Evaluating the Unseen Capabilities: How Many Theorems Do LLMs Know?

• URL: http://arxiv.org/abs/2506.02058v1
• Date: Sun, 01 Jun 2025 15:32:44 GMT
• Title: Evaluating the Unseen Capabilities: How Many Theorems Do LLMs Know?
• Authors: Xiang Li, Jiayi Xin, Qi Long, Weijie J. Su,
• Abstract summary: We introduce KnowSum, a statistical framework designed to provide a more comprehensive assessment by quantifying the unseen knowledge.<n>KnowSum estimates the unobserved portion by extrapolating from the appearance of frequencies of observed knowledge instances.<n>Our experiments reveal that a substantial volume of knowledge is omitted when relying solely on observed LLM performance.
• Score: 27.743708975564214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurate evaluation of large language models (LLMs) is crucial for understanding their capabilities and guiding their development. However, current evaluations often inconsistently reflect the actual capacities of these models. In this paper, we demonstrate that one of many contributing factors to this \textit{evaluation crisis} is the oversight of unseen knowledge -- information encoded by LLMs but not directly observed or not yet observed during evaluations. We introduce KnowSum, a statistical framework designed to provide a more comprehensive assessment by quantifying the unseen knowledge for a class of evaluation tasks. KnowSum estimates the unobserved portion by extrapolating from the appearance frequencies of observed knowledge instances. We demonstrate the effectiveness and utility of KnowSum across three critical applications: estimating total knowledge, evaluating information retrieval effectiveness, and measuring output diversity. Our experiments reveal that a substantial volume of knowledge is omitted when relying solely on observed LLM performance. Importantly, KnowSum yields significantly different comparative rankings for several common LLMs based on their internal knowledge.

Related papers

• Do LLMs Really Forget? Evaluating Unlearning with Knowledge Correlation and Confidence Awareness [44.37155305736321]
  Machine unlearning techniques aim to mitigate unintended memorization in large language models (LLMs)<n>We propose a knowledge unlearning evaluation framework that more accurately captures the implicit structure of real-world knowledge.<n>Our framework provides a more realistic and rigorous assessment of unlearning performance.
  arXiv  Detail & Related papers  (2025-06-06T04:35:19Z)
• Do Large Language Models Know How Much They Know? [18.566430365358556]
  Large Language Models (LLMs) have emerged as highly capable systems.<n>A desired attribute of an intelligent system is its ability to recognize the scope of its own knowledge.<n>This benchmark evaluates whether the models recall excessive, insufficient, or the precise amount of information.
  arXiv  Detail & Related papers  (2025-02-26T21:33:06Z)
• How Reliable are LLMs as Knowledge Bases? Re-thinking Facutality and Consistency [60.25969380388974]
  Large Language Models (LLMs) are increasingly explored as knowledge bases (KBs)<n>Current evaluation methods focus too narrowly on knowledge retention, overlooking other crucial criteria for reliable performance.<n>We propose new criteria and metrics to quantify factuality and consistency, leading to a final reliability score.
  arXiv  Detail & Related papers  (2024-07-18T15:20:18Z)
• What Matters in Memorizing and Recalling Facts? Multifaceted Benchmarks for Knowledge Probing in Language Models [15.057992220389604]
  Language models often struggle with handling factual knowledge, exhibiting factual hallucination issue. We introduce a knowledge probing benchmark, BELIEF(ICL), to evaluate the knowledge recall ability of both encoder- and decoder-based pre-trained language models. We semi-automatically create MyriadLAMA, which has massively diverse prompts.
  arXiv  Detail & Related papers  (2024-06-18T05:11:35Z)
• TrustScore: Reference-Free Evaluation of LLM Response Trustworthiness [58.721012475577716]
  Large Language Models (LLMs) have demonstrated impressive capabilities across various domains, prompting a surge in their practical applications. This paper introduces TrustScore, a framework based on the concept of Behavioral Consistency, which evaluates whether an LLMs response aligns with its intrinsic knowledge.
  arXiv  Detail & Related papers  (2024-02-19T21:12:14Z)
• EpiK-Eval: Evaluation for Language Models as Epistemic Models [16.485951373967502]
  We introduce EpiK-Eval, a novel question-answering benchmark tailored to evaluate LLMs' proficiency in formulating a coherent and consistent knowledge representation from segmented narratives. We argue that these shortcomings stem from the intrinsic nature of prevailing training objectives. The findings from this study offer insights for developing more robust and reliable LLMs.
  arXiv  Detail & Related papers  (2023-10-23T21:15:54Z)
• Exploring the Cognitive Knowledge Structure of Large Language Models: An Educational Diagnostic Assessment Approach [50.125704610228254]
  Large Language Models (LLMs) have not only exhibited exceptional performance across various tasks, but also demonstrated sparks of intelligence. Recent studies have focused on assessing their capabilities on human exams and revealed their impressive competence in different domains. We conduct an evaluation using MoocRadar, a meticulously annotated human test dataset based on Bloom taxonomy.
  arXiv  Detail & Related papers  (2023-10-12T09:55:45Z)
• Beyond Factuality: A Comprehensive Evaluation of Large Language Models as Knowledge Generators [78.63553017938911]
  Large language models (LLMs) outperform information retrieval techniques for downstream knowledge-intensive tasks. However, community concerns abound regarding the factuality and potential implications of using this uncensored knowledge. We introduce CONNER, designed to evaluate generated knowledge from six important perspectives.
  arXiv  Detail & Related papers  (2023-10-11T08:22:37Z)
• A Survey on Evaluation of Large Language Models [87.60417393701331]
  Large language models (LLMs) are gaining increasing popularity in both academia and industry. This paper focuses on three key dimensions: what to evaluate, where to evaluate, and how to evaluate.
  arXiv  Detail & Related papers  (2023-07-06T16:28:35Z)
• KoLA: Carefully Benchmarking World Knowledge of Large Language Models [87.96683299084788]
  We construct a Knowledge-oriented LLM Assessment benchmark (KoLA) We mimic human cognition to form a four-level taxonomy of knowledge-related abilities, covering $19$ tasks. We use both Wikipedia, a corpus prevalently pre-trained by LLMs, along with continuously collected emerging corpora, to evaluate the capacity to handle unseen data and evolving knowledge.
  arXiv  Detail & Related papers  (2023-06-15T17:20:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.