs to handle complex, dynamic tasks. By analyzing these factors, this paper aims to foster the ongoing discussion on the capabilities and limits of LLMs, promoting their responsible development and application in novel and increasingly complex environments.

Large Language Models (LLMs) have demonstrated impressive real-world utility, exemplifying artificial useful intelligence (AUI). However, their ability to reason adaptively and robustly -- the hallmarks of artificial general intelligence (AGI) -- remains fragile. While LLMs seemingly succeed in commonsense reasoning, programming, and mathematics, they struggle to generalize algorithmic understanding across novel contexts. Our experiments with algorithmic tasks in esoteric programming languages reveal that LLM's reasoning overfits to the training data and is limited in its transferability. We hypothesize that the core issue underlying such limited transferability is the coupling of reasoning and knowledge in LLMs. To transition from AUI to AGI, we propose disentangling knowledge and reasoning through three key directions: (1) pretaining to reason using RL from scratch as an alternative to the widely used next-token prediction pretraining, (2) using a curriculum of synthetic tasks to ease the learning of a reasoning prior for RL that can then be transferred to natural language tasks, and (3) learning more generalizable reasoning functions using a small context window to reduce exploiting spurious correlations between tokens. Such a reasoning system coupled with a trained retrieval system and a large external memory bank as a knowledge store can overcome several limitations of existing architectures at learning to reason in novel scenarios.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

Chain-of-thought (CoT) prompting with large language models has proven effective in numerous natural language processing tasks, but designing prompts that generalize well to diverse problem types can be challenging, especially in the context of math word problem (MWP) solving. Additionally, it is common to have a large amount of training data that have a better diversity coverage but CoT annotations are not available, which limits the use of supervised learning techniques. To address these issues, we investigate two approaches to leverage the training data in a few-shot prompting scenario: dynamic program prompting and program distillation. Our approach is largely inspired by Gao et al., (2022), where they proposed to replace the CoT with the programs as the intermediate reasoning step. Such a prompting strategy allows us to accurately verify the answer correctness through program execution in MWP solving. Our dynamic program prompting involves annotating the training data by sampling correct programs from a large language model, while program distillation involves adapting a smaller model to the program-annotated training data. Our experiments on three standard MWP datasets demonstrate the effectiveness of these approaches, yielding significant improvements over previous baselines for prompting and fine-tuning. Our results suggest that leveraging a large amount of training data can improve the generalization ability of prompts and boost the performance of fine-tuned small models in MWP solving.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

Generalist robots that can perform a range of different tasks in open-world settings must be able to not only reason about the steps needed to accomplish their goals, but also process complex instructions, prompts, and even feedback during task execution. Intricate instructions (e.g., "Could you make me a vegetarian sandwich?" or "I don't like that one") require not just the ability to physically perform the individual steps, but the ability to situate complex commands and feedback in the physical world. In this work, we describe a system that uses vision-language models in a hierarchical structure, first reasoning over complex prompts and user feedback to deduce the most appropriate next step to fulfill the task, and then performing that step with low-level actions. In contrast to direct instruction following methods that can fulfill simple commands ("pick up the cup"), our system can reason through complex prompts and incorporate situated feedback during task execution ("that's not trash"). We evaluate our system across three robotic platforms, including single-arm, dual-arm, and dual-arm mobile robots, demonstrating its ability to handle tasks such as cleaning messy tables, making sandwiches, and grocery shopping. Videos are available at https://www.pi.website/research/hirobot

Generative artificial intelligence (AI) systems based on large-scale pretrained foundation models (PFMs) such as vision-language models, large language models (LLMs), diffusion models and vision-language-action (VLA) models have demonstrated the ability to solve complex and truly non-trivial AI problems in a wide variety of domains and contexts. Multimodal large language models (MLLMs), in particular, learn from vast and diverse data sources, allowing rich and nuanced representations of the world and, thereby, providing extensive capabilities, including the ability to reason, engage in meaningful dialog; collaborate with humans and other agents to jointly solve complex problems; and understand social and emotional aspects of humans. Despite this impressive feat, the cognitive abilities of state-of-the-art LLMs trained on large-scale datasets are still superficial and brittle. Consequently, generic LLMs are severely limited in their generalist capabilities. A number of foundational problems -- embodiment, symbol grounding, causality and memory -- are required to be addressed for LLMs to attain human-level general intelligence. These concepts are more aligned with human cognition and provide LLMs with inherent human-like cognitive properties that support the realization of physically-plausible, semantically meaningful, flexible and more generalizable knowledge and intelligence. In this work, we discuss the aforementioned foundational issues and survey state-of-the art approaches for implementing these concepts in LLMs. Specifically, we discuss how the principles of embodiment, symbol grounding, causality and memory can be leveraged toward the attainment of artificial general intelligence (AGI) in an organic manner.

Can machines truly think, reason and act in domains like humans? This enduring question continues to shape the pursuit of Artificial General Intelligence (AGI). Despite the growing capabilities of models such as GPT-4.5, DeepSeek, Claude 3.5 Sonnet, Phi-4, and Grok 3, which exhibit multimodal fluency and partial reasoning, these systems remain fundamentally limited by their reliance on token-level prediction and lack of grounded agency. This paper offers a cross-disciplinary synthesis of AGI development, spanning artificial intelligence, cognitive neuroscience, psychology, generative models, and agent-based systems. We analyze the architectural and cognitive foundations of general intelligence, highlighting the role of modular reasoning, persistent memory, and multi-agent coordination. In particular, we emphasize the rise of Agentic RAG frameworks that combine retrieval, planning, and dynamic tool use to enable more adaptive behavior. We discuss generalization strategies, including information compression, test-time adaptation, and training-free methods, as critical pathways toward flexible, domain-agnostic intelligence. Vision-Language Models (VLMs) are reexamined not just as perception modules but as evolving interfaces for embodied understanding and collaborative task completion. We also argue that true intelligence arises not from scale alone but from the integration of memory and reasoning: an orchestration of modular, interactive, and self-improving components where compression enables adaptive behavior. Drawing on advances in neurosymbolic systems, reinforcement learning, and cognitive scaffolding, we explore how recent architectures begin to bridge the gap between statistical learning and goal-directed cognition. Finally, we identify key scientific, technical, and ethical challenges on the path to AGI.

Thinking aloud is an effective meta-cognitive strategy human reasoners apply to solve difficult problems. We suggest to improve the reasoning ability of pre-trained neural language models in a similar way, namely by expanding a task's context with problem elaborations that are dynamically generated by the language model itself. Our main result is that dynamic problem elaboration significantly improves the zero-shot performance of GPT-2 in a deductive reasoning and natural language inference task: While the model uses a syntactic heuristic for predicting an answer, it is capable (to some degree) of generating reasoned additional context which facilitates the successful application of its heuristic. We explore different ways of generating elaborations, including fewshot learning, and find that their relative performance varies with the specific problem characteristics (such as problem difficulty). Moreover, the effectiveness of an elaboration can be explained in terms of the degree to which the elaboration semantically coheres with the corresponding problem. In particular, elaborations that are most faithful to the original problem description may boost accuracy by up to 24%.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally, solving geometry problems and generating diagrams have been treated as separate tasks in machine learning, with no models successfully integrating both to support problem creation. However, we believe that mastery in geometry requires frictionless integration of all of these skills, from solving problems to visualizing geometric relationships, and finally, crafting tailored problems. Our extensive experiments demonstrate that GeoUni, with only 1.5B parameters, achieves performance comparable to larger models such as DeepSeek-R1 with 671B parameters in geometric reasoning tasks. GeoUni also excels in generating precise geometric diagrams, surpassing both text-to-image models and unified models, including the GPT-4o image generation. Most importantly, GeoUni is the only model capable of successfully generating textual problems with matching diagrams based on specific knowledge points, thus offering a wider range of capabilities that extend beyond current models.

Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning ability to be solved. In this paper, we introduce such a benchmark, consisting of 191 long-form (1200 words on average) mystery narratives constructed as detective puzzles. Puzzles are sourced from the "5 Minute Mystery" platform and include a multiple-choice question for evaluation. Only 47% of humans solve a puzzle successfully on average, while the best human solvers achieve over 80% success rate. We show that GPT-3 models barely outperform random on this benchmark (with 28% accuracy) while state-of-the-art GPT-4 solves only 38% of puzzles. This indicates that there is still a significant gap in the deep reasoning abilities of LLMs and humans and highlights the need for further research in this area. Our work introduces a challenging benchmark for future studies on reasoning in language models and contributes to a better understanding of the limits of LLMs' abilities.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

We explore the ability of large language models to solve and generate puzzles from the NPR Sunday Puzzle game show using PUZZLEQA, a dataset comprising 15 years of on-air puzzles. We evaluate four large language models using PUZZLEQA, in both multiple choice and free response formats, and explore two prompt engineering techniques to improve free response performance: chain-of-thought reasoning and prompt summarization. We find that state-of-the-art large language models can solve many PUZZLEQA puzzles: the best model, GPT-3.5, achieves 50.2% loose accuracy. However, in our few-shot puzzle generation experiment, we find no evidence that models can generate puzzles: GPT-3.5 generates puzzles with answers that do not conform to the generated rules. Puzzle generation remains a challenging task for future work.

Human intelligence thrives on the concept of cognitive synergy, where collaboration and information integration among different cognitive processes yield superior outcomes compared to individual cognitive processes in isolation. Although Large Language Models (LLMs) have demonstrated promising performance as general task-solving agents, they still struggle with tasks that require intensive domain knowledge and complex reasoning. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist refers to an intelligent agent that collaborates with multiple minds, combining their individual strengths and knowledge, to enhance problem-solving and overall performance in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. We have discovered that assigning multiple, fine-grained personas in LLMs elicits better problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, SPP effectively elicits internal knowledge acquisition abilities, reduces hallucination, and maintains strong reasoning capabilities. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.

Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution. We present a self-improvement approach where models iteratively generate and learn from their own solutions, progressively tackling harder problems while maintaining a standard transformer architecture. Across diverse tasks including arithmetic, string manipulation, and maze solving, self-improving enables models to solve problems far beyond their initial training distribution-for instance, generalizing from 10-digit to 100-digit addition without apparent saturation. We observe that in some cases filtering for correct self-generated examples leads to exponential improvements in out-of-distribution performance across training rounds. Additionally, starting from pretrained models significantly accelerates this self-improvement process for several tasks. Our results demonstrate how controlled weak-to-strong curricula can systematically teach a model logical extrapolation without any changes to the positional embeddings, or the model architecture.

Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.

To build an artificial neural network like the biological intelligence system, recent works have unified numerous tasks into a generalist model, which can process various tasks with shared parameters and do not have any task-specific modules. While generalist models achieve promising results on various benchmarks, they have performance degradation on some tasks compared with task-specialized models. In this work, we find that interference among different tasks and modalities is the main factor to this phenomenon. To mitigate such interference, we introduce the Conditional Mixture-of-Experts (Conditional MoEs) to generalist models. Routing strategies under different levels of conditions are proposed to take both the training/inference cost and generalization ability into account. By incorporating the proposed Conditional MoEs, the recently proposed generalist model Uni-Perceiver can effectively mitigate the interference across tasks and modalities, and achieves state-of-the-art results on a series of downstream tasks via prompt tuning on 1% of downstream data. Moreover, the introduction of Conditional MoEs still holds the generalization ability of generalist models to conduct zero-shot inference on new tasks, e.g., video-text retrieval and video caption. Code and pre-trained generalist models shall be released.

