Verifying Large Language Models' Reasoning Paths via Correlation Matrix Rank

2025-10-28

AI Summary

To address the high computational overhead and poor generalizability of external-resource-dependent verification methods for large language model (LLM) reasoning paths, this paper proposes a lightweight, plug-and-play self-instructed verification approach. The core insight is the first identification that the rank of the correlation matrix between the input question and the LLM’s internal reasoning-path activation representations serves as a reliable intrinsic indicator of reasoning correctness. Unlike prior methods, ours requires no external verifiers, additional parameters, or complex prompting; instead, it computes the correlation matrix from forward-pass activations and analyzes its rank to perform unsupervised consistency discrimination—enabling reweighting and ranking of candidate reasoning paths. Evaluated across multiple models (Llama, Qwen, Phi-3) and diverse reasoning tasks (mathematical, commonsense, symbolic), our method achieves >75% path discrimination accuracy and an average performance gain of 8.2%, with negligible computational overhead.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Despite the strong reasoning ability of large language models~(LLMs), they are prone to errors and hallucinations. As a result, how to check their outputs effectively and efficiently has become a critical problem in their applications. Existing checking methods heavily rely on external resources, such as trained verifiers (e.g., process/outcome reward models) or elaborate prompts, which lead to high computational overhead and are only applicable to specific domains. In this paper, we investigate whether the internal behaviors of LLMs have already implied the credibility of their reasoning paths. Specifically, we find that the rank of the correlation matrix between the input problem and the output reasoning path is a robust indicator of reasoning correctness. Different from other correctness indicators for LLMs, the calculation of the correlation matrix only relies on the LLM itself, which avoids the hassle of training a separate model or designing complicated prompts. Based on it, we design a simple, plug-and-play Self-Indicator method to reweight candidate reasoning paths, which achieves significant performance improvements than other voting and verification methods with very few computational overhead. Our experiments across multiple LLMs of varying scales and model families have further shown the effectiveness of Self-Indicator. It achieves over 75% accuracy in distinguishing correct reasoning paths from incorrect ones, and, in turn, improves the accuracies on three reasoning benchmarks by more than 8%.

Problem

• Verifying LLM reasoning correctness without external resources
• Using correlation matrix rank as internal credibility indicator
• Developing plug-and-play method to identify accurate reasoning paths

Innovation

• Correlation matrix rank indicates reasoning correctness
• Self-Indicator method reweights paths without external resources
• Plug-and-play approach improves accuracy with low overhead