Think Wider: Mitigating Latent Rank Collapse in Implicit Chain-of-Thought Reasoning

Implicit chain-of-thought (iCoT) methods aim to internalize reasoning in large language models, but often underperform explicit CoT prompting. We empirically find that hidden-state reasoning trajectories exhibit low-rank structure. Motivated by this observation, we propose a low-rank distillation framework that transfers reasoning by aligning teacher and student trajectories in a shared low-rank tensor subspace using first- and second-order statistics. The resulting formulation captures the global structure of reasoning while supporting a compact latent reasoning process. We evaluate the method across multiple model families, including LLaMA and Qwen, at different scales on mathematical reasoning benchmarks. Our approach consistently improves performance, especially on challenging multi-step tasks, approaching explicit CoT accuracy and outperforming prior iCoT distillation methods.

Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promising alternative, yet they often treat reasoning as uniformly compressible, causing precision-critical intermediate steps to be overly compressed and thereby degrading reasoning accuracy. In this work, we propose Selective Latent Thinking (SLT), a framework that selectively compresses redundant reasoning spans into latent representations while preserving precision-critical spans as explicit CoT within the same reasoning trajectory. Specifically, SLT first uses a lightweight decoder to anticipate a short upcoming reasoning span, and then applies confidence-based gating to determine the longest span that can be reliably compressed. The accepted span is encoded into a compact latent representation to improve reasoning efficiency, while uncertain or precision-critical reasoning remains in explicit CoT form to preserve accuracy. To learn this selective compression policy, SLT adopts a three-stage training strategy that combines span-level latent compression, reliability-aware future reasoning prediction, and trajectory-level reinforcement learning to optimize the trade-off between answer correctness and reasoning cost. Extensive experiments across four mathematical reasoning benchmarks demonstrate that SLT achieves 22.7% higher accuracy than latent reasoning baselines at comparable compression ratios, while reducing reasoning chain length by 58.4% with only 2.8% accuracy degradation compared to explicit CoT,Our code can be found in https://github.com/hunshi34/SLT.

Implicit Chain-of-Thought (CoT) reduces the inference cost of large language models by internalizing the explicit rationales. However, existing approaches typically lack alignment with explicit rationales and adaptivity to example complexity. In this work, we propose CIRF (\textit{\underline{C}hain-of-thoughts \underline{I}nto \underline{R}eusable \underline{F}unctional units}), an implicit CoT framework that performs reasoning as a dynamic sequence of discrete functional tokens. CIRF assigns a functional token to each semantically coherent reasoning unit in explicit CoT traces. The model is then fine-tuned to autoregressively generate functional tokens and their optional results, followed by the final answer. This design aligns latent reasoning with a sequence of functional units, facilitating parallel training, explicit rationale alignment, and adaptive reasoning. Extensive experiments on mathematical, symbolic, and commonsense reasoning benchmarks show that CIRF provides a favorable accuracy-latency trade-off compared with state-of-the-art implicit CoT methods. Further analyses demonstrate that CIRF constructs distinct, interpretable functional tokens, leading to consistent performance improvements.