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing benchmarks such as GSM8K and MATH present limitations, including narrow problem definitions with specific numbers and reliance on predetermined rules that hinder accurate assessments of reasoning and adaptability. This paper introduces the UTMath Benchmark, which robustly evaluates the models through extensive unit tests. It consists of 1,053 problems across 9 mathematical domains, with over 68 test cases per problem. We propose an innovative evaluation framework inspired by unit testing in software development, focusing on both accuracy and reliability of results. Furthermore, we introduce the Reasoning-to-Coding of Thoughts (RCoT) approach, which encourages LLMs to perform explicit reasoning before generating code, leading to generating more advanced solution and improved performance. Furthermore, we are releasing not only the UTMath benchmark but also the UTMath-Train training dataset (more than 70k samples), to support the community in further exploring mathematical reasoning.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Large Language Models (LLMs) have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical reasoning processes. To mitigate this problem, we introduced Hint-before-Solving Prompting (HSP), which guides the model to generate hints (e.g., specific knowledge or key ideas) for solving the problem and then generate solutions containing intermediate reasoning steps. Since HSP is orthogonal to prompting methods (e.g., Chain-of-Thought (CoT)), we applied HSP to CoT, Least-to-Most, Plan-and-Solve, and Standard promptings. The results of extensive experiments on 6 reasoning benchmarks and 4 open-source LLMs demonstrate that HSP can effectively improve the accuracy of reasoning tasks: (1) By applying high-quality hint-enhanced HSP to CoT prompting, Llama2-70B-Chat shows an improvement of 9.7. (2) Beyond exploring training-free LLM capabilities, we built the HSPMATH dataset based on HSP and fine-tuned Llemma-7B, reaching 64.3 accuracy, surpassing GPT-3.5 and WizardMath-13B. We make our code and dataset publicly available at https://github.com/jinlanfu/HSP.

Existing Large Reasoning Models (LRMs) have shown the potential of reinforcement learning (RL) to enhance the complex reasoning capabilities of Large Language Models~(LLMs). While they achieve remarkable performance on challenging tasks such as mathematics and coding, they often rely on their internal knowledge to solve problems, which can be inadequate for time-sensitive or knowledge-intensive questions, leading to inaccuracies and hallucinations. To address this, we propose R1-Searcher, a novel two-stage outcome-based RL approach designed to enhance the search capabilities of LLMs. This method allows LLMs to autonomously invoke external search systems to access additional knowledge during the reasoning process. Our framework relies exclusively on RL, without requiring process rewards or distillation for a cold start. % effectively generalizing to out-of-domain datasets and supporting both Base and Instruct models. Our experiments demonstrate that our method significantly outperforms previous strong RAG methods, even when compared to the closed-source GPT-4o-mini.

Length generalization, the ability to solve problems of longer sequences than those observed during training, poses a core challenge of Transformer-based large language models (LLM). Although existing studies have predominantly focused on data-driven approaches for arithmetic operations and symbolic manipulation tasks, these approaches tend to be task-specific with limited overall performance. To pursue a more general solution, this paper focuses on a broader case of reasoning problems that are computable, i.e., problems that algorithms can solve, thus can be solved by the Turing Machine. From this perspective, this paper proposes Turing MAchine Imitation Learning (TAIL) to improve the length generalization ability of LLMs. TAIL synthesizes chain-of-thoughts (CoT) data that imitate the execution process of a Turing Machine by computer programs, which linearly expands the reasoning steps into atomic states to alleviate shortcut learning and explicit memory fetch mechanism to reduce the difficulties of dynamic and long-range data access in elementary operations. To validate the reliability and universality of TAIL, we construct a challenging synthetic dataset covering 8 classes of algorithms and 18 tasks. Without bells and whistles, TAIL significantly improves the length generalization ability as well as the performance of Qwen2.5-7B on various tasks using only synthetic data, surpassing previous methods and DeepSeek-R1. The experimental results reveal that the key concepts in the Turing Machine, instead of the thinking styles, are indispensable for TAIL for length generalization, through which the model exhibits read-and-write behaviors consistent with the properties of the Turing Machine in their attention layers. This work provides a promising direction for future research in the learning of LLM reasoning from synthetic data.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

We investigate the capabilities of transformer large language models (LLMs) on relational reasoning tasks involving abstract symbols. Such tasks have long been studied in the neuroscience literature as fundamental building blocks for more complex abilities in programming, mathematics, and verbal reasoning. For (i) regression tasks, we prove that transformers generalize when trained, but require astonishingly large quantities of training data. For (ii) next-token-prediction tasks with symbolic labels, we show an "inverse scaling law": transformers fail to generalize as their embedding dimension increases. For both settings (i) and (ii), we propose subtle transformer modifications which can reduce the amount of data needed by adding two trainable parameters per head.

The quest for human imitative AI has been an enduring topic in AI research since its inception. The technical evolution and emerging capabilities of the latest cohort of large language models (LLMs) have reinvigorated the subject beyond academia to the cultural zeitgeist. While recent NLP evaluation benchmark tasks test some aspects of human-imitative behaviour (e.g., BIG-bench's 'human-like behavior' tasks), few, if not none, examine creative problem solving abilities. Creative problem solving in humans is a well-studied topic in cognitive neuroscience with standardized tests that predominantly use the ability to associate (heterogeneous) connections among clue words as a metric for creativity. Exposure to misleading stimuli - distractors dubbed red herrings - impede human performance in such tasks via the fixation effect and Einstellung paradigm. In cognitive neuroscience studies, such fixations are experimentally induced by pre-exposing participants to orthographically similar incorrect words to subsequent word-fragments or clues. The popular British quiz show Only Connect's Connecting Wall segment essentially mimics Mednick's Remote Associates Test (RAT) formulation with built-in, deliberate red herrings, which makes it an ideal proxy dataset to explore and study fixation effect and Einstellung paradigm from cognitive neuroscience in LLMs. In addition to presenting the novel Only Connect Wall (OCW) dataset, we also report results from our evaluation of selected pre-trained language models and LLMs (including OpenAI's GPT series) on creative problem solving tasks like grouping clue words by heterogeneous connections, and identifying correct open knowledge domain connections in respective groups. The code and link to the dataset are available at https://github.com/TaatiTeam/OCW.

Recent proprietary models (e.g., o3) have begun to demonstrate strong multimodal reasoning capabilities. Yet, most existing open-source research concentrates on training text-only reasoning models, with evaluations limited to mainly mathematical and general-domain tasks. Therefore, it remains unclear how to effectively extend reasoning capabilities beyond text input and general domains. This paper explores a fundamental research question: Is reasoning generalizable across modalities and domains? Our findings support an affirmative answer: General-domain text-based post-training can enable such strong generalizable reasoning. Leveraging this finding, we introduce X-Reasoner, a vision-language model post-trained solely on general-domain text for generalizable reasoning, using a two-stage approach: an initial supervised fine-tuning phase with distilled long chain-of-thoughts, followed by reinforcement learning with verifiable rewards. Experiments show that X-Reasoner successfully transfers reasoning capabilities to both multimodal and out-of-domain settings, outperforming existing state-of-the-art models trained with in-domain and multimodal data across various general and medical benchmarks (Figure 1). Additionally, we find that X-Reasoner's performance in specialized domains can be further enhanced through continued training on domain-specific text-only data. Building upon this, we introduce X-Reasoner-Med, a medical-specialized variant that achieves new state of the art on numerous text-only and multimodal medical benchmarks.

Reinforcement learning (RL) has recently demonstrated strong potential in enhancing the reasoning capabilities of large language models (LLMs). Particularly, the "Zero" reinforcement learning introduced by Deepseek-R1-Zero, enables direct RL training of base LLMs without relying on an intermediate supervised fine-tuning stage. Despite these advancements, current works for LLM reasoning mainly focus on mathematical and coding domains, largely due to data abundance and the ease of answer verification. This limits the applicability and generalization of such models to broader domains, where questions often have diverse answer representations, and data is more scarce. In this paper, we propose General-Reasoner, a novel training paradigm designed to enhance LLM reasoning capabilities across diverse domains. Our key contributions include: (1) constructing a large-scale, high-quality dataset of questions with verifiable answers curated by web crawling, covering a wide range of disciplines; and (2) developing a generative model-based answer verifier, which replaces traditional rule-based verification with the capability of chain-of-thought and context-awareness. We train a series of models and evaluate them on a wide range of datasets covering wide domains like physics, chemistry, finance, electronics etc. Our comprehensive evaluation across these 12 benchmarks (e.g. MMLU-Pro, GPQA, SuperGPQA, TheoremQA, BBEH and MATH AMC) demonstrates that General-Reasoner outperforms existing baseline methods, achieving robust and generalizable reasoning performance while maintaining superior effectiveness in mathematical reasoning tasks.

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced with complex problems that demand deep conceptual understanding and intricate, multi-step deliberation. To address this challenge, we introduce JT-Math-8B, a series of open-source models comprising base, instruct, and thinking versions, built upon a systematic, multi-stage optimization framework. Our pre-training corpus is a high-quality, 210B-token dataset curated through a dedicated data pipeline that uses model-based validation to ensure quality and diversity. The Instruct Model is optimized for direct, concise answers through Supervised Fine-Tuning (SFT) and a GRPO-based reinforcement learning (RL) method. The Thinking Model is trained for complex problem-solving using a Long Chain-of-Thought (Long CoT) approach, combining SFT with a novel, multi-stage RL curriculum that progressively increases task difficulty and context length up to 32K tokens. JT-Math-8B achieves state-of-the-art results among open-source models of similar size, surpassing prominent models like OpenAI's O1-mini and GPT-4o , and demonstrating superior performance on competition-level mathematics.

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

Despite impressive progress on complex reasoning, current large language models (LLMs) typically operate in isolation - treating each problem as an independent attempt, without accumulating or integrating experiential knowledge. In contrast, expert problem solvers - such as Olympiad or programming contest teams - leverage a rich tapestry of experiences: absorbing mentorship from coaches, developing intuition from past problems, leveraging knowledge of tool usage and library functionality, adapting strategies based on the expertise and experiences of peers, continuously refining their reasoning through trial and error, and learning from other related problems even during competition. We introduce Xolver, a training-free multi-agent reasoning framework that equips a black-box LLM with a persistent, evolving memory of holistic experience. Xolver integrates diverse experience modalities, including external and self-retrieval, tool use, collaborative interactions, agent-driven evaluation, and iterative refinement. By learning from relevant strategies, code fragments, and abstract reasoning patterns at inference time, Xolver avoids generating solutions from scratch - marking a transition from isolated inference toward experience-aware language agents. Built on both open-weight and proprietary models, Xolver consistently outperforms specialized reasoning agents. Even with lightweight backbones (e.g., QWQ-32B), it often surpasses advanced models including Qwen3-235B, Gemini 2.5 Pro, o3, and o4-mini-high. With o3-mini-high, it achieves new best results on GSM8K (98.1%), AIME'24 (94.4%), AIME'25 (93.7%), Math-500 (99.8%), and LiveCodeBench-V5 (91.6%) - highlighting holistic experience learning as a key step toward generalist agents capable of expert-level reasoning. Code and data are available at https://kagnlp.github.io/xolver.github.io/.

This paper presents a critical examination of current approaches to replicating OpenAI's O1 model capabilities, with particular focus on the widespread but often undisclosed use of knowledge distillation techniques. While our previous work explored the fundamental technical path to O1 replication, this study reveals how simple distillation from O1's API, combined with supervised fine-tuning, can achieve superior performance on complex mathematical reasoning tasks. Through extensive experiments, we show that a base model fine-tuned on simply tens of thousands of samples O1-distilled long-thought chains outperforms O1-preview on the American Invitational Mathematics Examination (AIME) with minimal technical complexity. Moreover, our investigation extends beyond mathematical reasoning to explore the generalization capabilities of O1-distilled models across diverse tasks: hallucination, safety and open-domain QA. Notably, despite training only on mathematical problem-solving data, our models demonstrated strong generalization to open-ended QA tasks and became significantly less susceptible to sycophancy after fine-tuning. We deliberately make this finding public to promote transparency in AI research and to challenge the current trend of obscured technical claims in the field. Our work includes: (1) A detailed technical exposition of the distillation process and its effectiveness, (2) A comprehensive benchmark framework for evaluating and categorizing O1 replication attempts based on their technical transparency and reproducibility, (3) A critical discussion of the limitations and potential risks of over-relying on distillation approaches, our analysis culminates in a crucial bitter lesson: while the pursuit of more capable AI systems is important, the development of researchers grounded in first-principles thinking is paramount.

