diff --git "a/KNFOT4oBgHgl3EQfyzQ_/content/tmp_files/load_file.txt" "b/KNFOT4oBgHgl3EQfyzQ_/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/KNFOT4oBgHgl3EQfyzQ_/content/tmp_files/load_file.txt" @@ -0,0 +1,1459 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf,len=1458 +page_content='Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Anson Bastos cs20resch11002@iith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='in IIT, Hyderabad India Kuldeep Singh kuldeep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='singh1@cerence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='com Zerotha Research and Cerence GmbH Germany Abhishek Nadgeri abhishek22596@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='com Zerotha Research and RWTH Aachen Germany Johannes Hoffart johannes@hoffart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='ai SAP Germany Toyotaro Suzumura suzumura@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='org The University of Tokyo Japan Manish Singh msingh@cse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='iith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='in IIT Hyderabad India ABSTRACT In this paper we present a novel method, Knowledge Persistence (KP), for faster evaluation of Knowledge Graph (KG) completion approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Current ranking-based evaluation is quadratic in the size of the KG, leading to long evaluation times and consequently a high carbon footprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP addresses this by representing the topol- ogy of the KG completion methods through the lens of topological data analysis, concretely using persistent homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The character- istics of persistent homology allow KP to evaluate the quality of the KG completion looking only at a fraction of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Experi- mental results on standard datasets show that the proposed metric is highly correlated with ranking metrics (Hits@N, MR, MRR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Per- formance evaluation shows that KP is computationally efficient: In some cases, the evaluation time (validation+test) of a KG com- pletion method has been reduced from 18 hours (using Hits@10) to 27 seconds (using KP), and on average (across methods & data) reduces the evaluation time (validation+test) by ≈ 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='96%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' ACM Reference Format: Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Johannes Hoffart, Toyotaro Suzumura, and Manish Singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='. In Proceedings of the Web Conference 2023 (WWW ’23), APRIL 30 - MAY 4, 2023, Texas, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' WWW, Texas, USA, 13 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' XXXXX/YYYYY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3449917 1 INTRODUCTION Publicly available Knowledge Graphs (KGs) find broad applicability in several downstream tasks such as entity linking, relation extrac- tion, fact-checking, and question answering [22, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' These KGs are large graph databases used to express facts in the form of relations between real-world entities and store these facts as triples (subject, Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Copyrights for third- party components of this work must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For all other uses, contact the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA © 2023 Copyright held by the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' ACM ISBN 978-Y-4500-YYYY-7/21/04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='XXXXX/YYYYY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3449917 relation, object).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KGs must be continuously updated because new en- tities might emerge or facts about entities are extended or updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Knowledge Graph Completion (KGC) task aims to fill the missing piece of information into an incomplete triple of KG [5, 18, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Several Knowledge Graph Embedding (KGE) approaches have been proposed to model entities and relations in vector space for missing link prediction in a KG [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KGE methods infer the connec- tivity patterns (symmetry, asymmetry, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=') in the KGs by defining a scoring function to calculate the plausibility of a knowledge graph triple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' While calculating plausibility of a KG triple τ = (𝑒ℎ,𝑟,𝑒𝑡), the predicted score by scoring function affirms the confidence of a model that entities 𝑒𝑡 and 𝑒ℎ are linked by 𝑟.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For evaluating KGE methods, ranking metrics have been widely used [22] which is based on the following criteria: given a KG triple with a missing head or tail entity, what is the ability of the KGE method to rank candidate entities averaged over triples in a held- out test set [28]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' These ranking metrics are useful as they intend to gauge the behavior of the methods in real world applications of KG completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Since 2019, over 100 KGE articles have been published in various leading conferences and journals that use ranking metrics as evaluation protocol1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Limitations of Ranking-based Evaluation: The key challenge while computing ranking metrics for model evaluation is the time taken to obtain them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Since the (most of) KGE models aim to rank all the negative triples that are not present in the KG [8, 9], comput- ing these metrics takes a quadratic time in the number of entities in the KG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Moreover, the problem gets alleviated in the case of hyper-relations [62] where more than two entities participate, lead- ing to exponential computation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For instance, Ali et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [2] spent 24,804 GPU hours of computation time while performing a large-scale benchmarking of KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' There are two issues with high model evaluation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Firstly, efficiency at evaluation time is not a widely-adapted criterion for assessing KGE models alongside accuracy and related measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' There are efforts to make KGE methods efficient at training time [52, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, these methods also use ranking-based protocols resulting in high evaluation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Secondly, the need for signifi- cant computational resources for the KG completion task excludes a large group of researchers in universities/labs with restricted GPU 1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='com/xinguoxia/KGE#papers arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='12929v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='LG] 30 Jan 2023 WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Such preliminary exclusion implicitly challenges the ba- sic notion of various diversity and inclusion initiatives for making the Web and its related research accessible to a wider community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In past, researchers have worked extensively towards efficient Web- related technologies such as Web Crawling [12], Web Indexing [25], RDF processing [17], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, for the KG completion task, similar to other efficient Web-based research, there is a necessity to develop alternative evaluation protocols to reduce the computation com- plexity, a crucial research gap in available KGE scientific literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Another critical issue in ranking metrics is that they are biased towards popular entities and such popularity bias is not captured by current evaluation metrics [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, we need a metric which is efficient than popular ranking metrics and also omits such biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Motivation and Contribution: In this work, we focus on ad- dressing above-mentioned key research gaps and aim for the first study to make KGE evaluation more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We introduce Knowl- edge Persistence(KP), a method for characterizing the topology of the learnt KG representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It builds upon Topological Data Analysis [58] based on the concepts from Persistent Homology(PH) [15], which has been proven beneficial for analyzing deep networks [29, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PH is able to effectively capture the geometry of the mani- fold on which the representations reside whilst requiring fraction of data [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This property allows to reduce the quadratic complexity of considering all the data points (KG triples in our case) for rank- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Another crucial fact that makes PH useful is its stability with respect to perturbations making KP robust to noise [19] mitigating the issues due to the open-world problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus we use PH due to its effectiveness for limited resources and noise [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Concretely, the following are our key contributions: (1) We propose (KP), a novel approach along with its theoreti- cal foundations to estimate the performance of KGE models through the lens of topological data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This allows us to drastically reduce the computation factor from order of O(|E|2) to O(|E|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The code is here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' (2) We run extensive experiments on families of KGE methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Translation, Rotation, Bi-Linear, Factorization, Neural Network methods) using standard benchmark datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The experiments show that KP correlates well with the stan- dard ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, KP could be used for faster prototyping of KGE methods and paves the way for efficient evaluation methods in this domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In the remainder of the paper, related work is in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Section 3 briefly explains the concept of persistent homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Section 4 describes the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Later, section 5 shows associated empirical results and we conclude in section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2 RELATED WORK Broadly, KG embeddings are classified into translation and semantic matching models [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Translation methods such as TransE [8], TransH [57], TransR [26] use distance-based scoring functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Whereas semantic matching models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', ComplEx [48], Distmult [60], RotatE [44]) use similarity-based scoring functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Kadlec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [23] first pointed limitations of KGE evaluation and its dependency on hyperparameter tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [45] with exhaus- tive evaluation (using ranking metrics) showed issues of scoring functions of KGE methods whereas [31] studied the effect of loss function of KGE performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Jain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [20] studied if KGE meth- ods capture KG semantic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Work in [35] provides a new dataset that allows the study of calibration results for KGE mod- els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Speranskaya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [43] used precision and recall rather than rankings to measure the quality of completion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Authors pro- posed a new dataset containing triples such that their completion is both possible and impossible based on queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, queries were build by creating a tight dependency on such queries for the evaluation as pointed by [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Rim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [37] proposed a capability- based evaluation where the focus is to evaluate KGE methods on various dimensions such as relation symmetry, entity hierarchy, entity disambiguation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Mohamed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [28] fixed the popularity bias of ranking metrics by introducing modified ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The geometric perspective of KGE methods was introduced by [40] and its correlation with task performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Berrendorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [6] sug- gested the adjusted mean rank to improve reciprocal rank, which is an ordinal scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Authors do not consider the effect of negative triples available for a given triple under evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [47] propose to balances the number of negatives per triple to improve rank- ing metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Authors suggested the preparation of training/testing splits by maintaining the topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Work in [24] proposes efficient non-sampling techniques for KG embedding training, few other initiatives improve efficiency of KGE training time [52–54], and hyperparameter search efficiency of embedding models [49, 56, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Overall, the literature is rich with evaluations of knowledge graph completion methods [4, 21, 38, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, to