CoT Compression

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.

Large reasoning models (LRMs) typically solve reasoning-intensive tasks by generating long chain-of-thought (CoT) traces, leading to substantial inference overhead. We identify a reproducible inference-time phenomenon, termed Self-Compression: when multiple independent and answerable questions are presented within a single prompt, the model spontaneously produces shorter reasoning traces for each question. This phenomenon arises from multi-question contextual pressure during generation and consistently manifests across models and benchmarks. Building on this observation, we propose ConPress (Learning from Contextual Pressure), a lightweight self-supervised fine-tuning approach. ConPress constructs multi-question prompts to induce self-compression, samples the resulting model outputs, and parses and filters per-question traces to obtain concise yet correct reasoning trajectories. These trajectories are directly used for supervised fine-tuning, internalizing compressed reasoning behavior in single-question settings without external teachers, manual pruning, or reinforcement learning. With only 8k fine-tuning examples, ConPress reduces reasoning token usage by 59% on MATH500 and 33% on AIME25, while maintaining competitive accuracy.

Long Chain-of-Thought (CoT) traces can improve reasoning accuracy, but repeatedly generating them is costly for smaller or latency-constrained language models. This paper studies a practical alternative: produce a rich rationale once with a capable \emph{thinking} model, compress it, and reuse the compressed trace as context for a cheaper \emph{answering} model. We introduce CoT-X, an adaptive framework for cross-model CoT transfer. CoT-X segments reasoning traces into semantic units, scores their diagnostic and logical importance, selects budget-feasible evidence paths, and reconstructs a coherent compressed rationale for the answering model. On $7,501$ Japanese medical licensing questions spanning $10$ specialties, CoT-X improves accuracy over direct truncation by up to $40.5\%$ under the same token budget, with the largest gains at $64$--$256$ tokens. Across $64$ thinking--answering pairs from eight DeepSeek-R1 and Qwen3 models (1.5B--32B parameters), reasoning transfer is most reliable within a model family, yet remains effective across families once compression normalizes the trace. A Gaussian Process Bayesian optimization layer finds near-optimal model--budget configurations with $15$ evaluations rather than an exhaustive search over all $64$ pairs, reducing evaluation cost by $84\%$. These results show that reasoning quality, token budget, and model compatibility can be optimized jointly, making CoT-style reasoning more practical under realistic deployment constraints.

Recent thinking models are capable of solving complex reasoning tasks by scaling test-time compute, but this scaling should be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient by generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under- and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention to identify key steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate a reasoning budget commensurate with example difficulty. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC generalizes well, with accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis shows that TRAAC learns to adjust its thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks.

Chain-of-Thought (CoT) prompting can substantially improve the reasoning ability of large language models (LLMs), but it often comes with high inference cost due to long and poorly controlled reasoning traces. This overhead is particularly problematic in software engineering tasks (e.g., code generation), where both latency and output reliability matter. To better understand this trade-off, we conduct an empirical study on widely used code generation benchmarks and observe that many modern reasoning models produce excessively verbose CoTs (often thousands of tokens), which frequently leads to truncation and unstable generation. Using a strict n-gram repetition detector, we find that most observed truncations are associated with degenerate looping behaviors. In addition, a HumanEval/129 case study shows that failed generations can be longer than successful ones, suggesting limited returns from overlong reasoning. Motivated by these findings, we propose SEER (Self-Enhancing Efficient Reasoning), a self-enhancing framework for adaptive CoT compression. SEER improves the conciseness of reasoning while preserving output quality, without relying on external compression tools. SEER refines self-generated CoT data via Best-of-N sampling to suppress looping and redundant traces, then applies a lightweight, data-driven filter to encourage concise yet correct reasoning. It then fine-tunes the model on the filtered data to internalize concise reasoning behaviors. Across four software engineering benchmarks on the evaluated DeepSeek-R1-Distill-Qwen-7B backbone, SEER reduces CoT length by 34.6% on average while improving task performance, with reduced truncation and fewer reasoning loops.

Large reasoning models (LRMs) often exhibit overthinking, producing verbose Chain-of-Thought (CoT) traces that increase inference cost and obscure the underlying reasoning process. Existing CoT compression methods mainly rely on global length rewards, which conflate necessary intermediate reasoning with redundant text and may therefore compromise reasoning fidelity. This paper revisits overthinking from a semantic-efficiency perspective and decomposes CoT redundancy into two distinct forms: internal redundancy, defined as informational stagnation before the first correct answer, and external redundancy, defined as superfluous continuation after the first correct answer. Based on this decomposition, we propose a dual-penalty reinforcement learning framework that separately optimizes reasoning progress and termination behavior. Specifically, a sliding-window semantic similarity metric penalizes low-progress reasoning segments, while a normalized external-redundancy metric discourages post-answer continuation. Experiments on GSM8K, MATH500, and AIME24 across different model scales show that our method reduces average reasoning length by 41.3% on the 1.5B model and 40.1% on the 7B model, while preserving competitive accuracy and achieving the best overall accuracy-efficiency score among evaluated baselines. The learned compression behavior further transfers to out-of-domain reasoning tasks, including GPQA and LiveCodeBench. More importantly, our analysis reveals a clear asymmetry between the two redundancy types: external redundancy can be largely removed with little performance loss, whereas internal redundancy compression follows a sensitive accuracy-efficiency trade-off. These results suggest that effective CoT compression should optimize semantic efficiency rather than sequence length alone, offering a principled route toward more concise, efficient, and interpretable LRMs.

Chain-of-Thought (CoT) prompting trades inference speed for reasoning accuracy. Existing compressors force a compromise as static gradient techniques treat tokens independently, severing sequential logic, while uncertainty-based pruning ignores the final answer. We introduce Adaptive GoGI-Skip, a framework that resolves this tension by non-linearly coupling Goal-Gradient Importance (GoGI) with Adaptive Dynamic Skipping (ADS). GoGI quantifies each token's functional contribution to answer correctness via gradient sensitivity. ADS leverages runtime entropy to dynamically modulate the GoGI threshold, preserving low-gradient tokens essential for structural coherence at high-uncertainty junctions. Trained on 7,472 MATH traces, our policy transfers zero-shot to AIME, GPQA, and GSM8K, reducing token volume by $>$45% and accelerating inference up to 2.0$\times$ without accuracy loss. These results suggest that thinking-optimal compression demands synergy between teleological goals and epistemic uncertainty.