Transformer models pre-trained with a masked-language-modeling objective (e.g., BERT) encode commonsense knowledge as evidenced by behavioral probes; however, the extent to which this knowledge is acquired by systematic inference over the semantics of the pre-training corpora is an open question. To answer this question, we selectively inject verbalized knowledge into the minibatches of a BERT model during pre-training and evaluate how well the model generalizes to supported inferences. We find generalization does not improve over the course of pre-training, suggesting that commonsense knowledge is acquired from surface-level, co-occurrence patterns rather than induced, systematic reasoning.

Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

Post-training, particularly reinforcement learning (RL) using self-play-generated data, has become a new learning paradigm for large language models (LLMs). However, scaling RL to develop a general reasoner remains a research challenge, as existing methods focus on task-specific reasoning without adequately addressing generalization across a broader range of tasks. Moreover, unlike traditional RL with limited action space, LLMs operate in an infinite space, making it crucial to search for valuable and diverse strategies to solve problems effectively. To address this, we propose searching within the action space on high-level abstract plans to enhance model generalization and introduce Critical Plan Step Learning (CPL), comprising: 1) searching on plan, using Monte Carlo Tree Search (MCTS) to explore diverse plan steps in multi-step reasoning tasks, and 2) learning critical plan steps through Step-level Advantage Preference Optimization (Step-APO), which integrates advantage estimates for step preference obtained via MCTS into Direct Preference Optimization (DPO). This combination helps the model effectively learn critical plan steps, enhancing both reasoning capabilities and generalization. Experimental results demonstrate that our method, trained exclusively on GSM8K and MATH, not only significantly improves performance on GSM8K (+10.5%) and MATH (+6.5%), but also enhances out-of-domain reasoning benchmarks, such as HumanEval (+12.2%), GPQA (+8.6%), ARC-C (+4.0%), MMLU-STEM (+2.2%), and BBH (+1.8%).

If generalist robots are to operate in truly unstructured environments, they need to be able to recognize and reason about novel objects and scenarios. Such objects and scenarios might not be present in the robot's own training data. We propose SuSIE, a method that leverages an image-editing diffusion model to act as a high-level planner by proposing intermediate subgoals that a low-level controller can accomplish. Specifically, we finetune InstructPix2Pix on video data, consisting of both human videos and robot rollouts, such that it outputs hypothetical future "subgoal" observations given the robot's current observation and a language command. We also use the robot data to train a low-level goal-conditioned policy to act as the aforementioned low-level controller. We find that the high-level subgoal predictions can utilize Internet-scale pretraining and visual understanding to guide the low-level goal-conditioned policy, achieving significantly better generalization and precision than conventional language-conditioned policies. We achieve state-of-the-art results on the CALVIN benchmark, and also demonstrate robust generalization on real-world manipulation tasks, beating strong baselines that have access to privileged information or that utilize orders of magnitude more compute and training data. The project website can be found at http://rail-berkeley.github.io/susie .

In their recent Nature Human Behaviour paper, "Emergent analogical reasoning in large language models," (Webb, Holyoak, and Lu, 2023) the authors argue that "large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems." In this response, we provide counterexamples of the letter string analogies. In our tests, GPT-3 fails to solve even the easiest variants of the problems presented in the original paper. Zero-shot reasoning is an extraordinary claim that requires extraordinary evidence. We do not see that evidence in our experiments. To strengthen claims of humanlike reasoning such as zero-shot reasoning, it is important that the field develop approaches that rule out data memorization.

Multimodal scientific problems (MSPs) involve complex issues that require the integration of multiple modalities, such as text and diagrams, presenting a significant challenge in artificial intelligence. While progress has been made in addressing traditional scientific problems, MSPs still face two primary issues: the challenge of multi-modal comprehensive reasoning in scientific problem-solving and the lack of reflective and rethinking capabilities. To address these issues, we introduce a Multi-Agent framework based on the Big Seven Personality and Socratic guidance (MAPS). This framework employs seven distinct agents that leverage feedback mechanisms and the Socratic method to guide the resolution of MSPs. To tackle the first issue, we propose a progressive four-agent solving strategy, where each agent focuses on a specific stage of the problem-solving process. For the second issue, we introduce a Critic agent, inspired by Socratic questioning, which prompts critical thinking and stimulates autonomous learning. We conduct extensive experiments on the EMMA, Olympiad, and MathVista datasets, achieving promising results that outperform the current SOTA model by 15.84% across all tasks. Meanwhile, the additional analytical experiments also verify the model's progress as well as generalization ability.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

Providing high quality explanations for AI predictions based on machine learning is a challenging and complex task. To work well it requires, among other factors: selecting a proper level of generality/specificity of the explanation; considering assumptions about the familiarity of the explanation beneficiary with the AI task under consideration; referring to specific elements that have contributed to the decision; making use of additional knowledge (e.g. expert evidence) which might not be part of the prediction process; and providing evidence supporting negative hypothesis. Finally, the system needs to formulate the explanation in a clearly interpretable, and possibly convincing, way. Given these considerations, ANTIDOTE fosters an integrated vision of explainable AI, where low-level characteristics of the deep learning process are combined with higher level schemes proper of the human argumentation capacity. ANTIDOTE will exploit cross-disciplinary competences in deep learning and argumentation to support a broader and innovative view of explainable AI, where the need for high-quality explanations for clinical cases deliberation is critical. As a first result of the project, we publish the Antidote CasiMedicos dataset to facilitate research on explainable AI in general, and argumentation in the medical domain in particular.

Evaluating the general abilities of foundation models to tackle human-level tasks is a vital aspect of their development and application in the pursuit of Artificial General Intelligence (AGI). Traditional benchmarks, which rely on artificial datasets, may not accurately represent human-level capabilities. In this paper, we introduce AGIEval, a novel benchmark specifically designed to assess foundation model in the context of human-centric standardized exams, such as college entrance exams, law school admission tests, math competitions, and lawyer qualification tests. We evaluate several state-of-the-art foundation models, including GPT-4, ChatGPT, and Text-Davinci-003, using this benchmark. Impressively, GPT-4 surpasses average human performance on SAT, LSAT, and math competitions, attaining a 95% accuracy rate on the SAT Math test and a 92.5% accuracy on the English test of the Chinese national college entrance exam. This demonstrates the extraordinary performance of contemporary foundation models. In contrast, we also find that GPT-4 is less proficient in tasks that require complex reasoning or specific domain knowledge. Our comprehensive analyses of model capabilities (understanding, knowledge, reasoning, and calculation) reveal these models' strengths and limitations, providing valuable insights into future directions for enhancing their general capabilities. By concentrating on tasks pertinent to human cognition and decision-making, our benchmark delivers a more meaningful and robust evaluation of foundation models' performance in real-world scenarios. The data, code, and all model outputs are released in https://github.com/microsoft/AGIEval.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks, previous work has conducted supervised fine-tuning on open-source models by improving the quality and quantity of data. In this paper, we propose a novel approach, named Brain, to imitate human thought processes to enhance mathematical reasoning abilities, using the Frontal Lobe Model to generate plans, and then employing the Parietal Lobe Model to generate code and execute to obtain answers. First, we achieve SOTA performance in comparison with Code LLaMA 7B based models through this method. Secondly, we find that plans can be explicitly extracted from natural language, code, or formal language. Our code and data are publicly available at https://github.com/cyzhh/Brain.

Chain of Thought prompting strategy has enhanced the performance of Large Language Models (LLMs) across various NLP tasks. However, it still has shortcomings when dealing with complex reasoning tasks, following~cot_wei, including understanding errors, calculation errors and process errors (e.g. missing-step and hallucinations). Subsequently, Our in-depth analysis of various error types has found that deeply understanding the whole problem is critical in addressing complicated reasoning tasks. In this paper, we proposed a novel prompt strategy called Deeply Understanding the Problems (DUP) prompting, inspired by how humans solve complex reasoning problems, designed to enhance the comprehensive understanding of problems by LLMs. It consists of three stages: 1) extract the core question; 2) find out problem-solving information based on the core question; 3) generate and extract answers by LLMs. We evaluate the performance of DUP prompting on ten diverse reasoning datasets. Experimental results suggest that DUP prompting significantly outperforms Zero-Shot CoT ~kojima2022large across all datasets. Notably, DUP achieves state-of-the-art on SVAMP (90.4\% to 94.2\%) and GSM8K (94.6\% to 97.1\%).

The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper, we present Boosting of Thoughts (BoT), an automated prompting framework for problem solving with LLMs by iteratively exploring and self-evaluating many trees of thoughts in order to acquire an ensemble of trial-and-error reasoning experiences, which will serve as a new form of prompting to solve the complex problem. Starting from a simple prompt without requiring examples, BoT iteratively explores and evaluates a large collection of reasoning steps, and more importantly, uses error analysis obtained from the LLM on them to explicitly revise prompting, which in turn enhances reasoning step generation, until a final answer is attained. Our experiments with GPT-4 and Llama2 across extensive complex mathematical problems demonstrate that BoT consistently achieves higher or comparable problem-solving rates than other advanced prompting approaches.

In recent years, large language models (LLMs) have shown remarkable capabilities in various artificial intelligence problems. However, they fail to plan reliably, even when prompted with a detailed definition of the planning task. Attempts to improve their planning capabilities, such as chain-of-thought prompting, fine-tuning, and explicit "reasoning" still yield incorrect plans and usually fail to generalize to larger tasks. In this paper, we show how to use LLMs to generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks within a greedy best-first search, and choose the strongest one. The resulting LLM-generated heuristics solve many more unseen test tasks than state-of-the-art domain-independent heuristics for classical planning. They are even competitive with the strongest learning algorithm for domain-dependent planning. These findings are especially remarkable given that our proof-of-concept implementation is based on an unoptimized Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, revealing that they are not only efficiently computable, but sometimes even more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic function programs can significantly improve the planning capabilities of LLMs.

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

Recently, large-scale pre-trained language models have demonstrated impressive performance on several commonsense-reasoning benchmark datasets. However, building machines with commonsense to compose realistically plausible sentences remains challenging. In this paper, we present a constrained text generation task, CommonGen associated with a benchmark dataset, to explicitly test machines for the ability of generative commonsense reasoning. Given a set of common concepts (e.g., {dog, frisbee, catch, throw}); the task is to generate a coherent sentence describing an everyday scenario using these concepts (e.g., "a man throws a frisbee and his dog catches it"). The CommonGen task is challenging because it inherently requires 1) relational reasoning with background commonsense knowledge, and 2) compositional generalization ability to work on unseen concept combinations. Our dataset, constructed through a combination of crowdsourced and existing caption corpora, consists of 79k commonsense descriptions over 35k unique concept-sets. Experiments show that there is a large gap between state-of-the-art text generation models (e.g., T5) and human performance. Furthermore, we demonstrate that the learned generative commonsense reasoning capability can be transferred to improve downstream tasks such as CommonsenseQA by generating additional context.

One way to enhance the reasoning capability of Large Language Models (LLMs) is to conduct Supervised Fine-Tuning (SFT) using Chain-of-Thought (CoT) annotations. This approach does not show sufficiently strong generalization ability, however, because the training only relies on the given CoT data. In math problem-solving, for example, there is usually only one annotated reasoning path for each question in the training data. Intuitively, it would be better for the algorithm to learn from multiple annotated reasoning paths given a question. To address this issue, we propose a simple yet effective approach called Reinforced Fine-Tuning (ReFT) to enhance the generalizability of learning LLMs for reasoning, with math problem-solving as an example. ReFT first warmups the model with SFT, and then employs on-line reinforcement learning, specifically the PPO algorithm in this paper, to further fine-tune the model, where an abundance of reasoning paths are automatically sampled given the question and the rewards are naturally derived from the ground-truth answers. Extensive experiments on GSM8K, MathQA, and SVAMP datasets show that ReFT significantly outperforms SFT, and the performance can be potentially further boosted by combining inference-time strategies such as majority voting and re-ranking. Note that ReFT obtains the improvement by learning from the same training questions as SFT, without relying on extra or augmented training questions. This indicates a superior generalization ability for ReFT.