the best of our knowledge, extensive attempts have not been made to im- prove KG evaluation protocols’ efficiency, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', to reduce run-time of widely-used ranking metrics for faster prototyping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We position our work orthogonal to existing attempts such as [40], [47], [28], and [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In contrast with these attempts, our approach provides a topological perspective of the learned KG embeddings and focuses on improving the efficiency of KGE evaluations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 3 PRELIMINARIES We now briefly describe concepts used in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ranking metrics have been used for evaluating KG embedding methods since the inception of the KG completion task [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' These metrics include the Mean Rank (MR), Mean Reciprocal Rank (MRR) and the cut-off hit ratio (Hits@N (N=1,3,10)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' MR reports the average predicted rank of all the labeled triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' MRR is the average of the inverse rank of the labelled triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hits@N evaluates the fraction of the labeled triples that are present in the top N predicted results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Persistent Homology (PH) [15, 19]: studies the topological features such as components in 0-dimension (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', a node), holes in 1-dimension (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', a void area bounded by triangle edges) and so on, spread over a scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus, one need not choose a scale before- hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The number(rank) of these topological features(homology group) in every dimension at a particular scale can be used for downstream applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider the simplicial complex ( e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', point is a 0-simplex, an edge is a 1-simplex, a triangle is a 2-simplex ) 𝐶 with weights 𝑎0 ≤ 𝑎1 ≤ 𝑎2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝑎𝑚−1, which could represent the edge weights, for example, the triple score from the KG embed- ding method in our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' One can then define a Filtration process [15], which refers to generating a nested sequence of complexes 𝜙 ⊆ 𝐶1 ⊆ 𝐶2 ⊆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝐶𝑚 = 𝐶 in time/scale as the simplices below Can Persistent Homology provide an efficient alternative WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Figure 1: Calculating Knowledge Persistence(KP) score from the given KG and KG embedding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The KG is sampled for positive(G+) and negative(G−) triples (step one), keeping the order O(|E|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The edge weights represent the score obtained from the KG embedding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In step two, the persistence diagram (PD) is computed using filtration process explained in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In final step, a Sliced Wasserstein distance (SW) is obtained between the PDs of G+ and G− to get the KP score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, ranking metrics run the KGE methods over all the O(|E|2) triples as explained in bottom left part of the figure(red box).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' the threshold weights are added in the complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The filtration pro- cess [15] results in the creation(birth) and destruction(death) of components, holes, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus each structure is associated with a birth-death pair (𝑎𝑖,𝑎𝑗) ∈ 𝑅2 with 𝑖 ≤ 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The persistence or life- time of each component can then be given by 𝑎𝑗 − 𝑎𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A persistence diagram (PD) summarizes the (birth,death) pair of each object on a 2D plot, with birth times on the x axis and death times on the y axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The points near the diagonal are shortlived components and generally are considered noise (local topology), whereas the persis- tent objects (global topology) are treated as features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We consider local and global topology to compare two PDs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', positive and negative triple graphs in our case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4 PROBLEM STATEMENT AND METHOD 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 Problem Setup We define a KG as a tuple 𝐾𝐺 = (E, R, T +) where E denotes the set of entities (vertices), R is the set of relations (edges), and T + ⊆ E × R × E is a set of all triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A triple τ = (𝑒ℎ,𝑟,𝑒𝑡) ∈ T + indicates that, for the relation 𝑟 ∈ R, 𝑒ℎ is the head entity (origin of the relation) while 𝑒𝑡 is the tail entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Since 𝐾𝐺 is a multigraph;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝑒ℎ = 𝑒𝑡 may hold and |{𝑟𝑒ℎ,𝑒𝑡 }| ≥ 0 for any two entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The KG completion task predicts the entity pairs ⟨𝑒𝑖,𝑒𝑗⟩ in the KG that have a relation 𝑟𝑐 ∈ R between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 Proposed Method In this section we describe our approach for evaluating KG embed- ding methods using the theory of persistent homology (PH) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This process is divided into three steps ( Figure 1), namely: (i) Graph con- struction, (ii) Filtration process and (iii) Sliced Wasserstein distance computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The first step creates two graphs (one for positive triples, another for negative triples) using sampling(O(V) triples), with scores calculated by a KGE method as edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The second step considers these graphs and, using a process called "fil- tration," converts to an equivalent lower dimension representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The last step calculates the distance between graphs to provide a final metric score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We now detail the approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 Graph Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We envisioned KGE from the topolog- ical lens while proposing an efficient solution for its evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Previous works such as [40] proposed a KGE metric only consider- ing embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, we intend to preserve the topology (graph structure and its topological feature) along with the KG em- bedding features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We first construct graphs of positive and negative triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We denote a graph as (V, E) where V is the set of 𝑁 nodes and E represents the edges between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider a KG embed- ding method M that takes as input the triple τ = (ℎ,𝑟,𝑡) ∈ T and gives the score 𝑠τ of it being a right triple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We construct a weighted directed graph G+ from positive triples τ ∈ T + in the train set, with the entities as the nodes and the relations between them as the edges having 𝑠τ as the edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Here, 𝑠τ is the score calculated by KGE method for a triple and we propose to use it as the edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Our idea is to capture topology of graph (G+) with repre- sentation learned by a KG embedding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We sample an order of O(|E|) triples, |E| being the number of entities to keep compu- tational time linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Similarly, we construct a negative graph G− by sampling the same number of unknown triples as the positive samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' One question may arise if KP is robust to sampling, that we answer theoretically in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 and empirically in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Note, here we do not take all the negative triples in the graphs and consider only a fraction of what the ranking metrics need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This is a fundamental difference with ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ranking metrics use all the unlabeled triples as negatives for ranking, thus incurring a computational cost of 𝑂(|E|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 Filtration Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Having constructed the Graphs G+ and G−, we now need some definition of a distance between them 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Graph Construction 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Filtration Process Winneror gt a=0 Einstein(HAE) Hans Prize(NP) Hans KG Embedding Einstein GrandSonof method Alfred Sonot n SupervisedBy r(A a=2 3Albert Einstein Homen Alfred Birth 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Sliced Wasserstein Distance Computation D+ O(E*)Graph with scores from the KGE method onthe edges HAE KP(G+, G-) = SW(D+, D-) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 Ranking Ranking metric Albert Einstein HE AK Hermann Einstein Birth Ranking Metrics D- process Sampled O(E) Graphs with scores from the KGE method on the edgesWWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 2: For a KGE method, the positive triple graph G+ is used as input (leftmost graph with edge weights) and filtration process is applied on the edge weights (calculated by KGE method) for the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The filtration starts with only nodes as first step, and based on the edge weights, edges are added to the nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The persistence diagram is given on the right with red dots indicating 0-dimensional homology (components) and the blue dots indicating 1-dimensional homology (cycles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Persistent Diagram generated from this filtration process is a condensed 2D representation of G+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A similar process is repeated for G−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' to define a metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, since the KGs could be large with many entities and relations, directly comparing the graphs could be computationally challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Therefore, we allude to the theory of persistent homology (PH) to summarize the structures in the graphs in the form of the persistence diagram (PD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Such summa- rizing is obtained by a process known as filtration [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' One can imagine a PD as mapping of higher dimensional data to a 2D plane upholding the representation of data points and we can then derive computational efficiency for distance comparison between 2D repre- sentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Specifically, we compute the 0-dimensional topological features (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', connected-nodes/components) for each graph (G− and G+) to keep the computation time linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We also experimented using the 1-dimensional features without much empirical benefit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider the positive triple graph G+ as input (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We would need a scale (as pointed in section 3) for the filtration process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Once the filtration process starts, initially, we have a graph structure containing only the nodes (entities) and no edges of G+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For capturing topological features at various scales, we define a variable 𝑎 which varies from −∞ to +∞ and it is then compared with edge weights (𝑠τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A scale allows to capture topology at various timesteps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus, we use the edge weights obtained from the scores (𝑠τ) of the KGE methods for filtration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' As the filtration proceeds, the graph structures (components) are generated/removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' At a given scale 𝑎, the graph structure ((G+ 𝑠𝑢𝑏)𝑎) contains those edges (triples) for which 𝑠τ ≤ 𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Formally, this is expressed as: (G+ 𝑠𝑢𝑏)𝑎 = {(V, E+ 𝑎)|E+ 𝑎 ⊆ E,𝑠τ ≤ 𝑎 ∀τ ∈ E+ 𝑎 } Alternatively, we add those edges for which score of the triple is greater than or equal to the filtration value, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', 𝑠τ ≥ 𝑎 defined as (G+ 𝑠𝑢𝑝𝑒𝑟)𝑎 = {(V, E𝑎+)|E𝑎+ ⊆ E,𝑠τ ≥ 𝑎 ∀τ ∈ E𝑎+} One can imagine that for filtration, graph G+ is subdivided into (G+ 𝑠𝑢𝑏)𝑎 and (G+𝑠𝑢𝑝𝑒𝑟)𝑎 as the filtration adds/deletes edges for cap- turing topological features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, specific components in a sub- graphs will appear and certain components will disappear at differ- ent scale levels (timesteps) 𝑎 = 1, 3, 5 and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Please note, Figure 2 explains creation of PD for (G+ 𝑠𝑢𝑏)𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A similar process is repeated for (G+𝑠𝑢𝑝𝑒𝑟)𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This expansion/contraction process enables capturing topology at different time-steps without worrying about defining an optimal scale (similar to hyperparameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Next step is the creation of persistent diagrams of (G+ 𝑠𝑢𝑏)𝑎 and (G+𝑠𝑢𝑝𝑒𝑟)𝑎 where the x-axis and y-axis denotes the timesteps of appearance/disappearance of components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For creating a 2D representation graph, components of graphs which appear(disappear) during filtration process