Daily Papers

Max sliced Wasserstein (Max-SW) distance has been widely known as a solution for less discriminative projections of sliced Wasserstein (SW) distance. In applications that have various independent pairs of probability measures, amortized projection optimization is utilized to predict the ``max" projecting directions given two input measures instead of using projected gradient ascent multiple times. Despite being efficient, Max-SW and its amortized version cannot guarantee metricity property due to the sub-optimality of the projected gradient ascent and the amortization gap. Therefore, we propose to replace Max-SW with distributional sliced Wasserstein distance with von Mises-Fisher (vMF) projecting distribution (v-DSW). Since v-DSW is a metric with any non-degenerate vMF distribution, its amortized version can guarantee the metricity when performing amortization. Furthermore, current amortized models are not permutation invariant and symmetric. To address the issue, we design amortized models based on self-attention architecture. In particular, we adopt efficient self-attention architectures to make the computation linear in the number of supports. With the two improvements, we derive self-attention amortized distributional projection optimization and show its appealing performance in point-cloud reconstruction and its downstream applications.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

An important and unsolved problem in computer vision is to ensure that the algorithms are robust to changes in image domains. We address this problem in the scenario where we have access to images from the target domains but no annotations. Motivated by the challenges of the OOD-CV benchmark where we encounter real world Out-of-Domain (OOD) nuisances and occlusion, we introduce a novel Bayesian approach to OOD robustness for object classification. Our work extends Compositional Neural Networks (CompNets), which have been shown to be robust to occlusion but degrade badly when tested on OOD data. We exploit the fact that CompNets contain a generative head defined over feature vectors represented by von Mises-Fisher (vMF) kernels, which correspond roughly to object parts, and can be learned without supervision. We obverse that some vMF kernels are similar between different domains, while others are not. This enables us to learn a transitional dictionary of vMF kernels that are intermediate between the source and target domains and train the generative model on this dictionary using the annotations on the source domain, followed by iterative refinement. This approach, termed Unsupervised Generative Transition (UGT), performs very well in OOD scenarios even when occlusion is present. UGT is evaluated on different OOD benchmarks including the OOD-CV dataset, several popular datasets (e.g., ImageNet-C [9]), artificial image corruptions (including adding occluders), and synthetic-to-real domain transfer, and does well in all scenarios outperforming SOTA alternatives (e.g. up to 10% top-1 accuracy on Occluded OOD-CV dataset).

Recently, Neural Topic Models (NTM), inspired by variational autoencoders, have attracted a lot of research interest; however, these methods have limited applications in the real world due to the challenge of incorporating human knowledge. This work presents a semi-supervised neural topic modeling method, vONTSS, which uses von Mises-Fisher (vMF) based variational autoencoders and optimal transport. When a few keywords per topic are provided, vONTSS in the semi-supervised setting generates potential topics and optimizes topic-keyword quality and topic classification. Experiments show that vONTSS outperforms existing semi-supervised topic modeling methods in classification accuracy and diversity. vONTSS also supports unsupervised topic modeling. Quantitative and qualitative experiments show that vONTSS in the unsupervised setting outperforms recent NTMs on multiple aspects: vONTSS discovers highly clustered and coherent topics on benchmark datasets. It is also much faster than the state-of-the-art weakly supervised text classification method while achieving similar classification performance. We further prove the equivalence of optimal transport loss and cross-entropy loss at the global minimum.

Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or conformations. The resulting distribution on geometries p(x) is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying modes in this distribution rather than generating true samples. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with sim1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25times speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.

Predicting how a drug-like molecule binds to a specific protein target is a core problem in drug discovery. An extremely fast computational binding method would enable key applications such as fast virtual screening or drug engineering. Existing methods are computationally expensive as they rely on heavy candidate sampling coupled with scoring, ranking, and fine-tuning steps. We challenge this paradigm with EquiBind, an SE(3)-equivariant geometric deep learning model performing direct-shot prediction of both i) the receptor binding location (blind docking) and ii) the ligand's bound pose and orientation. EquiBind achieves significant speed-ups and better quality compared to traditional and recent baselines. Further, we show extra improvements when coupling it with existing fine-tuning techniques at the cost of increased running time. Finally, we propose a novel and fast fine-tuning model that adjusts torsion angles of a ligand's rotatable bonds based on closed-form global minima of the von Mises angular distance to a given input atomic point cloud, avoiding previous expensive differential evolution strategies for energy minimization.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

Despite rapid progress on AI benchmarks, the real-world meaning of benchmark performance remains unclear. To quantify the capabilities of AI systems in terms of human capabilities, we propose a new metric: 50%-task-completion time horizon. This is the time humans typically take to complete tasks that AI models can complete with 50% success rate. We first timed humans with relevant domain expertise on a combination of RE-Bench, HCAST, and 66 novel shorter tasks. On these tasks, current frontier AI models such as Claude 3.7 Sonnet have a 50% time horizon of around 50 minutes. Furthermore, frontier AI time horizon has been doubling approximately every seven months since 2019, though the trend may have accelerated in 2024. The increase in AI models' time horizons seems to be primarily driven by greater reliability and ability to adapt to mistakes, combined with better logical reasoning and tool use capabilities. We discuss the limitations of our results -- including their degree of external validity -- and the implications of increased autonomy for dangerous capabilities. If these results generalize to real-world software tasks, extrapolation of this trend predicts that within 5 years, AI systems will be capable of automating many software tasks that currently take humans a month.

While large language models have facilitated breakthroughs in many applications of artificial intelligence, their inherent largeness makes them computationally expensive and challenging to deploy in resource-constrained settings. In this paper, we document the development of SmolLM2, a state-of-the-art "small" (1.7 billion parameter) language model (LM). To attain strong performance, we overtrain SmolLM2 on ~11 trillion tokens of data using a multi-stage training process that mixes web text with specialized math, code, and instruction-following data. We additionally introduce new specialized datasets (FineMath, Stack-Edu, and SmolTalk) at stages where we found existing datasets to be problematically small or low-quality. To inform our design decisions, we perform both small-scale ablations as well as a manual refinement process that updates the dataset mixing rates at each stage based on the performance at the previous stage. Ultimately, we demonstrate that SmolLM2 outperforms other recent small LMs including Qwen2.5-1.5B and Llama3.2-1B. To facilitate future research on LM development as well as applications of small LMs, we release both SmolLM2 as well as all of the datasets we prepared in the course of this project.