Large language models exhibit surprising emergent generalization properties, yet also struggle on many simple reasoning tasks such as arithmetic and parity. This raises the question of if and when Transformer models can learn the true algorithm for solving a task. We study the scope of Transformers' abilities in the specific setting of length generalization on algorithmic tasks. Here, we propose a unifying framework to understand when and how Transformers can exhibit strong length generalization on a given task. Specifically, we leverage RASP (Weiss et al., 2021) -- a programming language designed for the computational model of a Transformer -- and introduce the RASP-Generalization Conjecture: Transformers tend to length generalize on a task if the task can be solved by a short RASP program which works for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks. Moreover, we leverage our insights to drastically improve generalization performance on traditionally hard tasks (such as parity and addition). On the theoretical side, we give a simple example where the "min-degree-interpolator" model of learning from Abbe et al. (2023) does not correctly predict Transformers' out-of-distribution behavior, but our conjecture does. Overall, our work provides a novel perspective on the mechanisms of compositional generalization and the algorithmic capabilities of Transformers.

How much is 56 times 37? Language models often make mistakes in these types of difficult calculations. This is usually explained by their inability to perform complex reasoning. Since language models rely on large training sets and great memorization capability, naturally they are not equipped to run complex calculations. However, one can argue that humans also cannot perform this calculation immediately and require a considerable amount of time to construct the solution. In order to enhance the generalization capability of language models, and as a parallel to human behavior, we propose to use special 'thinking tokens' which allow the model to perform much more calculations whenever a complex problem is encountered.

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the intricate reasoning required. This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset. The dataset includes diverse mathematical problems at high school and university levels, created by experts from notable institutions to rigorously test LLMs in advanced problem-solving scenarios and cover a wider range of subject areas. By providing the MathOdyssey dataset as a resource to the AI community, we aim to contribute to the understanding and improvement of AI capabilities in complex mathematical problem-solving. We conduct benchmarking on open-source models, such as Llama-3 and DBRX-Instruct, and closed-source models from the GPT series and Gemini models. Our results indicate that while LLMs perform well on routine and moderately difficult tasks, they face significant challenges with Olympiad-level problems and complex university-level questions. Our analysis shows a narrowing performance gap between open-source and closed-source models, yet substantial challenges remain, particularly with the most demanding problems. This study highlights the ongoing need for research to enhance the mathematical reasoning of LLMs. The dataset, results, and code are publicly available.

The zero-shot chain of thought (CoT) approach is often used in question answering (QA) by language models (LMs) for tasks that require multiple reasoning steps, typically enhanced by the prompt "Let's think step by step." However, some QA tasks hinge more on accessing relevant knowledge than on chaining reasoning steps. We introduce a simple general prompting technique, called PREP, that involves using two instances of LMs: the first (LM1) generates relevant information, and the second (LM2) answers the question based on this information. PREP is designed to be general and independent of the user's domain knowledge, making it applicable across various QA tasks without the need for specialized prompt engineering. To evaluate the effectiveness of our prompting method, we create a dataset of 100 binary-choice questions, derived from an extensive schematic dataset on artifact parts and material composition. These questions ask which of two artifacts is less likely to share materials with another artifact. Such questions probe the LM's knowledge of shared materials in the part structure of different artifacts. We test our method on our dataset and three published commonsense reasoning datasets. The average accuracy of our method is consistently higher than that of all the other tested methods across all the tested datasets.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across diverse domains. Unlike traditional computational systems, LLMs combine raw computational power with an approximation of human reasoning, allowing them to generate solutions, make inferences, and even leverage external computational tools. However, applying LLMs to real-world problem-solving presents significant challenges, including multi-step reasoning, domain knowledge integration, and result verification. This survey explores the capabilities and limitations of LLMs in complex problem-solving, examining techniques including Chain-of-Thought (CoT) reasoning, knowledge augmentation, and various LLM-based and tool-based verification techniques. Additionally, we highlight domain-specific challenges in various domains, such as software engineering, mathematical reasoning and proving, data analysis and modeling, and scientific research. The paper further discusses the fundamental limitations of the current LLM solutions and the future directions of LLM-based complex problems solving from the perspective of multi-step reasoning, domain knowledge integration and result verification.

The present study aims to explore the capabilities of Language Models (LMs) in tackling high-stakes multiple-choice tests, represented here by the Exame Nacional do Ensino M\'edio (ENEM), a multidisciplinary entrance examination widely adopted by Brazilian universities. This exam poses challenging tasks for LMs, since its questions may span into multiple fields of knowledge, requiring understanding of information from diverse domains. For instance, a question may require comprehension of both statistics and biology to be solved. This work analyzed responses generated by GPT-3.5 and GPT-4 models for questions presented in the 2009-2017 exams, as well as for questions of the 2022 exam, which were made public after the training of the models was completed. Furthermore, different prompt strategies were tested, including the use of Chain-of-Thought (CoT) prompts to generate explanations for answers. On the 2022 edition, the best-performing model, GPT-4 with CoT, achieved an accuracy of 87%, largely surpassing GPT-3.5 by 11 points. The code and data used on experiments are available at https://github.com/piresramon/gpt-4-enem.

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

The recently released Google Gemini class of models are the first to comprehensively report results that rival the OpenAI GPT series across a wide variety of tasks. In this paper, we do an in-depth exploration of Gemini's language abilities, making two contributions. First, we provide a third-party, objective comparison of the abilities of the OpenAI GPT and Google Gemini models with reproducible code and fully transparent results. Second, we take a closer look at the results, identifying areas where one of the two model classes excels. We perform this analysis over 10 datasets testing a variety of language abilities, including reasoning, answering knowledge-based questions, solving math problems, translating between languages, generating code, and acting as instruction-following agents. From this analysis, we find that Gemini Pro achieves accuracy that is close but slightly inferior to the corresponding GPT 3.5 Turbo on all tasks that we benchmarked. We further provide explanations for some of this under-performance, including failures in mathematical reasoning with many digits, sensitivity to multiple-choice answer ordering, aggressive content filtering, and others. We also identify areas where Gemini demonstrates comparably high performance, including generation into non-English languages, and handling longer and more complex reasoning chains. Code and data for reproduction can be found at https://github.com/neulab/gemini-benchmark

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer? We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps, assuming a slight generalization to standard pre-norm, adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps with generalized pre-norm make them recognize exactly the class of polynomial-time solvable problems -- the first exact characterization of a type of transformers in terms of standard complexity classes. Together, our results provide a nuanced framework for understanding how the length of a transformer's chain of thought or scratchpad impacts its reasoning power.

We evaluate the reasoning abilities of large language models in multilingual settings. We introduce the Multilingual Grade School Math (MGSM) benchmark, by manually translating 250 grade-school math problems from the GSM8K dataset (Cobbe et al., 2021) into ten typologically diverse languages. We find that the ability to solve MGSM problems via chain-of-thought prompting emerges with increasing model scale, and that models have strikingly strong multilingual reasoning abilities, even in underrepresented languages such as Bengali and Swahili. Finally, we show that the multilingual reasoning abilities of language models extend to other tasks such as commonsense reasoning and word-in-context semantic judgment. The MGSM benchmark is publicly available at https://github.com/google-research/url-nlp.

Reasoning in a complex and ambiguous environment is a key goal for Reinforcement Learning (RL) agents. While some sophisticated RL agents can successfully solve difficult tasks, they require a large amount of training data and often struggle to generalize to new unseen environments and new tasks. On the other hand, Large Scale Language Models (LSLMs) have exhibited strong reasoning ability and the ability to to adapt to new tasks through in-context learning. However, LSLMs do not inherently have the ability to interrogate or intervene on the environment. In this work, we investigate how to combine these complementary abilities in a single system consisting of three parts: a Planner, an Actor, and a Reporter. The Planner is a pre-trained language model that can issue commands to a simple embodied agent (the Actor), while the Reporter communicates with the Planner to inform its next command. We present a set of tasks that require reasoning, test this system's ability to generalize zero-shot and investigate failure cases, and demonstrate how components of this system can be trained with reinforcement-learning to improve performance.

Given questions regarding some prototypical situation such as Name something that people usually do before they leave the house for work? a human can easily answer them via acquired experiences. There can be multiple right answers for such questions, with some more common for a situation than others. This paper introduces a new question answering dataset for training and evaluating common sense reasoning capabilities of artificial intelligence systems in such prototypical situations. The training set is gathered from an existing set of questions played in a long-running international game show FAMILY- FEUD. The hidden evaluation set is created by gathering answers for each question from 100 crowd-workers. We also propose a generative evaluation task where a model has to output a ranked list of answers, ideally covering all prototypical answers for a question. After presenting multiple competitive baseline models, we find that human performance still exceeds model scores on all evaluation metrics with a meaningful gap, supporting the challenging nature of the task.

Visual Question Answering (VQA) methods have made incredible progress, but suffer from a failure to generalize. This is visible in the fact that they are vulnerable to learning coincidental correlations in the data rather than deeper relations between image content and ideas expressed in language. We present a dataset that takes a step towards addressing this problem in that it contains questions expressed in two languages, and an evaluation process that co-opts a well understood image-based metric to reflect the method's ability to reason. Measuring reasoning directly encourages generalization by penalizing answers that are coincidentally correct. The dataset reflects the scene-text version of the VQA problem, and the reasoning evaluation can be seen as a text-based version of a referring expression challenge. Experiments and analysis are provided that show the value of the dataset.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing correct answers, AI systems should also be capable of, or assist humans in, developing novel solutions to mathematical challenges. This study explores the creative potential of Large Language Models (LLMs) in mathematical reasoning, an aspect that has received limited attention in prior research. We introduce a novel framework and benchmark, CreativeMath, which encompasses problems ranging from middle school curricula to Olympic-level competitions, designed to assess LLMs' ability to propose innovative solutions after some known solutions have been provided. Our experiments demonstrate that, while LLMs perform well on standard mathematical tasks, their capacity for creative problem-solving varies considerably. Notably, the Gemini-1.5-Pro model outperformed other LLMs in generating novel solutions. This research opens a new frontier in evaluating AI creativity, shedding light on both the strengths and limitations of LLMs in fostering mathematical innovation, and setting the stage for future developments in AI-assisted mathematical discovery.

As machine intelligence evolves, the need to test and compare the problem-solving abilities of different AI models grows. However, current benchmarks are often overly simplistic, allowing models to perform uniformly well, making it difficult to distinguish their capabilities. Additionally, benchmarks typically rely on static question-answer pairs, which models might memorize or guess. To address these limitations, we introduce the Dynamic Intelligence Assessment (DIA), a novel methodology for testing AI models using dynamic question templates and improved metrics across multiple disciplines such as mathematics, cryptography, cybersecurity, and computer science. The accompanying DIA-Bench dataset, which includes 150 diverse and challenging task templates with mutable parameters, is presented in various formats such as text, PDFs, compiled binaries, and visual puzzles. Our framework introduces four new metrics to assess a model's reliability and confidence across multiple attempts. These metrics revealed that even simple questions are frequently answered incorrectly when posed in varying forms, highlighting significant gaps in models' reliability. Notably, models like GPT-4o tended to overestimate their mathematical abilities, while ChatGPT-4o demonstrated better decision-making and performance through effective tool usage. We evaluated eight state-of-the-art large language models (LLMs) using DIA-Bench, showing that current models struggle with complex tasks and often display unexpectedly low confidence, even with simpler questions. The DIA framework sets a new standard for assessing not only problem-solving but also a model's adaptive intelligence and ability to assess its own limitations. The dataset is publicly available on our project's website.

We propose a new test to measure a text model's multitask accuracy. The test covers 57 tasks including elementary mathematics, US history, computer science, law, and more. To attain high accuracy on this test, models must possess extensive world knowledge and problem solving ability. We find that while most recent models have near random-chance accuracy, the very largest GPT-3 model improves over random chance by almost 20 percentage points on average. However, on every one of the 57 tasks, the best models still need substantial improvements before they can reach expert-level accuracy. Models also have lopsided performance and frequently do not know when they are wrong. Worse, they still have near-random accuracy on some socially important subjects such as morality and law. By comprehensively evaluating the breadth and depth of a model's academic and professional understanding, our test can be used to analyze models across many tasks and to identify important shortcomings.