at 𝑎𝑥 (𝑎𝑦) are plotted on (𝑎𝑥,𝑎𝑦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The persistence or lifetime of each compo- nent can then be given by 𝑎𝑦 − 𝑎𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' At implementation level, one can view PDs(∈ 𝑅𝑁×2) of (G+ 𝑠𝑢𝑏)𝑎 and (G+𝑠𝑢𝑝𝑒𝑟)𝑎 as tensors which are concatenated into one common tensor representing positive triple graph G+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, final PD of G+ is a concatenation of PDs of (G+ 𝑠𝑢𝑏)𝑎 and (G+𝑠𝑢𝑝𝑒𝑟)𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This final persistent diagram represents a summary of the local and global topological features of the graph G+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Following are the benefits of a persistent diagram against con- sidering the whole graph: 1) a 2D summary of a higher dimensional graph structure data is highly beneficial for large graphs in terms of the computational efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2) The summary could contain fewer data points than the original graph, preserving the topologi- cal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Similarly, the process is repeated for negative triple graph G− for creating its persistence diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Now, the two newly created PDs are used for calculating the proposed metric score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 Sliced Wasserstein distance computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' To compare two PDs, generally the Wasserstein distance between them is computed [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' As the Wasserstein distance could be computationally costly, we find the sliced Wasserstein distance [13] between the PDs, which we empirically observe to be eight times faster on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The Sliced Wasserstein distance(𝑆𝑊 ) between measures 𝜇 and 𝜈 is: 𝑆𝑊𝑝 (𝜇,𝜈) = �∫ 𝑆𝑑−1 𝑊 𝑝 𝑝 (𝑅𝜇 (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=',𝜃), 𝑅𝜈 (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=',𝜃)) � 1 𝑝 where 𝑅𝜇 (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=',𝜃) is the projection of 𝜇 along 𝜃,𝑊 is initial Wasserstein distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Generally a Monte Carlo average over 𝐿 samples is done instead of the integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The 𝑆𝑊 distance takes O(𝐿𝑁𝑑 +𝐿𝑁𝑙𝑜𝑔(𝑁)) time which can be improved to linear time O(𝑁𝑑) for 𝑆𝑊2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Euclidean distance) as a closed form solution [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus, KP(G+, G−) = 𝑆𝑊 (𝐷+, 𝐷−) (1) where 𝐷+, 𝐷− are the persistence diagrams for G+, G− respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Since the metric is obtained by summarizing the Knowledge graph using Persistence diagrams we term it as Knowledge Persistence(KP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' As KP correlates well with ranking metrics (sections 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 and 5), higher KP signifies a better performance of the KGE method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 Theoretical justification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This section briefly states the theo- retical results justifying the proposed method to approximate the 1Can Persistent Homology provide an efficient alternative WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We begin the analysis by assuming two distribu- tions: One for the positive graph’s edge weights(scores) and the other for the negative graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We define a metric "PERM" (Figure 3), that is a proxy to the ranking metrics while being continuous(for the definition of integrals and derivatives) for ease of theoretical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The proof sketches are given in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 3: Figure gives an intuition of the metric PERM which is designed to be a proxy to the ranking metrics for ease of theoretical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For a given positive triple 𝜏 with score 𝑥𝜏 the expected rank(𝐸𝑅(𝜏)) is defined as the area under the curve of the negative distribution from 𝑥𝜏 to ∞(shown in the shaded area above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PERM is then defined as the expectation of the expected rank under the positive distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 (Expected Ranking(ER)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider the positive triples to have the distribution 𝐷+ and the negative triples to have the distribution 𝐷−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For a positive triple with score 𝑎 its expected rank- ing(ER) is defined as, 𝐸𝑅(𝑎) = ∫ 𝑥=∞ 𝑥=𝑎 𝐷−(𝑥)𝑑𝑥 Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 (PERM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider the positive triples to have the distribution 𝐷+ and the negative triples to have the distribution 𝐷−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The PERM metric is then defined as, 𝑃𝐸𝑅𝑀 = ∫ 𝑥=∞ 𝑥=−∞ 𝐷+(𝑥)𝐸𝑅(𝑥)𝑑𝑥 It is easy to see that PERM has a monotone increasing corre- spondence with the actual ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' That is, as many of the negative triples get a higher score than the positive triples, the distribution of the negative triples will shift further right of the pos- itive distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, the area under the curve would increase for a given triple(x=a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We just established a monotone increasing correspondence of PERM with the ranking metrics, we now need show that there exists a one-one correspondence between PERM and KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For closed-form solutions, we work with normalised dis- tributions (can be extended to other distributions using [39]) of KGE score under the following mild consideration: As the KGE method converges, the mean statistic(𝑚𝜈) of the scores of the posi- tive triples consistently lies on one side of the half-plane formed by the mean statistic(𝑚𝜇) of the negative triples, irrespective of the data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP has a monotone increasing correspondence with the Proxy of the Expected Ranking Metrics(PERM) under the above stated considerations as 𝑚𝜈 deviates from 𝑚𝜇 The above lemma shows that there is a one-one correspondence between KP and PERM and by definition PERM has a one-one cor- respondence with the ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Therefore, the next theorem follows as a natural consequence: Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP has a one-one correspondence with the ranking metrics under the above stated considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The above theorem states that, with high probability, there exists a correlation between KP and the ranking metrics under certain considerations and proof details are in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In an ideal case, we seek a linear relationship between the proposed mea- sure and the ranking metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This would help interpret whether an increase/decrease in the measure would cause a corresponding increase/decrease in the ranking metric we wish to simulate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Such interpretation becomes essential when the proposed metric has different behavior from the existing metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' While the correlation could be high, for interpretability of the results, we would also like the change in KP to be bounded for a change in the scores(ranking metrics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The below theorem gives a sense for this bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Under the considerations of theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3, the relative change in KP on addition of random noise to the scores is bounded by a function of the original and noise-induced covariance matrix as ΔK P K P ≤ 𝑚𝑎𝑥((1 − |Σ+1 𝜇1 Σ−1 𝜇2 | 3 2 ), (1 − |Σ+1 𝜈1 Σ−1 𝜈2 | 3 2 )), where Σ𝜇1 and Σ𝜈1 are the covariance matrices of the positive and negative triples’ scores respectively and Σ𝜇2 and Σ𝜈2 are that of the corrupted scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 gives a bound on the change in KP while inducing noise in the KGE predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ideally, the error/change would be 0, and as the noise is increased(and the ranking changed), gradually, the KP value also changes in a bounded manner as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 5 EXPERIMENTAL SETUP For de-facto KGC task (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1), we use popular KG embed- ding methods from its various categories: (1) Translation: TransE [8], TransH [57], TransR [26] (2) Bilinear, Rotation, and Factoriza- tion: RotatE [44] TuckER [3], and ComplEx [48], (3) Neural Network based: ConvKB [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The method selection and evaluation choices are similar to [28, 37] that propose new metrics for KG embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' All methods run on a single P100 GPU machine for a maximum of 100 epochs each and evaluated every 5 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For training/testing the KG embedding methods we make use of the pykg2vec [61] library and validation runs are executed 20 times on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We use the standard/best hyperparameters for these datasets that the considered KGE methods reported [3, 8, 26, 44, 48, 57, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 Datasets We use standard English KG completion datasets: WN18, WN18RR, FB15k237, FB15k, YAGO3-10 [2, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The WN18 dataset is obtained from Wordnet [27] containing lexical relations between English words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' WN18RR removes the inverse relations in the WN18 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' FB15k is obtained from the Freebase [7] knowledge graph, and FB15k237 was created from FB15k by removing the inverse relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The dataset details are in the Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For scaling experiment, we rely on large scale YAGO3-10 dataset [2] and due to brevity, results for Yago3-10 are in appendix ( cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Figure 6 and table 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 Comparative Methods Considering ours is the first work of its kind, we select some com- petitive baselines as below and explain "why" we chose them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For evaluation, we report correlation [14] between KP and baselines with ranking metrics (Hits@N (N= 1,3,10), MRR and MR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Conicity [40]: It finds the average cosine of the angle between an embedding and the mean embedding vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In a sense, it gives PERM =E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' (ER(T) Distribution Distribution of positive ER(T) of neqative triples triples Score of a positive triple TWWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' spread of a KG embedding method in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We would like to observe instead of topology, if calculating geometric properties of a KG embedding method be an alternative for ranking metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Average Vector Length: This metric was also proposed by Sharma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [40] to study the geometry of the KG embedding methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It computes the average length of the embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Graph Kernel (GK): we use graph kernels to compare the two graphs(G+, G−) obtained for our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The rationale is to check if we could get some distance metric that correlates with the ranking metrics without persistent homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, this baseline empha- sizes a direct comparison for the validity of persistent homology in our proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' As an implementation, we employ the widely used shortest path kernel [10] to compare how the paths(edge weights/scores) change between the two graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Since the method is computationally expensive, we sample nodes [11] and apply the kernel on the sampled graph, averaging multiple runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Table 1: (Open-Source)Benchmark Datasets for Experi- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Dataset Triples Entities Relations FB15K 592,213 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='951 1,345 FB15K-237 272,115 14,541 237 WN18 151,442 40,943 18 WN18RR 93,003 40,943 11 Yago3-10 1,089,040 123,182 37 6 RESULTS AND DISCUSSION We conduct our experiments in response to the following research questions: RQ1: Is there a correlation between the proposed metric and ranking metrics for popular KG embedding methods?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' RQ2: Can the proposed metric be used to perform early stopping during training?