Aha-Flow Distillation: Flow Markers Matter in LLM Reasoning

Improving large language model (LLM) reasoning requires supervision that is both aligned with the model's own test-time states and informative at the token level. Reinforcement learning with verifiable rewards provides on-policy exploration but offers sparse, high-variance credit; supervised fine-tuning and distillation provide dense targets but often train on fixed trajectories or rely on stronger teachers. Recent privileged on-policy self-distillation explores a middle ground by scoring student rollouts with the same model under verified solution context. We revisit this setting through a contextual re-scoring lens: for reasoning, the important choices are not only whether privileged context is available, but how much of it should be revealed and where its distribution should shape the student. We propose PAINT (Partial-solution Adaptive INterpolated Training), which masks the verified solution according to rollout-reference overlap and applies a small energy-space interpolation on a sparse set of entropy-mismatch token positions. Across competition-level math benchmarks, PAINT consistently improves over a strong prior on-policy self-distillation baseline at all three Qwen3 scales. On Qwen3-8B, it raises macro Avg@12 by 2.1 points over this prior baseline and 2.9 points over GRPO.

Large language models often improve on difficult tasks by spending inference-time compute on a reasoning trace before producing the final answer. That extra computation can be useful, but it also raises latency, token cost, and deployment complexity. We introduce ThinkSwitch, a low-compute procedure for co-training paired instruct and thinking checkpoints. Starting from compatible Qwen3-4B instruct and thinking models, each iteration asks the thinking checkpoint to generate answers, removes the reasoning trace, distills the answer-only pairs into the instruct checkpoint with QLoRA, and reconstructs a thinking checkpoint with spherical weight interpolation. The only human-supplied inputs are task prompts; the labels are generated by the model itself. On a 30-question AIME 2026 evaluation, ThinkSwitch improves the instruct checkpoint from 10/30 to 20/30 and the thinking checkpoint from 14/30 to 22/30. On a 30-question PubMedQA subset, it improves the instruct checkpoint from 13/30 to 18/30 and the thinking checkpoint from 18/30 to 25/30. The complete experiment uses 15 training prompts per domain and costs $2.86 on a single cloud RTX 3070. The results are small-scale, but they indicate that targeted distillation loops can move part of the benefit of explicit reasoning into weights while preserving a separate thinking mode.

On-policy self-distillation (OPSD) has emerged as a promising paradigm for improving LLM reasoning, where a privileged teacher with access to reference solutions provides token-level supervision on the student's own generated trajectories. However, we find that OPSD consistently fails on long chain-of-thought (long-CoT) reasoning models, yielding at best marginal gains while destabilizing the reflective reasoning capability these models depend on. Through a novel decomposition of the teacher's supervision signal, we identify the root cause: the teacher's supervision is dominated by a reference-induced component that drives rote memorization of reference-specific shortcuts, while the question-conditioned, inference-transferable component is ignored or actively opposed. Based on this diagnosis, we propose a two-step solution. First, we construct a reference-only teacher (the same model conditioned on the reference without the question) to isolate the non-transferable component of the supervision signal; the residual after subtracting this component captures the question-conditioned, inference-transferable correction. Second, we use pointwise mutual information (PMI) as the mechanism to transform this residual into a well-formed PMI target distribution that the student can directly distill from, filtering out the reference-induced shortcut. Experiments on four long-CoT models across two datasets demonstrate consistent improvements over both the base model and standard OPSD, while preserving the models' natural epistemic behavior throughout training.