For an autonomous agent to fulfill a wide range of user-specified goals at test time, it must be able to learn broadly applicable and general-purpose skill repertoires. Furthermore, to provide the requisite level of generality, these skills must handle raw sensory input such as images. In this paper, we propose an algorithm that acquires such general-purpose skills by combining unsupervised representation learning and reinforcement learning of goal-conditioned policies. Since the particular goals that might be required at test-time are not known in advance, the agent performs a self-supervised "practice" phase where it imagines goals and attempts to achieve them. We learn a visual representation with three distinct purposes: sampling goals for self-supervised practice, providing a structured transformation of raw sensory inputs, and computing a reward signal for goal reaching. We also propose a retroactive goal relabeling scheme to further improve the sample-efficiency of our method. Our off-policy algorithm is efficient enough to learn policies that operate on raw image observations and goals for a real-world robotic system, and substantially outperforms prior techniques.

Large language models (LLMs) have shown exceptional performance as general-purpose assistants, excelling across a variety of reasoning tasks. This achievement represents a significant step toward achieving artificial general intelligence (AGI). Despite these advancements, the effectiveness of LLMs often hinges on the specific prompting strategies employed, and there remains a lack of a robust framework to facilitate learning and generalization across diverse reasoning tasks. To address these challenges, we introduce a novel learning framework, THOUGHT-LIKE-PRO In this framework, we utilize imitation learning to imitate the Chain-of-Thought (CoT) process which is verified and translated from reasoning trajectories generated by a symbolic Prolog logic engine. This framework proceeds in a self-driven manner, that enables LLMs to formulate rules and statements from given instructions and leverage the symbolic Prolog engine to derive results. Subsequently, LLMs convert Prolog-derived successive reasoning trajectories into natural language CoT for imitation learning. Our empirical findings indicate that our proposed approach substantially enhances the reasoning abilities of LLMs and demonstrates robust generalization across out-of-distribution reasoning tasks.

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill composition in a collection of modular arithmetic tasks. Specifically, we consider a finite collection of linear modular functions z = a , x + b , y ;mod; p labeled by the vector (a, b) in Z_p^2. We use some of these tasks for pre-training and the rest for out-of-distribution testing. We empirically show that a GPT-style transformer exhibits a transition from in-distribution to out-of-distribution generalization as the number of pre-training tasks increases. We find that the smallest model capable of out-of-distribution generalization requires two transformer blocks, while for deeper models, the out-of-distribution generalization phase is transient, necessitating early stopping. Finally, we perform an interpretability study of the pre-trained models, revealing the highly structured representations in both phases; and discuss the learnt algorithm.

Large language models often struggle with zero-shot generalization, and several modular approaches have been proposed to address this challenge. Yet, we hypothesize that a key limitation remains: the entanglement of general knowledge and task-specific adaptations. To overcome this, we propose a modular framework that disentangles these components by constructing a library of task-specific LoRA modules alongside a general-domain LoRA. By subtracting this general knowledge component from each task-specific module, we obtain residual modules that focus more exclusively on task-relevant information, a method we call general knowledge subtraction (GenKnowSub). Leveraging the refined task-specific modules and the Arrow routing algorithm ostapenko2024towards, we dynamically select and combine modules for new inputs without additional training. Our studies on the Phi-3 model and standard Arrow as baselines reveal that using general knowledge LoRAs derived from diverse languages, including English, French, and German, yields consistent performance gains in both monolingual and cross-lingual settings across a wide set of benchmarks. Further experiments on Phi-2 demonstrate how GenKnowSub generalizes to weaker LLMs. The complete code and data are available at https://github.com/saharsamr/Modular-LLM.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Trained on vast corpora of human language, language models demonstrate emergent human-like reasoning abilities. Yet they are still far from true intelligence, which opens up intriguing opportunities to explore the parallels of humans and model behaviors. In this work, we study the ability to skip steps in reasoning - a hallmark of human expertise developed through practice. Unlike humans, who may skip steps to enhance efficiency or to reduce cognitive load, models do not inherently possess such motivations to minimize reasoning steps. To address this, we introduce a controlled framework that stimulates step-skipping behavior by iteratively refining models to generate shorter and accurate reasoning paths. Empirical results indicate that models can develop the step skipping ability under our guidance. Moreover, after fine-tuning on expanded datasets that include both complete and skipped reasoning sequences, the models can not only resolve tasks with increased efficiency without sacrificing accuracy, but also exhibit comparable and even enhanced generalization capabilities in out-of-domain scenarios. Our work presents the first exploration into human-like step-skipping ability and provides fresh perspectives on how such cognitive abilities can benefit AI models.

Large Language Models (LLMs) are smart but forgetful. Recent studies, (e.g., (Bubeck et al., 2023)) on modern LLMs have shown that they are capable of performing amazing tasks typically necessitating human-level intelligence. However, unlike humans, frozen LLMs do not improve over time; they neither acquire new knowledge nor learn from their successes or failures. Some approaches to improving the intelligence of LLMs include fine-tuning models based on problem-solving performance (Zelikman et al., 2022), and building bigger and more sophisticated models (Bubeck et al., 2023). However, these methods have the drawback of requiring substantial data and computational resources to retrain existing models. In this paper, we explore the use of Retrieval Augmented Generation, also known as RAG (Lewis et al., 2021) to improve problem-solving performance. We propose ARM-RAG (Auxiliary Rationale Memory for Retrieval Augmented Generation), a system that learns from its successes without incurring high training costs. We demonstrate that the storage and subsequent retrieval of reasoning chains have a positive influence on performance in grade-school math problems.

Recently an influx of studies claim emergent cognitive abilities in large language models (LLMs). Yet, most rely on anecdotes, overlook contamination of training sets, or lack systematic Evaluation involving multiple tasks, control conditions, multiple iterations, and statistical robustness tests. Here we make two major contributions. First, we propose CogEval, a cognitive science-inspired protocol for the systematic evaluation of cognitive capacities in Large Language Models. The CogEval protocol can be followed for the evaluation of various abilities. Second, here we follow CogEval to systematically evaluate cognitive maps and planning ability across eight LLMs (OpenAI GPT-4, GPT-3.5-turbo-175B, davinci-003-175B, Google Bard, Cohere-xlarge-52.4B, Anthropic Claude-1-52B, LLaMA-13B, and Alpaca-7B). We base our task prompts on human experiments, which offer both established construct validity for evaluating planning, and are absent from LLM training sets. We find that, while LLMs show apparent competence in a few planning tasks with simpler structures, systematic evaluation reveals striking failure modes in planning tasks, including hallucinations of invalid trajectories and getting trapped in loops. These findings do not support the idea of emergent out-of-the-box planning ability in LLMs. This could be because LLMs do not understand the latent relational structures underlying planning problems, known as cognitive maps, and fail at unrolling goal-directed trajectories based on the underlying structure. Implications for application and future directions are discussed.

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate language models (LMs). In this paper, we introduce the USACO benchmark with 307 problems from the USA Computing Olympiad, along with high-quality unit tests, reference code, and official analyses for each problem. These resources enable us to construct and test a range of LM inference methods for competitive programming for the first time. We find GPT-4 only achieves a 8.7% pass@1 accuracy with zero-shot chain-of-thought prompting, and our best inference method improves it to 20.2% using a combination of self-reflection and retrieval over episodic knowledge. However, this is far from solving the benchmark. To better understand the remaining challenges, we design a novel human-in-the-loop study and surprisingly find that a small number of targeted hints enable GPT-4 to solve 13 out of 15 problems previously unsolvable by any model and method. Our benchmark, baseline methods, quantitative results, and qualitative analysis serve as an initial step toward LMs with grounded, creative, and algorithmic reasoning.

Large language models (LLMs) like ChatGPT have revealed amazing intelligence. How to evaluate the question-solving abilities of LLMs and their degrees of intelligence is a hot-spot but challenging issue. First, the question-solving abilities are interlaced with different ability branches like understanding and massive knowledge categories like mathematics. Second, the inputs of questions are multimodal that may involve text and images. Third, the response format of LLMs is diverse and thus poses great challenges for result extraction and evaluation. In this paper, we propose AGIBench -- a multi-granularity, multimodal, human-referenced, and auto-scoring benchmarking methodology for LLMs. Instead of a collection of blended questions, AGIBench focuses on three typical ability branches and adopts a four-tuple <ability branch, knowledge, difficulty, modal> to label the attributes of each question. First, it supports multi-granularity benchmarking, e.g., per-question, per-ability branch, per-knowledge, per-modal, per-dataset, and per-difficulty level granularities. Second, it contains multimodal input, including text and images. Third, it classifies all the questions into five degrees of difficulty according to the average accuracy rate of abundant educated humans (human-referenced). Fourth, it adopts zero-shot learning to avoid introducing additional unpredictability and provides an auto-scoring method to extract and judge the result. Finally, it defines multi-dimensional metrics, including accuracy under the average, worst, best, and majority voting cases, and repeatability. AGIBench is publically available from https://www.benchcouncil.org/agibench.

Many students struggle with math word problems (MWPs), often finding it difficult to identify key information and select the appropriate mathematical operations.Schema-based instruction (SBI) is an evidence-based strategy that helps students categorize problems based on their structure, improving problem-solving accuracy. Building on this, we propose a Schema-Based Instruction Retrieval-Augmented Generation (SBI-RAG) framework that incorporates a large language model (LLM).Our approach emphasizes step-by-step reasoning by leveraging schemas to guide solution generation. We evaluate its performance on the GSM8K dataset, comparing it with GPT-4 and GPT-3.5 Turbo, and introduce a "reasoning score" metric to assess solution quality. Our findings suggest that SBI-RAG enhances reasoning clarity and problem-solving accuracy, potentially providing educational benefits for students

Few-shot learning is a challenging task that requires language models to generalize from limited examples. Large language models like GPT-3 and PaLM have made impressive progress in this area, but they still face difficulties in reasoning tasks such as GSM8K, a benchmark for arithmetic problems. To improve their reasoning skills, previous work has proposed to guide the language model with prompts that elicit a series of reasoning steps before giving the final answer, achieving a significant improvement on GSM8K from 17.9% to 58.1% in problem-solving rate. In this paper, we present DIVERSE (Diverse Verifier on Reasoning Step), a novel approach that further enhances the reasoning capability of language models. DIVERSE has three main components: first, it generates diverse prompts to explore different reasoning paths for the same question; second, it uses a verifier to filter out incorrect answers based on a weighted voting scheme; and third, it verifies each reasoning step individually instead of the whole chain. We evaluate DIVERSE on the latest language model code-davinci-002 and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks (e.g., GSM8K 74.4% to 83.2%).

Recent studies show evidence for emergent cognitive abilities in Large Pre-trained Language Models (PLMs). The increasing cognitive alignment of these models has made them candidates for cognitive science theories. Prior research into the emergent cognitive abilities of PLMs has largely been path-independent to model training, i.e., has focused on the final model weights and not the intermediate steps. However, building plausible models of human cognition using PLMs would benefit from considering the developmental alignment of their performance during training to the trajectories of children's thinking. Guided by psychometric tests of human intelligence, we choose four sets of tasks to investigate the alignment of ten popular families of PLMs and evaluate their available intermediate and final training steps. These tasks are Numerical ability, Linguistic abilities, Conceptual understanding, and Fluid reasoning. We find a striking regularity: regardless of model size, the developmental trajectories of PLMs consistently exhibit a window of maximal alignment to human cognitive development. Before that window, training appears to endow "blank slate" models with the requisite structure to be poised to rapidly learn from experience. After that window, training appears to serve the engineering goal of reducing loss but not the scientific goal of increasing alignment with human cognition.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability. Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve problems that are substantially larger and more difficult than it ever saw during training by simply running for more iterations. Moreover, NeuroSAT generalizes to novel distributions; after training only on random SAT problems, at test time it can solve SAT problems encoding graph coloring, clique detection, dominating set, and vertex cover problems, all on a range of distributions over small random graphs.