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' RQ3: What is the computational efficiency of proposed metric wrt ranking metrics for KGE evaluation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP for faster prototyping of KGE methods: Our core hypoth- esis in the paper is to develop an efficient alternative (proxy) to the ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, for a fair evaluation, we use the triples in the test set for computing KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ideally, this should be able to simulate the evaluation of the ranking metrics on the same (test) set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' If true, there exists a high correlation between the two mea- sures, namely the KP and the ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Table 2 shows the linear correlations between the ranking metrics and our method & baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We report the linear(Pearson’s) correlation because we would like a linear relationship between the proposed measure and the ranking metric (for brevity, other correlations are in appendix Tables 7, 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This would help interpret whether an increase/decrease in the measure would cause a corresponding increase/decrease in the ranking metric that we wish to simulate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Specifically we train all the KG embedding methods for a predefined number of epochs and evaluate the finally obtained models to get the ranking metrics and KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The correlations are then computed between KP and each of the ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We observe that KP(test) configuration (triples are sampled from the test set) achieves the highest correla- tion coefficient value among all the existing geometric and kernel baseline methods in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For instance, on FB15K, KP(test) reports high correlation value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 with Hits@1, whereas best baseline for this dataset (AVL) has corresponding correlation value as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Similarly for WN18RR, KP(test) has correlation value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='482 compared to AVL with -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='272 correlation with Hits@1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Conicity and AVL that provide geometric perspective shows mostly low positive correlation with ranking metrics whereas the Graph Kernel based method shows highly negative correlations, making these methods unsuitable for direct applicability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It indicates that the topology of the KG induced by the learnt representations seems a good predictor of the performance on similar data distributions with high correlation with ranking metric (answering RQ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Furthermore, the results also report a configuration KP(train) in which we compute KP on the triples of the train set and find the correlation with the ranking metrics obtained from the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Here our rationale is to study whether the proposed metric would be able to capture the generalizability of the unseen test (real world) data that is of a similar distribution as the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Initial re- sults in Table 2 are promising with high correlation of KP(train) with ranking metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, it may enable the use of KP in settings without test/validation data while using the available (possibly lim- ited) data for training, for example, in few-shot scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We leave this promising direction of research for future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 KP as a criterion for early stopping Does KP hold correlation while early stopping?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' To know when to stop the training process to prevent overfitting, we must be able to estimate the variance of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This is generally done by observing the validation/test set error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus, to use a method as a criterion for early stopping, it should be able to predict this gen- eralization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Table 2 explains that KP(Train) can predict the generalizability of methods on the last epoch, it remains to empiri- cally verify that KP also predicts the performance at every interval during the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hence, we study the correlations of the proposed method with the ranking metrics for individual KG embedding methods in the intra-method setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Specifically, for a given method, we obtain the KP score and the ranking metrics on the test set and compute the correlations at every evaluation interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Results in Table 3 suggest that KP has a decent correla- tion in the intra-method setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It indicates that KP could be used in place of the ranking metrics for deciding a criterion on early stopping if the score keeps persistently falling (answering RQ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' What is the relative error of early stopping between KP and Ranking Metric?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' To further cross-validate our response to RQ2, we now compute the absolute relative error between the rank- ing metrics of the best models selected by KP and the expected ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ideally, we would expect the performance of the model obtained using this process on unseen test data(preferably of the same distribution) to be close to the best achievable result, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', the relative error should be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This is important as if we were to use any metric for faster prototyping, it should also be a good criterion for model selection(selecting a model with less generalization error) and being efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Table 4 shows that the relative error is marginal, of the order of 10−2, in most cases(with few exceptions), indicating that KP could be used for early stop- ping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The deviation is higher for some methods, such as ConvKB, Can Persistent Homology provide an efficient alternative WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Metrics FB15K FB15K237 WN18 WN18RR Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Conicity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='156 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='170 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='202 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='085 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='183 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='509 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='379 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='356 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='352 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='424 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='052 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='096 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='123 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='389 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='096 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='267 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='471 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='510 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='266 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='448 AVL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='339 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='325 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='261 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='423 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='308 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='527 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='149 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='188 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='284 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='805 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='825 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='856 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='884 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='840 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='272 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='456 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='488 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='303 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='438 GK(train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='825 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='852 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='815 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='952 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='843 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='903 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='955 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='972 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='970 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='965 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='645 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='648 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='669 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='611 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='663 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='518 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='808 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='840 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='591 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='779 GK(test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='318 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='247 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='629 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='300 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='031 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='123 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='101 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='095 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='579 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='565 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='569 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='412 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='575 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='276 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='589 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='658 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='470 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='549 KP (Train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='482 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='418 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='449 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='072 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='433 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='773 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='711 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='702 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='745 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='769 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='769 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='782 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='682 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='780 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='809 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='852 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='755 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='777 KP (Test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='731 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='661 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='669 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='721 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='825 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='870 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='864 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='861 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='875 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='887 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='909 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='884 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='899 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='482 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='816 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='863 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='683 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='776 Table 2: Pearson’s linear correlation (𝑟) scores computed from the metric scores with respect to the ranking metrics on the standard KG embedding datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The KG methods are evaluated after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Green values are the best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Datasets FB15K237 WN18RR KG methods r 𝜌 𝜏 r 𝜌 𝜏 TransE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='955 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='861 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='709 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='876 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='833 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='722 TransH 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='688 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='570 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='409 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='864 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='717 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='555 TransR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='975 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='942 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='811 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='954 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='967 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='889 Complex 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='938 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='788 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='610 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='833 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='933 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='833 RotatE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='896 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='735 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='579 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='774 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='983 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='944 TuckER 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='906 