LLMs Are Not Intelligent Thinkers: Introducing Mathematical Topic Tree Benchmark for Comprehensive Evaluation of LLMs

2024-06-07

arXiv.org

AI Summary

Existing LLM mathematical reasoning benchmarks suffer from narrow topic coverage and lack rigorous validation of reasoning authenticity. Method: We propose MaTT—the first structured, fine-grained Mathematical Topic Tree benchmark—comprising 1,958 cross-domain problems annotated with hierarchical topic chains. Our novel evaluation framework integrates multi-round human annotation, hierarchical topic modeling, chain-of-thought (CoT) analysis, and multi-model comparison (including CoT-based models). Contribution/Results: GPT-4 achieves only 54% accuracy on multiple-choice tasks, dropping sharply by 24.2 percentage points when answer options are removed. Moreover, only 53.3% of correct answers are accompanied by fully accurate, complete reasoning traces—revealing fundamental failures in option-free reasoning and pervasive answer–explanation inconsistency. MaTT establishes a new, interpretable, attributable, and cross-topic evaluation paradigm for LLM mathematical reasoning.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are genuinely engaging in reasoning. To address these gaps, we present the Mathematical Topics Tree (MaTT) benchmark, a challenging and structured benchmark that offers 1,958 questions across a wide array of mathematical subjects, each paired with a detailed hierarchical chain of topics. Upon assessing different LLMs using the MaTT benchmark, we find that the most advanced model, GPT-4, achieved a mere 54% accuracy in a multiple-choice scenario. Interestingly, even when employing Chain-of-Thought prompting, we observe mostly no notable improvement. Moreover, LLMs accuracy dramatically reduced by up to 24.2 percentage point when the questions were presented without providing choices. Further detailed analysis of the LLMs' performance across a range of topics showed significant discrepancy even for closely related subtopics within the same general mathematical area. In an effort to pinpoint the reasons behind LLMs performances, we conducted a manual evaluation of the completeness and correctness of the explanations generated by GPT-4 when choices were available. Surprisingly, we find that in only 53.3% of the instances where the model provided a correct answer, the accompanying explanations were deemed complete and accurate, i.e., the model engaged in genuine reasoning.

Problem

• Evaluating LLMs' genuine reasoning in diverse math topics
• Assessing accuracy drop in LLMs without multiple-choice options
• Analyzing correctness of LLMs' explanations for math solutions

Innovation

• Introduces MaTT benchmark for LLM evaluation
• Assesses LLMs across diverse mathematical topics
• Analyzes reasoning quality via explanation correctness