思维认知循环：基于可逆层次马尔可夫链的高效数学推理
Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning
AI总结：
提出基于可逆层次马尔可夫链的思维认知循环框架，通过层次分解和反向验证机制减少冗余、增强推理鲁棒性，在数学推理任务上取得显著提升。
摘要：
多步思维链通过利用显式推理步骤显著提升了大型语言模型的数学推理能力。然而，长思维链的广泛采用往往导致序列长度超出可管理的计算限制。现有方法尝试通过类似马尔可夫链的结构减少KV缓存冗余来缓解这一问题，但引入了两个关键限制：固有的无记忆性（上下文丢失）和有限的反向推理能力。为了解决这些限制，我们提出了一种基于可逆层次马尔可夫链的新型思维链框架，称为思维认知循环，以及一个反向推理数据集CLoT-Instruct。在CLoT中，问题被分解为具有层次依赖关系的子问题。受人类认知过程的启发，我们在每个层次层引入反向验证机制。此外，我们实施了一种剪枝策略：一旦高层子问题得到验证，冗余的低层子问题就会被剪枝以最大化效率。这种方法有效缓解了错误传播并增强了推理鲁棒性。在四个数学基准上的实验证明了我们方法的有效性。值得注意的是，在使用GPT-4o-mini的AddSub数据集上，CLoT达到了99.0%的准确率，分别比传统思维链和思维链自洽性高出4.1%和2.9%。
英文摘要：
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.
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