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='676 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='527 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='352 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='167 ConvKB 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='007 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='276 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='569 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='422 Table 3: Correlation scores computed between KP and the ranking metric(Hits@10) on the standard KG embedding datasets with the methods evaluated at every interval as the training progresses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Here, r: Pearson correlation co-efficient, 𝜌: Spearman’s correlation co-efficient, 𝜏: Kendall’s Tau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' which had convergence issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We infer from observed behavior that if the KG embedding method has not converged(to good re- sults), the correlation and, thus, the early stopping prediction may suffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Despite a few outliers, the promising results shall encourage the community to research, develop, and use KGE benchmarking methods that are also computationally efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Datasets FB15K237 WN18RR KG methods hits@1 hits@10 MRR hits@1 hits@10 MRR TransE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='007 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='007 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='004 TransH 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='045 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='019 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='018 0023 TransR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='074 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='045 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='053 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='242 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='062 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='016 Complex 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='021 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='028 RotatE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='007 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='009 TuckER 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='008 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='293 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='101 ConvKB 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='043 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='043 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='659 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='453 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='569 Table 4: Early stopping using KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The values depict the ab- solute relative error between the metrics of the best models selected using KP and ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 Timing analysis and carbon footprint We now study the time taken for running the evaluation (including evaluation at intervals) of the same methods as in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 on the standard datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Table 5 shows the evaluation times (valida- tion+test) and speedup for each method on the respective datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The training time is constant for ranking metric and KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In some cases (ConvKB), we observe KP achieves a speedup of up to 2576 times on model evaluation time drastically reducing evaluation time from 18 hours to 27 seconds;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' the latter is even roughly equal to the carbon footprint of making a cup of coffee2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Furthermore, Figure 2https://tinyurl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='com/4w2xmwry Figure 4: Figure shows a study on the carbon footprint on WN18RR when using KP vs Hits@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The x-axis shows the the carbon footprint in g eq 𝐶𝑂2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4 illustrates the carbon footprints [33, 59] of the overall process (training + evaluation) for the methods when using KP vs ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Due to evaluation time drastically reduced by KP, it also reduces overall carbon footprints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The promising results validate our attempt to develop alternative method for faster prototyping of KGE methods, thus saving carbon footprint (answering RQ3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 Ablation Studies We systematically provide several studies to support our evaluation and characterize different properties of KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Robustness to noise induced by sampling: An important property that makes persistent homology worthwhile is its stability concerning perturbations of the filtration function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This means that persistent homology is robust to noise and encodes the intrinsic topological properties of the data [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, in our applica- tion of predicting the performance of KG embedding methods, one source of noise is because of sampling the negative and positive triples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It could cause perturbations in the graph topology due to the addition and deletion of edges (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Therefore, we would like the proposed metric to be stable concerning perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' To understand the behavior of KP against this noise, we conduct a study by incrementally adding samples to the graph and observing the mean and standard deviation of the correlation at each stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In an ideal case, assuming the KG topology remains similar, the mean correlations should be in a narrow range with slight standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We observe a similar effect in Figure 5 where we report the mean correlation at various fractions of triples sampled, with the standard deviation(error bands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Here, the mean correlation coefficients are within the range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='06(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='04), and the average stan- dard deviations are about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='02(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='02) for the FB15K237(WN18RR) Carbon Footprint of the Overall KGE prototyping process Carbon Footprint using KP Carbon Footprint using ranking metrics TransE TransH TransR Complex RotatE ConvKB TuckER 0 100 200 300 400WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Metrics Hits@10 KP Speedup ↑ Dataset FB15K237 WN18RR FB15K237 WN18RR FB15K237 WN18RR split val + test val + test val + test val + test Avg Avg TransE 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='337 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='120 x 322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='8 x 754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 TransH 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='099 x 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 x 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 TransR 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='352 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='135 x 572.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 x 1066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 Complex 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='340 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='142 x 420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 x 1121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='7 RotatE 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='359 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='142 x 509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='5 x 1145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 TuckER 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='8 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='332 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='098 x 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 x 241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='9 ConvKB 1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='451 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='139 x 2576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 x 1044.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 Table 5: Evaluation Metric Comparison wrt Computing Time (in minutes, for 100 epochs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Column 1 denotes popular KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Depicted values denote evalua- tion(validation+test) time for computing a metric and corre- sponding speedup using KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP significantly reduces the evaluation time (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' This shows that KP inherits the robustness of the topo- logical data analysis techniques, enabling linear time by sampling from the graph for dense KGs while keeping it robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 5: Effect of sample size on the correlation coefficient between KP and the ranking metrics on FB15K237 (left dia- gram) and WN18RR datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The correlations for the differ- ent sampling fractions are comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Also, the standard deviation is less, indicating the method’s robustness due to changes in local topology while doing sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Generalizability Study- Correlation with Stratified Rank- ing Metric: Mohamed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [28] proposed a new stratified metric (strat-metric) that can be tuned to focus on the unpopular entities, unlike the standard ranking metrics, using certain hyperparameters (𝛽𝑒 ∈ (−1, 1), 𝛽𝑟 ∈ (−1, 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Special cases of these hyperparame- ters give the micro and macro ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Goal here is to study whether our method can predict strat-metric for the spe- cial case of 𝛽𝑒 = 1, 𝛽𝑟 = 0, which estimates the performance for unpopular(sparse) entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Also, we aim to observe if KP holds a correlation with variants of the ranking metric concerning its generalization ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The results (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', Table 6) shows that KP has a good correlation with each of the stratified ranking metrics which indicate KP also takes into account the local geometry/topology [1] of the sparse entities and relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 Summary of Results and Open Directions To sum up, following are key observations gleaning from empirical studies: 1) KP shows high correlation with ranking metrics (Ta- ble 2) and its stratified version (Table 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' It paves the way for the use of KP for faster prototyping of KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2) KP holds Datasets FB15K237 WN18RR Metrics r 𝜌 𝜏 r 𝜌 𝜏 Strat-Hits@1 (↑) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='965 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='857 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='513 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='482 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='411 Strat-Hits@3 (↑) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='898 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='691 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 Strat-Hits@10 (↑) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='870 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 Strat-MR (↓) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='813 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='701 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 Strat-MRR (↑) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='806 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='658 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 Table 6: KP correlation with stratified ranking metrics as proposed in [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' a high correlation at every interval during the training process (Table 3) with marginal relative error;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' hence, it could be used for early stopping of a KGE method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 3) KP inherits key properties of persistent homology, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', it is robust to noise induced by sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 4) The overall carbon footprints of the evaluation cycle is drastically reduced if KP is preferred over ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' What’s Next?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We show that topological data analysis based on persistent homology can act as a proxy for ranking metrics with conclusive empirical evidence and supporting theoretical founda- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, it is the first step toward a more extensive research agenda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We believe substantial work is needed collectively in the research community to develop strong foundations, solving scal- ing issues (across embedding methods, datasets, KGs, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=') until persistent homology-based methods are widely adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For example, there could be methods/datasets where the correla- tion turns out to be a small positive value or even negative, in which case we may not be able to use KP in the existing form to simu- late the ranking metrics for these methods/datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In those cases, some alteration may exist for the same and seek further exploration similar to what stratified ranking metric [28] does by fixing issues encountered in the ranking metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Furthermore, theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 would be a key to understand error bounds when interpreting limited per- formance (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=', when the correlation is a small positive).