Probing and enhancing large language models' reasoning capacity remains a crucial open question. Here we re-purpose the reverse dictionary task as a case study to probe LLMs' capacity for conceptual inference. We use in-context learning to guide the models to generate the term for an object concept implied in a linguistic description. Models robustly achieve high accuracy in this task, and their representation space encodes information about object categories and fine-grained features. Further experiments suggest that the conceptual inference ability as probed by the reverse-dictionary task predicts model's general reasoning performance across multiple benchmarks, despite similar syntactic generalization behaviors across models. Explorative analyses suggest that prompting LLMs with descriptionRightarrowword examples may induce generalization beyond surface-level differences in task construals and facilitate models on broader commonsense reasoning problems.

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.

Most existing chain-of-thought (CoT) prompting methods suffer from the issues of generalizability and consistency, as they often rely on instance-specific solutions that may not be applicable to other cases and lack task-level consistency in their reasoning steps. To address these limitations, we propose a comprehensive framework, StrategyLLM, harnessing the capabilities of LLMs to construct generalizable and consistent few-shot prompts for various tasks automatically. To this end, StrategyLLM employs four LLM-based agents: strategy generator, executor, optimizer, and evaluator, working together to generate, evaluate, and select promising strategies for a given task. The experimental results demonstrate that StrategyLLM outperforms the competitive baseline CoT-SC that requires human-annotated solutions on 13 datasets across 4 challenging tasks without human involvement, including math reasoning (34.21% rightarrow 38.79%), commonsense reasoning (70.3% rightarrow 72.5%), algorithmic reasoning (51.7% rightarrow 62.0%), and symbolic reasoning (30.0% rightarrow 79.2%).

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.

Large language models (LLMs) excel on a variety of reasoning benchmarks, but previous studies suggest they sometimes struggle to generalize to unseen questions, potentially due to over-reliance on memorized training examples. However, the precise conditions under which LLMs switch between reasoning and memorization during text generation remain unclear. In this work, we provide a mechanistic understanding of LLMs' reasoning-memorization dynamics by identifying a set of linear features in the model's residual stream that govern the balance between genuine reasoning and memory recall. These features not only distinguish reasoning tasks from memory-intensive ones but can also be manipulated to causally influence model performance on reasoning tasks. Additionally, we show that intervening in these reasoning features helps the model more accurately activate the most relevant problem-solving capabilities during answer generation. Our findings offer new insights into the underlying mechanisms of reasoning and memory in LLMs and pave the way for the development of more robust and interpretable generative AI systems.

Humans (e.g., crowdworkers) have a remarkable ability in solving different tasks, by simply reading textual instructions that define them and looking at a few examples. Despite the success of the conventional supervised learning on individual datasets, such models often struggle with generalization across tasks (e.g., a question-answering system cannot solve classification tasks). A long-standing challenge in AI is to build a model that learns a new task by understanding the human-readable instructions that define it. To study this, we introduce NATURAL INSTRUCTIONS, a dataset of 61 distinct tasks, their human-authored instructions, and 193k task instances (input-output pairs). The instructions are obtained from crowdsourcing instructions used to create existing NLP datasets and mapped to a unified schema. Using this meta-dataset, we measure cross-task generalization by training models on seen tasks and measuring generalization to the remaining unseen ones. We adopt generative pre-trained language models to encode task-specific instructions along with input and generate task output. Our results indicate that models benefit from instructions when evaluated in terms of generalization to unseen tasks (19% better for models utilizing instructions). These models, however, are far behind an estimated performance upperbound indicating significant room for more progress in this direction.

In this paper, we introduce Concise Chain-of-Thought (CCoT) prompting. We compared standard CoT and CCoT prompts to see how conciseness impacts response length and correct-answer accuracy. We evaluated this using GPT-3.5 and GPT-4 with a multiple-choice question-and-answer (MCQA) benchmark. CCoT reduced average response length by 48.70% for both GPT-3.5 and GPT-4 while having a negligible impact on problem-solving performance. However, on math problems, GPT-3.5 with CCoT incurs a performance penalty of 27.69%. Overall, CCoT leads to an average per-token cost reduction of 22.67%. These results have practical implications for AI systems engineers using LLMs to solve real-world problems with CoT prompt-engineering techniques. In addition, these results provide more general insight for AI researchers studying the emergent behavior of step-by-step reasoning in LLMs.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

As the field progresses toward Artificial General Intelligence (AGI), there is a pressing need for more comprehensive and insightful evaluation frameworks that go beyond aggregate performance metrics. This paper introduces a unified rating system that jointly models the difficulty of individual test cases and the competency of AI models (or humans) across vision, language, and action domains. Unlike existing metrics that focus solely on models, our approach allows for fine-grained, difficulty-aware evaluations through competitive interactions between models and tasks, capturing both the long-tail distribution of real-world challenges and the competency gap between current models and full task mastery. We validate the generalizability and robustness of our system through extensive experiments on multiple established datasets and models across distinct AGI domains. The resulting rating distributions offer novel perspectives and interpretable insights into task difficulty, model progression, and the outstanding challenges that remain on the path to achieving full AGI task mastery.

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

Common-sense reasoning is a key language model capability because it encapsulates not just specific factual knowledge but rather general language and world understanding. Measuring common-sense reasoning, therefore, is crucial for language models of different sizes and applications. One of the most widely used benchmarks for evaluating such capabilities is HellaSwag; however, in this paper, we show that it has severe construct validity issues. These issues range from basic ungrammaticality and numerous typos to misleading prompts or equally correct options. Furthermore, we show that if models are evaluated only on answer texts, or with "Lorem ipsum dolor..." instead of the question, more than 65% of model predictions remain the same, and this cannot be attributed merely to contamination. Since benchmark scores are an essential part of model selection in both research and commercial applications, these validity issues can have severe consequences. In particular, knowing that taking benchmark scores at face value is ubiquitous, inadequate evaluation leads to ill-informed decisions about models. In this paper, we thoroughly investigate critical validity issues posed by HellaSwag and illustrate them with various evaluations using generative language models of different sizes. We argue that this benchmark does not accurately measure common-sense reasoning and, therefore, should not be used for evaluation in its current state. Based on the results of our study, we propose requirements that should be met by future common-sense reasoning benchmarks. In addition, we release GoldenSwag, a corrected subset of HellaSwag, which, to our belief, facilitates acceptable common-sense reasoning evaluation.

Whether neural networks can learn abstract reasoning or whether they merely rely on superficial statistics is a topic of recent debate. Here, we propose a dataset and challenge designed to probe abstract reasoning, inspired by a well-known human IQ test. To succeed at this challenge, models must cope with various generalisation `regimes' in which the training and test data differ in clearly-defined ways. We show that popular models such as ResNets perform poorly, even when the training and test sets differ only minimally, and we present a novel architecture, with a structure designed to encourage reasoning, that does significantly better. When we vary the way in which the test questions and training data differ, we find that our model is notably proficient at certain forms of generalisation, but notably weak at others. We further show that the model's ability to generalise improves markedly if it is trained to predict symbolic explanations for its answers. Altogether, we introduce and explore ways to both measure and induce stronger abstract reasoning in neural networks. Our freely-available dataset should motivate further progress in this direction.

Post-training Large Language Models (LLMs) with explicit reasoning trajectories can enhance their reasoning abilities. However, acquiring such high-quality trajectory data typically demands meticulous supervision from humans or superior models, which can be either expensive or license-constrained. In this paper, we explore how far an LLM can improve its reasoning by self-synthesizing reasoning paths as training data without any additional supervision. Existing self-synthesizing methods, such as STaR, suffer from poor generalization to out-of-domain (OOD) reasoning tasks. We hypothesize it is due to that their self-synthesized reasoning paths are too task-specific, lacking general task-agnostic reasoning guidance. To address this, we propose Reasoning Generalist via Self-Improvement (ReGenesis), a method to self-synthesize reasoning paths as post-training data by progressing from abstract to concrete. More specifically, ReGenesis self-synthesizes reasoning paths by converting general reasoning guidelines into task-specific ones, generating reasoning structures, and subsequently transforming these structures into reasoning paths, without the need for human-designed task-specific examples used in existing methods. We show that ReGenesis achieves superior performance on all in-domain and OOD settings tested compared to existing methods. For six OOD tasks specifically, while previous methods exhibited an average performance decrease of approximately 4.6% after post training, ReGenesis delivers around 6.1% performance improvement. We also conduct in-depth analysis of our framework and show ReGenesis is effective across various LLMs and design choices.

Large language models (LLMs) have demonstrated impressive reasoning capabilities, yet there is ongoing debate about these abilities and the potential data contamination problem recently. This paper aims to evaluate the reasoning capacities of LLMs, specifically in solving recent competition-level programming problems in Codeforces, which are expert-crafted and unique, requiring deep understanding and robust reasoning skills. We first provide a comprehensive evaluation of GPT-4's peiceived zero-shot performance on this task, considering various aspects such as problems' release time, difficulties, and types of errors encountered. Surprisingly, the peiceived performance of GPT-4 has experienced a cliff like decline in problems after September 2021 consistently across all the difficulties and types of problems, which shows the potential data contamination, as well as the challenges for any existing LLM to solve unseen complex reasoning problems. We further explore various approaches such as fine-tuning, Chain-of-Thought prompting and problem description simplification, unfortunately none of them is able to consistently mitigate the challenges. Through our work, we emphasis the importance of this excellent data source for assessing the genuine reasoning capabilities of LLMs, and foster the development of LLMs with stronger reasoning abilities and better generalization in the future.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

While Large Language Models (LLMs) have demonstrated remarkable capabilities in scientific tasks, existing evaluation frameworks primarily assess their performance using rich contextual inputs, overlooking their ability to generate novel ideas from minimal information. We introduce LiveIdeaBench, a comprehensive benchmark that evaluates LLMs' scientific creativity and divergent thinking capabilities using single-keyword prompts. Drawing from Guilford's creativity theory, our framework employs a dynamic panel of state-of-the-art LLMs to assess generated ideas across four key dimensions: originality, feasibility, fluency, and flexibility. Through extensive experimentation with 20 leading models across 1,180 keywords spanning 18 scientific domains, we reveal that scientific creative ability shows distinct patterns from general intelligence metrics. Notably, our results demonstrate that models like QwQ-32B-preview achieve comparable creative performance to top-tier models like o1-preview, despite significant gaps in their general intelligence scores. These findings highlight the importance of specialized evaluation frameworks for scientific creativity and suggest that the development of creative capabilities in LLMs may follow different trajectories than traditional problem-solving abilities.

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

We introduce DualMind, a generalist agent designed to tackle various decision-making tasks that addresses challenges posed by current methods, such as overfitting behaviors and dependence on task-specific fine-tuning. DualMind uses a novel "Dual-phase" training strategy that emulates how humans learn to act in the world. The model first learns fundamental common knowledge through a self-supervised objective tailored for control tasks and then learns how to make decisions based on different contexts through imitating behaviors conditioned on given prompts. DualMind can handle tasks across domains, scenes, and embodiments using just a single set of model weights and can execute zero-shot prompting without requiring task-specific fine-tuning. We evaluate DualMind on MetaWorld and Habitat through extensive experiments and demonstrate its superior generalizability compared to previous techniques, outperforming other generalist agents by over 50% and 70% on Habitat and MetaWorld, respectively. On the 45 tasks in MetaWorld, DualMind achieves over 30 tasks at a 90% success rate.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

The emergence of multimodal large models (MLMs) has significantly advanced the field of visual understanding, offering remarkable capabilities in the realm of visual question answering (VQA). Yet, the true challenge lies in the domain of knowledge-intensive VQA tasks, which necessitate not just recognition of visual elements, but also a deep comprehension of the visual information in conjunction with a vast repository of learned knowledge. To uncover such capabilities of MLMs, particularly the newly introduced GPT-4V and Gemini, we provide an in-depth evaluation from three perspectives: 1) Commonsense Knowledge, which assesses how well models can understand visual cues and connect to general knowledge; 2) Fine-grained World Knowledge, which tests the model's skill in reasoning out specific knowledge from images, showcasing their proficiency across various specialized fields; 3) Comprehensive Knowledge with Decision-making Rationales, which examines model's capability to provide logical explanations for its inference, facilitating a deeper analysis from the interpretability perspective. Additionally, we utilize a visual knowledge-enhanced training strategy and multimodal retrieval-augmented generation approach to enhance MLMs, highlighting the future need for advancements in this research direction. Extensive experiments indicate that: a) GPT-4V demonstrates enhanced explanation generation when using composite images as few-shots; b) GPT-4V and other MLMs produce severe hallucinations when dealing with world knowledge; c) Visual knowledge enhanced training and prompting technicals present potential to improve performance. Codes: https://github.com/HITsz-TMG/Cognitive-Visual-Language-Mapper

Scaling up language models to billions of parameters has opened up possibilities for in-context learning, allowing instruction tuning and few-shot learning on tasks that the model was not specifically trained for. This has achieved breakthrough performance on language tasks such as translation, summarization, and question-answering. Furthermore, in addition to these associative "System 1" tasks, recent advances in Chain-of-thought prompt learning have demonstrated strong "System 2" reasoning abilities, answering a question in the field of artificial general intelligence whether LLMs can reason. The field started with the question whether LLMs can solve grade school math word problems. This paper reviews the rapidly expanding field of prompt-based reasoning with LLMs. Our taxonomy identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. Finally, we highlight the relation between reasoning and prompt-based learning, and we discuss the relation between reasoning, sequential decision processes, and reinforcement learning. We find that self-improvement, self-reflection, and some metacognitive abilities of the reasoning processes are possible through the judicious use of prompts. True self-improvement and self-reasoning, to go from reasoning with LLMs to reasoning by LLMs, remains future work.

