Benchmarking Abstract and Reasoning Abilities Through A Theoretical Perspective

• URL: http://arxiv.org/abs/2505.23833v1
• Date: Wed, 28 May 2025 09:02:45 GMT
• Title: Benchmarking Abstract and Reasoning Abilities Through A Theoretical Perspective
• Authors: Qingchuan Ma, Yuhang Wu, Xiawu Zheng, Rongrong Ji,
• Abstract summary: We develop a mathematic framework that defines abstract reasoning as the ability to extract essential patterns.<n>We introduce two novel complementary metrics: (scoreGamma) measures basic reasoning accuracy, while (scoreDelta) quantifies a model's reliance on specific symbols.
• Score: 59.7140089198992
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines abstract reasoning as the ability to: (i) extract essential patterns independent of surface representations, and (ii) apply consistent rules to these abstract patterns. Based on this framework, we introduce two novel complementary metrics: \(\scoreGamma\) measures basic reasoning accuracy, while \(\scoreDelta\) quantifies a model's reliance on specific symbols rather than underlying patterns - a key indicator of true abstraction versus mere memorization. To implement this measurement, we design a benchmark: systematic symbol remapping in rule-based tasks, which forces models to demonstrate genuine pattern recognition beyond superficial token matching. Extensive LLM evaluations using this benchmark (commercial API models, 7B-70B, multi-agent) reveal:1) critical limitations in non-decimal arithmetic and symbolic reasoning; 2) persistent abstraction gaps despite chain-of-thought prompting; and 3) \(\scoreDelta\)'s effectiveness in robustly measuring memory dependence by quantifying performance degradation under symbol remapping, particularly highlighting operand-specific memorization. These findings underscore that current LLMs, despite domain-specific strengths, still lack robust abstract reasoning, highlighting key areas for future improvement.

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