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' However, this does not limit the use of KP for KGE methods as it captures and contrasts the topology of the positive and negative sampled graphs learned from these methods, which could be a useful metric by itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In this paper, the emphasis is on the need for evaluation and benchmarking methods that are computationally efficient rather than providing an exhaustive one method fits all metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We believe that there is much scope for future research in this direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Some promising directions include 1) better sampling techniques(instead of the random sampling used in this paper), 2) rigorous theoretical analysis drawing the boundaries on the abilities/limitations across settings (zero-shot, few-shot, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' ), 3) using KP (and related metrics) in continuous spaces, that could be differentiable and approximate the ranking metrics, in the optimization process of KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 7 CONCLUSION We propose Knowledge Persistence (KP), first work that uses tech- niques from topological data analysis, as a predictor of the ranking metrics to efficiently evaluate the performance of KG embedding approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' With theoretical and empirical evidences, our work brings efficiency at center stage in the evaluation of KG embedding methods along with traditional way of reporting their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Finally, with efficiency as crucial criteria for evaluation, we hope Hits@10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='90 MRR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='84 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='78 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='95 Hits@10 MRR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0Can Persistent Homology provide an efficient alternative WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA KGE research becomes more inclusive and accessible to the broader research community with limited computing resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Acknowledgment This work was partly supported by JSPS KAKENHI Grant Number JP21K21280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' REFERENCES [1] Henry Adams and Michael Moy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Topology Applied to Machine Learning: From Global to Local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Frontiers in Artificial Intelligence 4 (2021), 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [2] Mehdi Ali, Max Berrendorf, Charles Tapley Hoyt, Laurent Vermue, Mikhail Galkin, Sahand Sharifzadeh, Asja Fischer, Volker Tresp, and Jens Lehmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Bringing light into the dark: A large-scale evalua- tion of knowledge graph embedding models under a unified framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' IEEE Transactions on Pattern Analysis and Machine Intelligence (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [3] Ivana Balažević, Carl Allen, and Timothy Hospedales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' TuckER: Tensor Factorization for Knowledge Graph Completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Pro- cessing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 5185–5194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [4] Iti Bansal, Sudhanshu Tiwari, and Carlos R Rivero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The impact of negative triple generation strategies and anomalies on knowledge graph completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 29th ACM International Con- ference on Information & Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 45–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [5] Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Saeedeh Shekarpour, Isaiah Onando Mulang, and Johannes Hoffart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Hopfe: Knowl- edge graph representation learning using inverse hopf fibrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 30th ACM International Conference on Information & Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 89–99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [6] Max Berrendorf, Evgeniy Faerman, Laurent Vermue, and Volker Tresp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Interpretable and Fair Comparison of Link Prediction or Entity Alignment Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In 2020 IEEE/WIC/ACM International Joint Con- ference on Web Intelligence and Intelligent Agent Technology (WI-IAT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' IEEE, 371–374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [7] Kurt D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Bollacker, Robert P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Cook, and Patrick Tufts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Freebase: A Shared Database of Structured General Human Knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [8] Antoine Bordes, Nicolas Usunier, Alberto Garcia-Duran, Jason Weston, and Oksana Yakhnenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Translating embeddings for modeling multi-relational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In NeurlPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [9] Antoine Bordes, Jason Weston, Ronan Collobert, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Learning structured embeddings of knowledge bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Twenty- fifth AAAI conference on artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [10] Karsten M Borgwardt and Hans-Peter Kriegel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Shortest-path kernels on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Fifth IEEE international conference on data mining (ICDM’05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' IEEE, 8–pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [11] Karsten M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Borgwardt, Tobias Petri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Vishwanathan, and Hans- Peter Kriegel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' An Efficient Sampling Scheme For Comparison of Large Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Mining and Learning with Graphs, MLG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [12] Andrei Z Broder, Marc Najork, and Janet L Wiener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Efficient URL caching for world wide web crawling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 12th international conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 679–689.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [13] Mathieu Carrière, Marco Cuturi, and Steve Oudot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Sliced Wasser- stein Kernel for Persistence Diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 34th In- ternational Conference on Machine Learning (Proceedings of Machine Learning Research), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PMLR, 664–673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [14] Nian Shong Chok.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Pearson’s versus Spearman’s and Kendall’s cor- relation coefficients for continuous data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' University of Pittsburgh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [15] Herbert Edelsbrunner, David Letscher, and Afra Zomorodian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Topological persistence and simplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings 41st annual symposium on foundations of computer science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' IEEE, 454–463.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [16] Brittany Fasy, Yu Qin, Brian Summa, and Carola Wenk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Compar- ing Distance Metrics on Vectorized Persistence Summaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In NeurIPS 2020 Workshop on Topological Data Analysis and Beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [17] Luis Galárraga, Katja Hose, and Ralf Schenkel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Partout: a dis- tributed engine for efficient RDF processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 23rd International Conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 267–268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [18] Genet Asefa Gesese, Russa Biswas, Mehwish Alam, and Harald Sack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A survey on knowledge graph embeddings with literals: Which model links better literal-ly?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Semantic Web Preprint (2019), 1–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [19] Felix Hensel, Michael Moor, and Bastian Rieck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A survey of topo- logical machine learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Frontiers in Artificial Intelligence 4 (2021), 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [20] Nitisha Jain, Jan-Christoph Kalo, Wolf-Tilo Balke, and Ralf Krestel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Do Embeddings Actually Capture Knowledge Graph Semantics?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='. In European Semantic Web Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Springer, 143–159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [21] Prachi Jain, Sushant Rathi, Soumen Chakrabarti, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Knowl- edge base completion: Baseline strikes back (again).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' arXiv preprint arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='00804 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [22] Shaoxiong Ji, Shirui Pan, Erik Cambria, Pekka Marttinen, and Philip S Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A survey on knowledge graphs: Representation, acquisition and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' EEE Transactions on Neural Networks and Learning Systems (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [23] Rudolf Kadlec, Ondřej Bajgar, and Jan Kleindienst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Knowledge Base Completion: Baselines Strike Back.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 2nd Workshop on Representation Learning for NLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 69–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [24] Zelong Li, Jianchao Ji, Zuohui Fu, Yingqiang Ge, Shuyuan Xu, Chong Chen, and Yongfeng Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Efficient non-sampling knowledge graph embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the Web Conference 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1727– 1736.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [25] Lipyeow Lim, Min Wang, Sriram Padmanabhan, Jeffrey Scott Vitter, and Ramesh Agarwal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Dynamic maintenance of web indexes using landmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 12th international conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 102–111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [26] Yankai Lin, Zhiyuan Liu, Maosong Sun, Yang Liu, and Xuan Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Learning entity and relation embeddings for knowledge graph com- pletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [27] George A Miller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' WordNet: a lexical database for English.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Com- mun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' ACM 38, 11 (1995), 39–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [28] Aisha Mohamed, Shameem Parambath, Zoi Kaoudi, and Ashraf Aboul- naga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Popularity agnostic evaluation of knowledge graph em- beddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Conference on Uncertainty in Artificial Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PMLR, 1059–1068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [29] Michael Moor, Max Horn, Bastian Rieck, and Karsten Borgwardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Topological autoencoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International conference on machine learn- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PMLR, 7045–7054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [30] Kimia Nadjahi, Alain Durmus, Pierre E Jacob, Roland Badeau, and Umut Simsekli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Advances in Neural Information Processing Systems 34 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [31] Mojtaba Nayyeri, Chengjin Xu, Yadollah Yaghoobzadeh, Hamed Shariat Yazdi, and Jens Lehmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Toward Un- derstanding The Effect Of Loss function On Then Performance Of Knowledge Graph Embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='00519 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [32] Tu Dinh Nguyen, Dat Quoc Nguyen, Dinh Phung, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In NAACL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 327–333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [33] David Patterson, Joseph Gonzalez, Urs Hölzle, Quoc Le, Chen Liang, Lluis-Miquel Munguia, Daniel Rothchild, David So, Maud Texier, and Jeff Dean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The Carbon Footprint of Machine Learning Training Will Plateau, Then Shrink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='05149 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [34] Xutan Peng, Guanyi Chen, Chenghua Lin, and Mark Stevenson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Highly Efficient Knowledge Graph Embedding Learning with Orthog- onal Procrustes Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In NAACL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2364–2375.