ReCal: Calibrating Structured Pruning for On-Policy Distillation Recovery

Large reasoning models (LRMs) generate long chain-of-thought traces before answering, creating significant inference overhead. Pruning can reduce this cost, but its effectiveness depends on the calibration data used to estimate parameter importance. Recent work calibrates on the model's own rollouts instead of generic dataset, but treats all reasoning tokens uniformly, regardless of whether they contribute to successful reasoning. As a result, pruning protects weights by statistical salience rather than by their contribution to correct reasoning, so weights behind erroneous computation survive as readily as those behind correct computation. These erroneous patterns then get carried into the pruned model, degrading reasoning quality, producing both lower accuracy and longer reasoning traces. We propose Outcome-Based Calibration for Large Reasoning Model Pruning (OBC-Prune) to close this gap. OBC first constructs difficulty-matched pairs of correct and incorrect rollouts from problems the model answers inconsistently. It then estimates the causal importance of each reasoning sentence through intervention-based analysis, quantifying how removing its influence affects subsequent predictions. These causal importance scores are converted into per-token weights that rescale the calibration activations used by one-shot pruning methods (SparseGPT, Wanda, ALPS), without modifying the underlying pruning algorithms. Experiments on DeepSeek-R1-Distill-Qwen 1.5B, 7B, and 14B models at 40% and 50% sparsity demonstrate consistent improvements over state-of-the-art calibration baselines across most model sizes and sparsity levels on MATH500, LiveCodeBench, and AIME 2025. These results indicate that preserving causally important reasoning circuits is a substantially more effective pruning objective than uniformly preserving observed activations.

On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD$^2$). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD$^2$ consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

Structured pruning is a hardware-friendly way to compress LLMs, but it is mostly validated on multiple-choice recognition tasks, while the same compressed checkpoints can collapse on the free-form generation that deployment actually requires. Two observations trace this gap. First, greedy \textsc{pass}@$1$ nearly vanishes after compression, yet \textsc{pass}@$k$ recovers substantially under repeated sampling: useful generations are demoted, not erased. Second, the recoverable regime fails mainly through suffix repetition. Recovery should therefore train on the compressed model's own on-policy states with dense token-level supervision, which On-Policy Distillation (OPD) provides by reusing the pre-compression model as a frozen teacher. However, long on-policy rollouts spend early recovery budget on low-information repetitive suffixes, delaying loss descent. To mitigate this waste, we propose \textbf{\shortopd}, a short-to-long OPD schedule that detects teacher-confirmed repetitive suffixes, treats the surviving prefix as each rollout's effective length, and allocates future rollout budgets to the effective lengths the policy can currently use. Across math, code, and open-ended generation, \shortopd\ raises the compressed model's score to about $9\times$ its unrecovered value and $1.6$--$4.4\times$ standard recovery recipes (SFT w/o KD, KD, and SeqKD), and it matches a fixed $8192$-token rollout horizon within two points using a quarter of the training time ($8.5$ vs.\ $35.9$ hours) and $71\%$ fewer rollout tokens. We hope this recipe helps move structured pruning beyond marginal gains on perplexity and multiple-choice benchmarks, a step closer to deployment-ready generation quality.