arXiv:2606. 09059v1 Announce Type: cross Abstract: Two-stage post-training -- a Stage-1 warm-start (supervised fine-tuning, SFT, or on-policy distillation, OPD) followed by Stage-2 reinforcement learning (RL) -- is increasingly used for vision-language models (VLMs).
arXiv:2608. 09447v1 Announce Type: cross Abstract: On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation.
The paper investigates why reinforcement learning with verifiable rewards (RLVR) reduces the diversity of solutions in reasoning tasks. By analyzing the Countdown task, the authors show that RLVR contracts the solution space mainly at the entrance—before the first arithmetic operation—causing a 67% drop in solution coverage. They demonstrate that providing an unselected entrance prefix or applying entrance‑targeted interventions can restore or even improve coverage without harming accuracy.
The study measured the impact of a single training example on a GPT‑2 model by running 24 counterfactual experiments. 32 models were trained from scratch on OpenWebText, and at a specific training step a single batch row was replaced with a 194‑token passage under three conditions (fluent prose, fabricated subject, random characters) or left unchanged. Results showed that the passage was learned from one exposure and decayed, with measurable differences in cross‑entropy up to 50 steps after injection but no lasting effect at the final step.
The paper introduces Selective Supervision for Direct-OPD (S$^2$D-OPD), a refinement of Direct On-Policy Distillation that filters out states where the teacher’s policy change is minimal, as measured by the teacher‑reference Jensen‑Shannon divergence. By masking low‑divergence states and keeping only the top 10% of states per response, S$^2$D-OPD improves held‑out accuracy on AIME and HMMT benchmarks across multiple teacher‑student pairs without additional forward passes.
The paper introduces Circuit Reasoning Score (CRS), a data‑selection signal for reinforcement learning with verifiable rewards that uses attention‑head activity from a frozen base model to gauge reasoning engagement. CRS is computed in a single forward pass without reward labels or rollouts, and it shows that selecting problems with the lowest reasoning‑circuit engagement can outperform random selection on several medium‑difficulty benchmarks. However, the benefit depends on domain, model scale, and reward conditions, indicating that data selection in this setting is regime‑dependent rather than a fixed ranking of problem quality.
arXiv:2610.02391v1 Announce Type: new Abstract: When a large language model solves a mathematical problem, its reasoning is largely hierarchical, and the solution often branches at a few tokens where...
arXiv:2609.01274v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and sear...
The paper investigates why on‑policy distillation (OPD) can fail, observing that larger‑scale teachers often hit early loss plateaus while self‑RL teachers achieve much greater loss reductions. By modeling OPD as a continuous‑time dynamical system and analyzing training logs, the authors link plateaus to a rapid decline in a gradient‑based learning‑signal proxy, even though loss remains high. They also prove a local recovery guarantee for teachers close to the initial student and note that minimal parameter changes and high representation similarity suggest limited adaptation may cause learning‑signal collapse.
arXiv:2606. 11709v1 Announce Type: new Abstract: On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with the distribution it produces under privileged context, typically a verified solution.
arXiv:2609.37066v1 Announce Type: cross Abstract: Post-training is central to mathematical reasoning in modern large language models (LLMs), but endpoint pass@1 alone underidentifies what has changed...
The paper introduces On‑Policy Warmup (OPW), a teacher‑guided training stage where a student agent learns from a teacher on its own interaction trajectories before switching to reinforcement learning with verifiable rewards (RLVR). OPW differs from traditional imitation by focusing on states generated by the student’s own decisions, including imperfect actions and recovery situations. The authors provide a theoretical link between on‑policy reverse‑KL distillation and trajectory‑level distribution matching, showing that, under a competent teacher and low distillation loss, OPW can lower bound initial verifier success and reduce reward‑discovery complexity, thereby accelerating RLVR performance.
The study compares supervised fine-tuning (SFT) and reinforcement learning (RL) as teacher training methods for on-policy distillation (OPD) in a single-teacher setting. Using Qwen3.5-9B models across Agentic, Reasoning, and Perception domains, RL-trained teachers consistently produce stronger students and better recovery of performance gains than SFT-trained teachers. The authors attribute this advantage to RL teachers’ smaller parameter shifts from the shared initialization, which facilitates learning through OPD.