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [35] Pouya Pezeshkpour, Yifan Tian, and Sameer Singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Revisit- ing evaluation of knowledge base completion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Automated Knowledge Base Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [36] Bastian Rieck, Matteo Togninalli, Christian Bock, Michael Moor, Max Horn, Thomas Gumbsch, and Karsten Borgwardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Neural Per- sistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International Conference on Learning Represen- tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [37] Wiem Ben Rim, Carolin Lawrence, Kiril Gashteovski, Mathias Niepert, and Naoaki Okazaki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Behavioral Testing of Knowledge Graph Embedding Models for Link Prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In 3rd Conference on Automated Knowledge Base Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [38] Tara Safavi and Danai Koutra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' CoDEx: A Comprehensive Knowl- edge Graph Completion Benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 2020 Confer- ence on Empirical Methods in Natural Language Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 8328–8350.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [39] Remi M Sakia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The Box-Cox transformation technique: a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series D (The Statistician) 41, 2 (1992), 169–178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [40] Aditya Sharma, Partha Talukdar, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Towards understanding the geometry of knowledge graph embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 122–131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [41] Kuldeep Singh, Arun Sethupat Radhakrishna, Andreas Both, Saeedeh Shekarpour, Ioanna Lytra, Ricardo Usbeck, Akhilesh Vyas, Akmal Khikmatullaev, Dharmen Punjani, Christoph Lange, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Why reinvent the wheel: Let’s build question answering systems together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 2018 world wide web conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1247–1256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Spearman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Demonstration of Formulæ for True Measurement of Correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The American Journal of Psychology 18, 2 (1907), 161– 169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='jstor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='org/stable/1412408 [43] Marina Speranskaya, Martin Schmitt, and Benjamin Roth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Rank- ing vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Classifying: Measuring Knowledge Base Completion Quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Automated Knowledge Base Construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [44] Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie, and Jian Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Ro- tatE: Knowledge Graph Embedding by Relational Rotation in Complex Space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [45] Zhiqing Sun, Shikhar Vashishth, Soumya Sanyal, Partha Talukdar, and Yiming Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A Re-evaluation of Knowledge Graph Completion Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 5516–5522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [46] Pedro Tabacof and Luca Costabello.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Probability Calibration for Knowledge Graph Embedding Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International Conference on Learning Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [47] Sudhanshu Tiwari, Iti Bansal, and Carlos R Rivero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Revisiting the evaluation protocol of knowledge graph completion methods for link prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the Web Conference 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 809–820.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [48] Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, and Guillaume Bouchard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Complex embeddings for simple link prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PMLR, 2071–2080.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [49] Ke Tu, Jianxin Ma, Peng Cui, Jian Pei, and Wenwu Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Au- tone: Hyperparameter optimization for massive network embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 216–225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [50] Renata Turkeš, Guido Montúfar, and Nina Otter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' On the effec- tiveness of persistent homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 10551 [51] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Villani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Optimal transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 338 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [52] Haoyu Wang, Yaqing Wang, Defu Lian, and Jing Gao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A light- weight knowledge graph embedding framework for efficient inference and storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 30th ACM International Conference on Information & Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1909–1918.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [53] Kai Wang, Yu Liu, Qian Ma, and Quan Z Sheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Mulde: Multi- teacher knowledge distillation for low-dimensional knowledge graph embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the Web Conference 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 1716–1726.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [54] Kai Wang, Yu Liu, and Quan Z Sheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Swift and Sure: Hardness- aware Contrastive Learning for Low-dimensional Knowledge Graph Embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the ACM Web Conference 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 838–849.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [55] Quan Wang, Zhendong Mao, Bin Wang, and Li Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Knowledge graph embedding: A survey of approaches and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering 29, 12 (2017), 2724– 2743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [56] Xin Wang, Shuyi Fan, Kun Kuang, and Wenwu Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Explain- able automated graph representation learning with hyperparameter importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' PMLR, 10727–10737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [57] Zhen Wang, Jianwen Zhang, Jianlin Feng, and Zheng Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Knowledge graph embedding by translating on hyperplanes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Pro- ceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [58] Larry Wasserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Topological data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Annual Review of Statistics and Its Application 5 (2018), 501–532.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [59] Carole-Jean Wu, Ramya Raghavendra, Udit Gupta, Bilge Acun, New- sha Ardalani, Kiwan Maeng, Gloria Chang, Fiona Aga, Jinshi Huang, Charles Bai, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Sustainable ai: Environmental implications, challenges and opportunities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Proceedings of Machine Learning and Systems 4 (2022), 795–813.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [60] Bishan Yang, Wen-tau Yih, Xiaodong He, Jianfeng Gao, and Li Deng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Embedding Entities and Relations for Learning and Inference in Knowledge Bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In 3rd International Conference on Learning Repre- sentations, ICLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [61] Shih-Yuan Yu, Sujit Rokka Chhetri, Arquimedes Canedo, Palash Goyal, and Mohammad Abdullah Al Faruque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Pykg2vec: A Python Library for Knowledge Graph Embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 22 (2021), 16–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [62] Yufeng Zhang, Weiqing Wang, Wei Chen, Jiajie Xu, An Liu, and Lei Zhao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Meta-Learning Based Hyper-Relation Feature Modeling for Out-of-Knowledge-Base Embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' In Proceedings of the 30th ACM International Conference on Information & Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2637–2646.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [63] Yongqi Zhang, Zhanke Zhou, Quanming Yao, and Yong Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KG- Tuner: Efficient Hyper-parameter Search for Knowledge Graph Learn- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' CoRR abs/2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='02460 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' [64] Afra Zomorodian and Gunnar Carlsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Computing persistent homology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Discrete & Computational Geometry 33, 2 (2005), 249–274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 8 APPENDIX Figure 6: Study on the carbon footprint of the evaluation phase of the KGE methods on YAGO3-10 when using KP vs Hits@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The x-axis shows the the carbon footprint in g eq 𝐶𝑂2 in log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 7: Study on the carbon footprint of the evaluation phase of the KGE methods on Wikidata when using KP vs Hits@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The x-axis shows the the carbon footprint in g eq 𝐶𝑂2 in log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 Extended Evaluation Effect of KP on Efficient KGE Methods Evaluation: The re- search community has recently proposed several KGE methods to improve training efficiency [34, 52, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Our idea in this experi- ment is to perceive if efficient KGE methods improve their overall carbon footprint using KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For the same, we selected state-of-the- art efficient KGE methods: Procrustes [34] and HalE [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 8 illustrates that using KP for evaluation drastically reduces the carbon footprints of already efficient KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For instance, the carbon footprint of HalE is reduced from 110g (using hits@10) to 20g of CO2 (using KP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Carbon Footprint of the Evaluation phase of the KGE prototyping process (YAGO3_10) Carbon Footprint using Kp Carbon Footprint using ranking metrics TransE TransH TransR Method Complex RotatE ConvKB TuckER 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='5 L0Carbon Footprint of the Evaluation phase of the KGE prototyping process (Wikidata) Carbon Footprint using KP Carbon Footprint using ranking metrics TransE TransH TransR Method Complex RotatE ConvkB TuckER LOCan Persistent Homology provide an efficient alternative WWW ’23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' APRIL 30 - MAY 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 2023,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Texas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' USA Metrics FB15K FB15K237 WN18 WN18RR Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Conicity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='071 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='071 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='214 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='393 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='250 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='071 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='250 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='393 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='357 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 AVL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='214 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='250 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='179 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='393 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='250 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='886 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='886 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='886 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='771 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='886 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='464 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 Graph Kernel (Train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='536 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='357 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='964 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='393 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='929 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='357 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='571 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 Graph Kernel (Test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='893 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='464 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='657 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='657 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='657 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='657 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='393 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 KP (Train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='214 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='536 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='607 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='893 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='786 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='286 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 KP (Test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='964 