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

ACL ARR 2026 January Submission2229 Authors

Keywords: Large Language Model, Mixture of Experts, LoRA, Fine-Tuning

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—where reasoning is revisited to verify conclusions—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. Our code is publicly available at: https://anonymous.4open.science/r/CLoT-7EBD.

Paper Type: Long

Research Area: Interpretability and Analysis of Models for NLP

Research Area Keywords: explanation faithfulness, knowledge tracing/discovering/inducing, free-text/natural language explanations

Contribution Types: Model analysis & interpretability

Languages Studied: English

Submission Number: 2229