Learning to Reason Efficiently with Interventional Step Credit

Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping methods offer limited control over how reasoning effort is allocated across tokens. To bridge the gap, we propose IAPO, an information-theoretic post-training framework that assigns token-wise advantages based on each token's conditional mutual information (MI) with the final answer. This yields an explicit, principled mechanism for identifying informative reasoning steps and suppressing low-utility exploration. We provide a theoretical analysis showing that our IAPO can induce monotonic reductions in reasoning verbosity without harming correctness. Empirically, IAPO consistently improves reasoning accuracy while reducing reasoning length by up to 36%, outperforming existing token-efficient RL methods across various reasoning datasets. Extensive empirical evaluations demonstrate that information-aware advantage shaping is a powerful and general direction for token-efficient post-training. The code is available at https://github.com/YinhanHe123/IAPO.