Valid $\ne$ Necessary: Diagnosing Latent Inefficiency in Chain-of-Thought

• URL: http://arxiv.org/abs/2607.11266v1
• Date: Mon, 13 Jul 2026 08:50:26 GMT
• Title: Valid $\ne$ Necessary: Diagnosing Latent Inefficiency in Chain-of-Thought
• Abstract summary: Chain-of-Thought prompting incurs substantial computational costs due to over-reasoning.<n>We propose CAID, a training-free metric grounded in information theory that identifies low-utility steps.
• Score: 13.898770874357446
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Large Language Models (LLMs), yet it often incurs substantial computational costs due to over-reasoning: the generation of redundant, verbose, or irrelevant steps. While existing reasoning step evaluators effectively detect logical fallacies and factual errors, our analysis reveals a critical blind spot: they fail to penalize valid but inefficient reasoning steps that inflate token usage without contributing to the solution. To systematically diagnose this limitation, we introduce RIV-GSM8K, a diagnostic benchmark injected with five distinct types of inefficiencies, including circular reasoning and excessive decomposition. Diagnostic experiments reveal that state-of-the-art evaluators struggle to distinguish these inefficiencies from necessary reasoning. To address this gap, we propose CAID (Context-Aware Information Density), a training-free metric grounded in information theory that identifies low-utility steps. To validate the metric's practical utility, we apply it within PACE, a post-hoc compression strategy. Additional control experiments show that the gains of PACE are not explained by trivial pruning: compared with random step removal and PRM-based compression baselines, it preserves accuracy at substantially higher compression rates. Empirical results on GSM8K, StrategyQA, and ARC-Challenge demonstrate that PACE reduces token consumption by 31-53% while maintaining accuracy, confirming that CAID successfully distills informational froth from reasoning chains without compromising deductive validity.

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