Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck

Extended chain-of-thought (CoT) traces improve LLM reasoning but incur substantial computational and memory costs. While existing CoT compression methods mitigate this by condensing thought steps into compact representations via memory tokens and retaining only these representations at inference time, the loss of fine-grained information makes subsequent steps more error-prone. To alleviate this, we propose HybridThinker, where in addition to preserved these representations, thought steps are also temporarily retained to provide fine-grained details. However, we observe that naively keeping thought steps accessible to subsequent steps during training lets the model bypass memory tokens by retrieving information directly from these steps, leaving the model's ability to compress and retrieve information through memory tokens insufficiently trained. We therefore introduce a hybrid training scheme, in which only some thought steps are directly accessible through attention to subsequent steps, while the other thought steps are masked, forcing the model to use memory tokens for compression and retrieval. Across 4 reasoning benchmarks, HybridThinker matches the uncompressed baseline, advancing the state of the art in CoT compression by 5.8 points on average accuracy with similar inference time. Ablation studies confirm that both temporary thought-step retention and the hybrid training scheme contribute to these gains.

Large Reasoning Models (LRMs) excel on complex tasks through long chain-of-thought (CoT) reasoning, but their lengthy intermediate steps cause severe overthinking that inflates inference cost. KV-cache compression is a common solution, yet existing reasoning-oriented methods apply a uniform policy across the trajectory and judge compression only by what it removes from the cache. Two observations point the other way. First, a reasoning state's tolerance to context loss varies along the trajectory, and process reward tracks it: deleting tokens at high-reward steps preserves accuracy far better than deleting the same budget at random. Second, compression is not free on the generation side, since a smaller cache leads the model to generate more tokens, partly canceling the saving. Together these motivate coordinating both sides under a single process reward. We propose ReCo (Reward-Coordinated Compression), a step-wise framework in which a lightweight process-reward estimator scores each completed step and drives three components: (1) reward-adaptive KV-cache compression that shrinks the retained cache harder at high-reward steps and less at low-reward ones, (2) a reward-banded penalty on reflection tokens that curbs redundant generation, and (3) confidence-based early stopping that triggers when the reasoning is reliable. Across three reasoning models and six benchmarks, ReCo reduces generated tokens by 37%-65% and end-to-end latency by 2.08x-2.35x over Full CoT, all while largely preserving accuracy.

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.