Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning

TL;DR

This paper introduces the Cognitive Loop of Thought (CLoT), a hierarchical reversible Markov chain framework that improves mathematical reasoning in large language models by enabling backward verification and efficient problem decomposition.

Contribution

The paper proposes a novel hierarchical reversible Markov chain model with backward reasoning and pruning, addressing memory and context limitations in multi-step reasoning.

Findings

CLoT achieves 99.0% accuracy on AddSub with GPT-4o-mini.

Outperforms traditional CoT and CoT-SC by 4.1% and 2.9%.

Enhances reasoning robustness and efficiency through hierarchical decomposition.

Abstract

Multi-step Chain-of-Thought (CoT) has significantly advanced the mathematical reasoning capabilities of LLMs by leveraging explicit reasoning steps. However, the widespread adoption of Long CoT often results in sequence lengths that exceed manageable computational limits. While existing approaches attempt to alleviate this by reducing KV Cache redundancy via Markov chain-like structures, they introduce two critical limitations: inherent memorylessness (loss of context) and limited backward reasoning capability. To address these limitations, we propose a novel Chain-of-Thought framework based on Reversible Hierarchical Markov Chain, termed Cognitive Loop of Thought (CLoT), and a backward reasoning dataset CLoT-Instruct. In CLoT, problems are decomposed into sub-problems with hierarchical dependencies. Inspired by human cognitive processes, we introduce a backward verification mechanism at each hierarchical layer. Furthermore, we implement a pruning strategy: once higher-level sub-problems are verified, redundant lower-level sub-problems are pruned to maximize efficiency. This approach effectively mitigates error propagation and enhances reasoning robustness. Experiments on four mathematical benchmarks demonstrate the effectiveness of our method. Notably, on the AddSub dataset using GPT-4o-mini, CLoT achieves 99.0% accuracy, outperforming traditional CoT and CoT-SC by 4.1% and 2.9%, respectively.