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='536 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='821 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='857 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='750 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='857 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='829 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='943 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='286 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 Table 7: Spearman’s ranked correlation (𝜌) scores computed from the metric scores with respect to the ranking metrics on the standard KG embedding datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The KG methods are evaluated after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Metrics FB15K FB15K237 WN18 WN18RR Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Hits1(↑) Hits3(↑) Hits10(↑) MR(↓) MRR(↑) Conicity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 AVL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 Graph Kernel (Train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='905 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='810 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 Graph Kernel (Test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='810 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 KP (Train) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='048 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='467 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 KP (Test) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='905 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='619 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='867 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='238 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 Table 8: Kendall’s tau (𝜏) scores computed from the metric scores with respect to the ranking metrics on the standard KG embedding datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The KG methods are evaluated after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Figure 8: Study on efficient KGE methods and their the car- bon footprint on WN18RR when using KP vs Hits@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The x-axis shows the the carbon footprint in g eq 𝐶𝑂2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Robustness and Efficiency on large KGs: This ablation study aims to gauge the correlation behavior of KP and ranking metric on a large-scale KG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' For the experiment, we use Yago3-10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' A key reason to select the Yago-based dataset is that besides being large-scale, it has rich semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Results in Table 9 illustrate KP shows a stable and high correlation with the ranking metric, con- firming the robustness of KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We show carbon footprint results in Figure 6 for the yago dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Further we also study the efficiency of KP on the wikidata dataset in Figure 7 which reaffirms that KP maintains its efficiency on large scale datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Efficiency comparison of Sliced Wasserstein vs Wasserstein as distance metric in KP: In this study we empirically provide a rationale for using sliced wasserstein as a distance metric over the wasserstein distance in KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The results are in table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We see that KP using sliced wasserstein distance provides a significant computational advantage over wasserstein distance, while having a good performance as seen in the previous experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Thus we need an efficient approximation such as the sliced wasserstein distance as the distance metric in place of wasserstein distance in KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Metrics Hits@1(↑) Hits@3(↑) Hits@10(↑) MR(↓) MRR(↑) r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='657 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='594 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='414 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='920 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='572 𝜌 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='679 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='643 𝜏 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='524 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 Table 9: KP correlations on the YAGO dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Metrics KP(W) KP(SW) Speedup ↑ Dataset FB15K237 WN18RR FB15K237 WN18RR FB15K237 WN18RR split val + test val + test val + test val + test Avg Avg TransE 1136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='766 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='655 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='114 x 3540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 x 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='6 TransH 2943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='869 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='549 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='095 x 9278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='5 x 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='8 TransR 1734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='576 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='423 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='336 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='129 x 5168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 x 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='4 Complex 1054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='721 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='324 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='135 x 3255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 x 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 RotatE 865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='417 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='783 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='342 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='136 x 2531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 x 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='3 TuckER 1021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='649 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='840 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='316 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='098 x 3230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 x 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1 ConvKB 719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='310 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='154 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='132 x 1675.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='7 x 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='0 Table 10: Evaluation Metric Comparison wrt Computing Time (in minutes, for 100 epochs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Column 1 denotes popular KGE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Depicted values denote evalua- tion(validation+test) time for computing a metric and cor- responding speedup using KP(𝑆𝑊 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP(𝑆𝑊 ) with sliced wasserstein as the distance metric significantly reduces the evaluation time (green) in comparison with KP(𝑊 ) which uses the wasserstein distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 Theoretical Proof Sketches We work under the following considerations: As the KGE method converges the mean statistic(𝑚𝜈) of the scores of the positive triples consistently lies on one side of the half plane formed by the mean statistic(𝑚𝜇) of the negative triples, irrespective of the data distri- bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' The detail proofs are here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP has a monotone increasing correspondence with the Proxy of the Expected Ranking Metrics(PERM) under the above stated considerations as 𝑚𝜈 deviates from 𝑚𝜇 Carbon Footprint of the Overall KGE prototyping process using methods that save on training time(WN18RR) Carbon Footprint using KP Carbon Footprint using ranking metrics HaLE Method ProcrustEs 0 25 50 75 100 125WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Bastos, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Proof Sketch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Considering the 0-dimensional PD as used by KP and a normal distribution for the edge weights (can be extended to other distributions using techniques like [39]) of the graph(scores of the triples), we have univariate gaussian measures [40] 𝜇 and 𝜈 for the positive and negative distributions respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Denote by 𝑚𝜇 and 𝑚𝜈 the means of the distributions 𝜇 and 𝜈 respectively and by Σ𝜇, Σ𝜈 the respective covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝑊 2 2 (𝜇,𝜈) = ∥𝜇 − 𝜈∥2 + 𝐵(Σ𝜇, Σ𝜈)2 (2) where 𝐵(Σ𝜇, Σ𝜈)2 = 𝑡𝑟 (Σ𝜇 + Σ𝜈 − 2(Σ 1 2𝜇 Σ𝜈Σ 1 2𝜇 ) 1 2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Next we see how that changing the means of the distribution(and also variance) changes PERM and KP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' We can show that,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝑃 = ∫ 𝑥=∞ 𝑥=−∞ 𝐷+(𝑥) �∫ 𝑦=∞ 𝑦=𝑥 𝐷−(𝑥)𝑑𝑦 � 𝑑𝑥 𝜕𝑃 𝜕𝑚𝜈 = ∫ 𝑥=∞ 𝑥=−∞ 𝐷+(𝑥) �∫ 𝑦=∞ 𝑦=𝑥 𝜕𝐷−(𝑥) 𝜕𝑚𝜈 𝑑𝑦 � 𝑑𝑥 ≥ 0 𝜕𝑃 𝜕Σ𝜈 = ∫ 𝑥=∞ 𝑥=−∞ 𝐷+(𝑥) �∫ 𝑦=∞ 𝑦=𝑥 𝜕𝐷−(𝑦) 𝜕Σ𝜈 𝑑𝑦 � 𝑑𝑥 ≤ 0 𝜕𝑃 𝜕Σ𝜇 = ∫ 𝑥=∞ 𝑥=−∞ 𝜕𝐷+(𝑥) 𝜕Σ𝜈 �∫ 𝑦=∞ 𝑦=𝑥 𝐷−(𝑦)𝑑𝑦 � 𝑑𝑥 Since KP is the (sliced) wasserstein distance between PDs we can show the respective gradients are as below,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝜕𝑊 2 2 (𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝜈) 𝜕𝑚𝜈 = 2|𝑚𝜇 − 𝑚𝜈 | ≥ 0 𝜕𝑊 2 2 (𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝜈) 𝜕Σ𝜈 = 𝐼 − Σ 1 2𝜇 (Σ 1 2𝜇 Σ𝜈Σ 1 2𝜇 ) −1 2 Σ 1 2𝜇 As the generating process of the scores changes the gradient of PERM along the direction (𝑑𝑚𝜈,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎𝜈) can be shown to be the following � (𝑑𝑚𝜈,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' � 𝜕𝑃𝐸𝑅𝑀 𝜕𝑚𝜈 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝜕𝑃𝐸𝑅𝑀 𝜕Σ𝜇 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝜕𝑃𝐸𝑅𝑀 𝜕Σ𝜈 �� ≥ 0 Similarly the gradient of KP along the direction (𝑑𝑚𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎𝜈) is � (𝑑𝑚𝜈,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑑𝜎),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' ( 𝜕𝑊 2 2 (𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝜈) 𝜕𝑚𝜈 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝜕𝑊 2 2 (𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝜈) 𝜕Σ𝜇 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' 𝜕𝑊 2 2 (𝜇,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝜈) 𝜕Σ𝜈 ) � ≥ 0 Since both PERM and and KP vary in the same manner as the distribution changes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' the two have a one-one correspondence [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' □ The above lemma shows that there is a one-one correspondence between KP and PERM and by definition PERM has a one-one cor- respondence with the ranking metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Therefore, the next theorem follows as a natural consequence Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' KP has a one-one correspondence with the Ranking Metrics under the above stated considerations Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Under the considerations of theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='1, the relative change in KP on addition of random noise to the scores is bounded by a function of the original and noise-induced covariance matrix as ΔK P K P ≤ 𝑚𝑎𝑥((1 − |Σ+1 𝜇1 Σ−1 𝜇2 | 3 2 ), (1 − |Σ+1 𝜈1 Σ−1 𝜈2 | 3 2 )), where Σ𝜇1 and Σ𝜈1 are the covariance matrices of the positive and negative triples’ scores respectively and Σ𝜇2 and Σ𝜈2 are that of the corrupted scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Proof Sketch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Consider a zero mean random noise to simulate the process of varying the distribution of the scores of the KGE method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Let 𝑚𝜇1 and 𝑚𝜈1 be the means of the positive and negative triples’ scores of the original method and Σ𝜇1, Σ𝜈1 be the respective covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Let 𝑚𝜇2 and 𝑚𝜈2 be the means of the positive and negative triples’ scores of the corrupted method and Σ𝜇2, Σ𝜈2 be the respective covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' Considering the kantorovich duality [51] and taking the difference between the two measures we have KP1 − KP2 = 𝑖𝑛𝑓 𝛾1∈Π(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦) ∫ 𝛾1 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦)𝑑𝛾1(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦) − 𝑖𝑛𝑓 𝛾2∈Π(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦) ∫ 𝛾2 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦)𝑑𝛾2(𝑥,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='𝑦) ≤ 𝑠𝑢𝑝 Φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='Ψ ∫ 𝑥 Φ(𝑥)𝑑𝜇1(𝑥) + ∫ 𝑦 Ψ(𝑦)𝑑𝜈1(𝑦) − ∫ 𝑥 Φ(𝑥)𝑑𝜇2(𝑥) − ∫ 𝑦 Ψ(𝑦)𝑑𝜈2(𝑦) ≤ 𝑠𝑢𝑝 Φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='Ψ ∫ 𝑥 Φ(𝑥)(𝑑𝜇1(𝑥) − 𝑑𝜇2(𝑥)) + ∫ 𝑦 Ψ(𝑦)(𝑑𝜈1(𝑦) − 𝑑𝜈2(𝑦)) Now by definition of the measure 𝜇1 we have 𝜕𝜇1 𝜕𝑥 = −𝜇1Σ−1 𝜇1 (𝑥 − 𝑚𝜇1) 𝑑𝜇1(𝑥𝑖) = −(𝜇1Σ−1 𝜇1 (𝑥 − 𝑚𝜇1))[𝑖]𝑑𝑥𝑖 ∴ 𝑑𝜇1(𝑥) = 𝑑𝑒𝑡(𝑑𝑖𝑎𝑔(−𝜇1Σ−1 𝜇1 (𝑥 − 𝑚𝜇1)))𝑑𝑥 From the above results we can show the following KP1 − KP2 ≤ 𝑚𝑎𝑥((1 − 𝑑𝑒𝑡(Σ𝜇1Σ−1 𝜇2 ) 𝑛 2 +1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' (1 − 𝑑𝑒𝑡(Σ𝜈1Σ−1 𝜈2 ) 𝑛 2 +1))KP1 ∴ ΔKP KP ≤ 𝑚𝑎𝑥 �� 1 − 𝑑𝑒𝑡(Σ𝜇1Σ−1 𝜇2 ) 𝑛 2 +1� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' � 1 − 𝑑𝑒𝑡(Σ𝜈1Σ−1 𝜈2 ) 𝑛 2 +1�� In our case as we work in the univariate setting 𝑛 = 1 and thus we have ΔK P K P ≤ 𝑚𝑎𝑥 �� 1 − 𝑑𝑒𝑡(Σ𝜇1Σ−1 𝜇2 ) 3 2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' � 1 − 𝑑𝑒𝑡(Σ𝜈1Σ−1 𝜈2 ) 3 2 �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content=' □ Can Persistent Homology provide an efficient alternative WWW ’23, APRIL 30 - MAY 4, 2023, Texas, USA Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'} +page_content='2 shows that as noise is induced gradually, the KP value changes in a bounded manner as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNFOT4oBgHgl3EQfyzQ_/content/2301.12929v1.pdf'}