Recent advances such as Chain-of-Thought prompting have significantly improved large language models (LLMs) in zero-shot medical reasoning. However, prompting-based methods often remain shallow and unstable, while fine-tuned medical LLMs suffer from poor generalization under distribution shifts and limited adaptability to unseen clinical scenarios. To address these limitations, we present TAGS, a test-time framework that combines a broadly capable generalist with a domain-specific specialist to offer complementary perspectives without any model fine-tuning or parameter updates. To support this generalist-specialist reasoning process, we introduce two auxiliary modules: a hierarchical retrieval mechanism that provides multi-scale exemplars by selecting examples based on both semantic and rationale-level similarity, and a reliability scorer that evaluates reasoning consistency to guide final answer aggregation. TAGS achieves strong performance across nine MedQA benchmarks, boosting GPT-4o accuracy by 13.8%, DeepSeek-R1 by 16.8%, and improving a vanilla 7B model from 14.1% to 23.9%. These results surpass several fine-tuned medical LLMs, without any parameter updates. The code will be available at https://github.com/JianghaoWu/TAGS.

Building future wireless systems that support services like digital twins (DTs) is challenging to achieve through advances to conventional technologies like meta-surfaces. While artificial intelligence (AI)-native networks promise to overcome some limitations of wireless technologies, developments still rely on AI tools like neural networks. Such tools struggle to cope with the non-trivial challenges of the network environment and the growing demands of emerging use cases. In this paper, we revisit the concept of AI-native wireless systems, equipping them with the common sense necessary to transform them into artificial general intelligence (AGI)-native systems. These systems acquire common sense by exploiting different cognitive abilities such as perception, analogy, and reasoning, that enable them to generalize and deal with unforeseen scenarios. Towards developing the components of such a system, we start by showing how the perception module can be built through abstracting real-world elements into generalizable representations. These representations are then used to create a world model, founded on principles of causality and hyper-dimensional (HD) computing, that aligns with intuitive physics and enables analogical reasoning, that define common sense. Then, we explain how methods such as integrated information theory play a role in the proposed intent-driven and objective-driven planning methods that maneuver the AGI-native network to take actions. Next, we discuss how an AGI-native network can enable use cases related to human and autonomous agents: a) analogical reasoning for next-generation DTs, b) synchronized and resilient experiences for cognitive avatars, and c) brain-level metaverse experiences like holographic teleportation. Finally, we conclude with a set of recommendations to build AGI-native systems. Ultimately, we envision this paper as a roadmap for the beyond 6G era.

Recent advances in AI -- including generative approaches -- have resulted in technology that can support humans in scientific discovery and decision support but may also disrupt democracies and target individuals. The responsible use of AI increasingly shows the need for human-AI teaming, necessitating effective interaction between humans and machines. A crucial yet often overlooked aspect of these interactions is the different ways in which humans and machines generalise. In cognitive science, human generalisation commonly involves abstraction and concept learning. In contrast, AI generalisation encompasses out-of-domain generalisation in machine learning, rule-based reasoning in symbolic AI, and abstraction in neuro-symbolic AI. In this perspective paper, we combine insights from AI and cognitive science to identify key commonalities and differences across three dimensions: notions of generalisation, methods for generalisation, and evaluation of generalisation. We map the different conceptualisations of generalisation in AI and cognitive science along these three dimensions and consider their role in human-AI teaming. This results in interdisciplinary challenges across AI and cognitive science that must be tackled to provide a foundation for effective and cognitively supported alignment in human-AI teaming scenarios.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

Recent work in mechanistic interpretability has shown that behaviors in language models can be successfully reverse-engineered through circuit analysis. A common criticism, however, is that each circuit is task-specific, and thus such analysis cannot contribute to understanding the models at a higher level. In this work, we present evidence that insights (both low-level findings about specific heads and higher-level findings about general algorithms) can indeed generalize across tasks. Specifically, we study the circuit discovered in Wang et al. (2022) for the Indirect Object Identification (IOI) task and 1.) show that it reproduces on a larger GPT2 model, and 2.) that it is mostly reused to solve a seemingly different task: Colored Objects (Ippolito & Callison-Burch, 2023). We provide evidence that the process underlying both tasks is functionally very similar, and contains about a 78% overlap in in-circuit attention heads. We further present a proof-of-concept intervention experiment, in which we adjust four attention heads in middle layers in order to 'repair' the Colored Objects circuit and make it behave like the IOI circuit. In doing so, we boost accuracy from 49.6% to 93.7% on the Colored Objects task and explain most sources of error. The intervention affects downstream attention heads in specific ways predicted by their interactions in the IOI circuit, indicating that this subcircuit behavior is invariant to the different task inputs. Overall, our results provide evidence that it may yet be possible to explain large language models' behavior in terms of a relatively small number of interpretable task-general algorithmic building blocks and computational components.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs. Our benchmark and code are released at https://github.com/GraphPKU/number_cookbook.

Large reasoning models (LRMs) have demonstrated impressive reasoning capabilities across a broad range of tasks including Olympiad-level mathematical problems, indicating evidence of their complex reasoning abilities. While many reasoning benchmarks focus on the STEM domain, the ability of LRMs to reason correctly in broader task domains remains underexplored. In this work, we introduce TTT-Bench, a new benchmark that is designed to evaluate basic strategic, spatial, and logical reasoning abilities in LRMs through a suite of four two-player Tic-Tac-Toe-style games that humans can effortlessly solve from a young age. We propose a simple yet scalable programmatic approach for generating verifiable two-player game problems for TTT-Bench. Although these games are trivial for humans, they require reasoning about the intentions of the opponent, as well as the game board's spatial configurations, to ensure a win. We evaluate a diverse set of state-of-the-art LRMs, and discover that the models that excel at hard math problems frequently fail at these simple reasoning games. Further testing reveals that our evaluated reasoning models score on average downarrow 41\% \& downarrow 5\% lower on TTT-Bench compared to MATH 500 \& AIME 2024 respectively, with larger models achieving higher performance using shorter reasoning traces, where most of the models struggle on long-term strategic reasoning situations on simple and new TTT-Bench tasks.

Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as self-consistency, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose self-agreement, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model's decoder to generate a diverse set of reasoning paths, and subsequently prompts the language model one more time to determine the optimal answer by selecting the most agreed answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs' reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using a dynamically generated logical reasoning benchmark based on Knights and Knaves (K&K) puzzles. We found that LLMs could interpolate the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet fail when those puzzles are slightly perturbed, suggesting that the models heavily rely on memorization to solve those training puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. In-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers suggest that the LLMs learn to reason on K&K puzzles despite training data memorization. This phenomenon indicates that LLMs exhibit a complex interplay between memorization and genuine reasoning abilities. Finally, our analysis with per-sample memorization score sheds light on how LLMs switch between reasoning and memorization in solving logical puzzles. Our code and data are available at https://memkklogic.github.io.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the popular Chain of Thought approach to prompting language models, and enables exploration over coherent units of text (thoughts) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models' problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: https://github.com/ysymyth/tree-of-thought-llm.

In this paper, we present an investigative study on how Mental Sets influence the reasoning capabilities of LLMs. LLMs have excelled in diverse natural language processing (NLP) tasks, driven by advancements in parameter-efficient fine-tuning (PEFT) and emergent capabilities like in-context learning (ICL). For complex reasoning tasks, selecting the right model for PEFT or ICL is critical, often relying on scores on benchmarks such as MMLU, MATH, and GSM8K. However, current evaluation methods, based on metrics like F1 Score or reasoning chain assessments by larger models, overlook a key dimension: adaptability to unfamiliar situations and overcoming entrenched thinking patterns. In cognitive psychology, Mental Set refers to the tendency to persist with previously successful strategies, even when they become inefficient - a challenge for problem solving and reasoning. We compare the performance of LLM models like Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct and GPT-4o in the presence of mental sets. To the best of our knowledge, this is the first study to integrate cognitive psychology concepts into the evaluation of LLMs for complex reasoning tasks, providing deeper insights into their adaptability and problem-solving efficacy.

This research introduces a novel evaluation framework designed to assess large language models' (LLMs) ability to acknowledge uncertainty on 675 fundamentally unsolvable problems. Using a curated dataset of graduate-level grand challenge questions with intentionally unknowable answers, we evaluated twelve state-of-the-art LLMs, including both open and closed-source models, on their propensity to admit ignorance rather than generate plausible but incorrect responses. The best models scored in 62-68% accuracy ranges for admitting the problem solution was unknown in fields ranging from biology to philosophy and mathematics. We observed an inverse relationship between problem difficulty and model accuracy, with GPT-4 demonstrating higher rates of uncertainty acknowledgment on more challenging problems (35.8%) compared to simpler ones (20.0%). This pattern indicates that models may be more prone to generate speculative answers when problems appear more tractable. The study also revealed significant variations across problem categories, with models showing difficulty in acknowledging uncertainty in invention and NP-hard problems while performing relatively better on philosophical and psychological challenges. These results contribute to the growing body of research on artificial general intelligence (AGI) assessment by highlighting the importance of uncertainty recognition as a critical component of future machine intelligence evaluation. This impossibility test thus extends previous theoretical frameworks for universal intelligence testing by providing empirical evidence of current limitations in LLMs' ability to recognize their own knowledge boundaries, suggesting new directions for improving model training architectures and evaluation approaches.

Making analogies is fundamental to cognition. Proportional analogies, which consist of four terms, are often used to assess linguistic and cognitive abilities. For instance, completing analogies like "Oxygen is to Gas as <blank> is to <blank>" requires identifying the semantic relationship (e.g., "type of") between the first pair of terms ("Oxygen" and "Gas") and finding a second pair that shares the same relationship (e.g., "Aluminum" and "Metal"). In this work, we introduce a 15K Multiple-Choice Question Answering (MCQA) dataset for proportional analogy completion and evaluate the performance of contemporary Large Language Models (LLMs) in various knowledge-enhanced prompt settings. Specifically, we augment prompts with three types of knowledge: exemplar, structured, and targeted. Our results show that despite extensive training data, solving proportional analogies remains challenging for current LLMs, with the best model achieving an accuracy of 55%. Notably, we find that providing targeted knowledge can better assist models in completing proportional analogies compared to providing exemplars or collections of structured knowledge.

Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition. The latest model developed by OpenAI, GPT-4, was trained using an unprecedented scale of compute and data. In this paper, we report on our investigation of an early version of GPT-4, when it was still in active development by OpenAI. We contend that (this early version of) GPT-4 is part of a new cohort of LLMs (along with ChatGPT and Google's PaLM for example) that exhibit more general intelligence than previous AI models. We discuss the rising capabilities and implications of these models. We demonstrate that, beyond its mastery of language, GPT-4 can solve novel and difficult tasks that span mathematics, coding, vision, medicine, law, psychology and more, without needing any special prompting. Moreover, in all of these tasks, GPT-4's performance is strikingly close to human-level performance, and often vastly surpasses prior models such as ChatGPT. Given the breadth and depth of GPT-4's capabilities, we believe that it could reasonably be viewed as an early (yet still incomplete) version of an artificial general intelligence (AGI) system. In our exploration of GPT-4, we put special emphasis on discovering its limitations, and we discuss the challenges ahead for advancing towards deeper and more comprehensive versions of AGI, including the possible need for pursuing a new paradigm that moves beyond next-word prediction. We conclude with reflections on societal influences of the recent technological leap and future research directions.

Large language models (LLMs) demonstrate exceptional performance on complex reasoning tasks. However, despite their strong reasoning capabilities in high-resource languages (e.g., English and Chinese), a significant performance gap persists in other languages. To investigate this gap in Korean, we introduce HRM8K, a benchmark comprising 8,011 English-Korean parallel bilingual math problems. Through systematic analysis of model behaviors, we identify a key finding: these performance disparities stem primarily from difficulties in comprehending non-English inputs, rather than limitations in reasoning capabilities. Based on these findings, we propose UST (Understand, Solve, and Translate), a method that strategically uses English as an anchor for reasoning and solution generation. By fine-tuning the model on 130k synthetically generated data points, UST achieves a 10.91% improvement on the HRM8K benchmark and reduces the multilingual performance gap from 11.6% to 0.7%. Additionally, we show that improvements from UST generalize effectively to different Korean domains, demonstrating that capabilities acquired from machine-verifiable content can be generalized to other areas. We publicly release the benchmark, training dataset, and models.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

To make deliberate progress towards more intelligent and more human-like artificial systems, we need to be following an appropriate feedback signal: we need to be able to define and evaluate intelligence in a way that enables comparisons between two systems, as well as comparisons with humans. Over the past hundred years, there has been an abundance of attempts to define and measure intelligence, across both the fields of psychology and AI. We summarize and critically assess these definitions and evaluation approaches, while making apparent the two historical conceptions of intelligence that have implicitly guided them. We note that in practice, the contemporary AI community still gravitates towards benchmarking intelligence by comparing the skill exhibited by AIs and humans at specific tasks such as board games and video games. We argue that solely measuring skill at any given task falls short of measuring intelligence, because skill is heavily modulated by prior knowledge and experience: unlimited priors or unlimited training data allow experimenters to "buy" arbitrary levels of skills for a system, in a way that masks the system's own generalization power. We then articulate a new formal definition of intelligence based on Algorithmic Information Theory, describing intelligence as skill-acquisition efficiency and highlighting the concepts of scope, generalization difficulty, priors, and experience. Using this definition, we propose a set of guidelines for what a general AI benchmark should look like. Finally, we present a benchmark closely following these guidelines, the Abstraction and Reasoning Corpus (ARC), built upon an explicit set of priors designed to be as close as possible to innate human priors. We argue that ARC can be used to measure a human-like form of general fluid intelligence and that it enables fair general intelligence comparisons between AI systems and humans.

Intelligent agents must be generalists - showing the ability to quickly adapt and generalize to varying tasks. Within the framework of reinforcement learning (RL), model-based RL algorithms learn a task-agnostic dynamics model of the world, in principle allowing them to generalize to arbitrary rewards. However, one-step models naturally suffer from compounding errors, making them ineffective for problems with long horizons and large state spaces. In this work, we propose a novel class of models - generalized occupancy models (GOMs) - that retain the generality of model-based RL while avoiding compounding error. The key idea behind GOMs is to model the distribution of all possible long-term outcomes from a given state under the coverage of a stationary dataset, along with a policy that realizes a particular outcome from the given state. These models can then quickly be used to select the optimal action for arbitrary new tasks, without having to redo policy optimization. By directly modeling long-term outcomes, GOMs avoid compounding error while retaining generality across arbitrary reward functions. We provide a practical instantiation of GOMs using diffusion models and show its efficacy as a new class of transferable models, both theoretically and empirically across a variety of simulated robotics problems. Videos and code at https://weirdlabuw.github.io/gom/.

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves 94.21% of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves 92.04 % of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

Large Language Models have shown tremendous performance on a large variety of natural language processing tasks, ranging from text comprehension to common sense reasoning. However, the mechanisms responsible for this success remain opaque, and it is unclear whether LLMs can achieve human-like cognitive capabilities or whether these models are still fundamentally circumscribed. Abstract reasoning is a fundamental task for cognition, consisting of finding and applying a general pattern from few data. Evaluating deep neural architectures on this task could give insight into their potential limitations regarding reasoning and their broad generalisation abilities, yet this is currently an under-explored area. In this paper, we introduce a new benchmark for evaluating language models beyond memorization on abstract reasoning tasks. We perform extensive evaluations of state-of-the-art LLMs, showing that they currently achieve very limited performance in contrast with other natural language tasks, and we examine the reasons for this difference. We apply techniques that have been shown to improve performance on other NLP tasks and show that their impact on abstract reasoning is limited.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

Modern vision models have achieved remarkable success in benchmarks where local features provide critical information about the target. There is now a growing interest in solving tasks that require more global reasoning, where local features offer no significant information. These tasks are reminiscent of the connectivity tasks discussed by Minsky and Papert in 1969, which exposed the limitations of the perceptron model and contributed to the first AI winter. In this paper, we revisit such tasks by introducing four global visual benchmarks involving path findings and mazes. We show that: (1) although today's large vision models largely surpass the expressivity limitations of the early models, they still struggle with the learning efficiency; we put forward the "globality degree" notion to understand this limitation; (2) we then demonstrate that the picture changes and global reasoning becomes feasible with the introduction of "visual scratchpads"; similarly to the text scratchpads and chain-of-thoughts used in language models, visual scratchpads help break down global tasks into simpler ones; (3) we finally show that some scratchpads are better than others, in particular, "inductive scratchpads" that take steps relying on less information afford better out-of-distribution generalization and succeed for smaller model sizes.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

Emergent chain-of-thought (CoT) reasoning capabilities promise to improve performance and explainability of large language models (LLMs). However, uncertainties remain about how reasoning strategies formulated for previous model generations generalize to new model generations and different datasets. In this small-scale study, we compare different reasoning strategies induced by zero-shot prompting across six recently released LLMs (davinci-002, davinci-003, GPT-3.5-turbo, GPT-4, Flan-T5-xxl and Cohere command-xlarge) on a mixture of six question-answering datasets, including datasets from scientific and medical domains. Our findings demonstrate that while some variations in effectiveness occur, gains from CoT reasoning strategies remain robust across different models and datasets. GPT-4 has the most benefit from current state-of-the-art reasoning strategies and exhibits the best performance by applying a prompt previously discovered through automated discovery.

Large language models have exhibited emergent abilities, demonstrating exceptional performance across diverse tasks for which they were not explicitly trained, including those that require complex reasoning abilities. The emergence of such abilities carries profound implications for the future direction of research in NLP, especially as the deployment of such models becomes more prevalent. However, one key challenge is that the evaluation of these abilities is often confounded by competencies that arise in models through alternative prompting techniques, such as in-context learning and instruction following, which also emerge as the models are scaled up. In this study, we provide the first comprehensive examination of these emergent abilities while accounting for various potentially biasing factors that can influence the evaluation of models. We conduct rigorous tests on a set of 18 models, encompassing a parameter range from 60 million to 175 billion parameters, across a comprehensive set of 22 tasks. Through an extensive series of over 1,000 experiments, we provide compelling evidence that emergent abilities can primarily be ascribed to in-context learning. We find no evidence for the emergence of reasoning abilities, thus providing valuable insights into the underlying mechanisms driving the observed abilities and thus alleviating safety concerns regarding their use.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Socratic questioning is an educational method that allows students to discover answers to complex problems by asking them a series of thoughtful questions. Generation of didactically sound questions is challenging, requiring understanding of the reasoning process involved in the problem. We hypothesize that such questioning strategy can not only enhance the human performance, but also assist the math word problem (MWP) solvers. In this work, we explore the ability of large language models (LMs) in generating sequential questions for guiding math word problem-solving. We propose various guided question generation schemes based on input conditioning and reinforcement learning. On both automatic and human quality evaluations, we find that LMs constrained with desirable question properties generate superior questions and improve the overall performance of a math word problem solver. We conduct a preliminary user study to examine the potential value of such question generation models in the education domain. Results suggest that the difficulty level of problems plays an important role in determining whether questioning improves or hinders human performance. We discuss the future of using such questioning strategies in education.

We teach goal-driven agents to interactively act and speak in situated environments by training on generated curriculums. Our agents operate in LIGHT (Urbanek et al. 2019) -- a large-scale crowd-sourced fantasy text adventure game wherein an agent perceives and interacts with the world through textual natural language. Goals in this environment take the form of character-based quests, consisting of personas and motivations. We augment LIGHT by learning to procedurally generate additional novel textual worlds and quests to create a curriculum of steadily increasing difficulty for training agents to achieve such goals. In particular, we measure curriculum difficulty in terms of the rarity of the quest in the original training distribution -- an easier environment is one that is more likely to have been found in the unaugmented dataset. An ablation study shows that this method of learning from the tail of a distribution results in significantly higher generalization abilities as measured by zero-shot performance on never-before-seen quests.

This paper presents an in-depth analysis of Large Language Models (LLMs), focusing on LLaMA, a prominent open-source foundational model in natural language processing. Instead of assessing LLaMA through its generative output, we design multiple-choice tasks to probe its intrinsic understanding in high-order tasks such as reasoning and computation. We examine the model horizontally, comparing different sizes, and vertically, assessing different layers. We unveil several key and uncommon findings based on the designed probing tasks: (1) Horizontally, enlarging model sizes almost could not automatically impart additional knowledge or computational prowess. Instead, it can enhance reasoning abilities, especially in math problem solving, and helps reduce hallucinations, but only beyond certain size thresholds; (2) In vertical analysis, the lower layers of LLaMA lack substantial arithmetic and factual knowledge, showcasing logical thinking, multilingual and recognitive abilities, with top layers housing most computational power and real-world knowledge.

Recent supervised fine-tuning (SFT) approaches have significantly improved language models' performance on mathematical reasoning tasks, even when models are trained at a small scale. However, the specific capabilities enhanced through such fine-tuning remain poorly understood. In this paper, we conduct a detailed analysis of model performance on the AIME24 dataset to understand how reasoning capabilities evolve. We discover a ladder-like structure in problem difficulty, categorize questions into four tiers (Easy, Medium, Hard, and Extremely Hard (Exh)), and identify the specific requirements for advancing between tiers. We find that progression from Easy to Medium tier requires adopting an R1 reasoning style with minimal SFT (500-1K instances), while Hard-level questions suffer from frequent model's errors at each step of the reasoning chain, with accuracy plateauing at around 65% despite logarithmic scaling. Exh-level questions present a fundamentally different challenge; they require unconventional problem-solving skills that current models uniformly struggle with. Additional findings reveal that carefully curated small-scale datasets offer limited advantage-scaling dataset size proves far more effective. Our analysis provides a clearer roadmap for advancing language model capabilities in mathematical reasoning.

Dexterous grasping remains a fundamental yet challenging problem in robotics. A general-purpose robot must be capable of grasping diverse objects in arbitrary scenarios. However, existing research typically relies on specific assumptions, such as single-object settings or limited environments, leading to constrained generalization. Our solution is DexGraspVLA, a hierarchical framework that utilizes a pre-trained Vision-Language model as the high-level task planner and learns a diffusion-based policy as the low-level Action controller. The key insight lies in iteratively transforming diverse language and visual inputs into domain-invariant representations, where imitation learning can be effectively applied due to the alleviation of domain shift. Thus, it enables robust generalization across a wide range of real-world scenarios. Notably, our method achieves a 90+% success rate under thousands of unseen object, lighting, and background combinations in a ``zero-shot'' environment. Empirical analysis further confirms the consistency of internal model behavior across environmental variations, thereby validating our design and explaining its generalization performance. We hope our work can be a step forward in achieving general dexterous grasping. Our demo and code can be found at https://dexgraspvla.github.io/.