Daily Papers

On-policy distillation (OPD) has been widely studied as a post-training method in which a student model obtains token-level supervision from a stronger teacher on its own rollouts. Recent studies have improved OPD through alternative distillation reward formulations and teacher configurations, while the objective of distillation remains centered on mimicking the teacher. However, when a stronger teacher has limited distributional overlap with the student, such positive guidance can provide insufficient learning signals. In this work, we introduce Negative-Policy OPD (NP-OPD), which complements teacher supervision with rollouts from a lower-performing, lower-capability negative policy that serves as a negative reference for the student. Rather than modifying the distillation reward formulation, NP-OPD introduces the negative policy at the rollout stage, continuously supplying tokens preferred by the negative policy over the teacher so that they remain exposed to teacher supervision throughout training. This provides an explicit negative signal through negative-policy rollouts while preserving the positive teacher supervision used in OPD. Through extensive experiments, we show that NP-OPD improves OPD across model scales, generation modes, reasoning domains, and different OPD variants. Furthermore, our analyses show that NP-OPD effectively suppresses tokens preferred by the negative policy over the teacher and moves the student away from the negative policy. These results support our design of introducing negative signals through negative-policy rollouts and provide new insight into the role of the rollout policy in OPD. Code will be available at https://github.com/naver-ai/np-opd.

Recent reinforcement learning methods for diffusion large language models (dLLMs) commonly rely on on-policy rollouts generated by the target dLLM itself. When successful on-policy rollouts are scarce, however, on-policy training may receive little positive reward and make only limited progress. To mitigate this problem, we explore incorporating higher-reward rollouts generated by a stronger external policy alongside on-policy rollouts from the target dLLM. However, directly incorporating these external rollouts introduces two practical challenges: differences in rollout length and instability when jointly processing rewards from on-policy and external rollouts. To address these challenges, we propose External Rollout Integration with Length Control and Source-Specific Processing (ERILS), which controls external-rollout length and processes the rewards of on-policy and external rollouts separately. Experiments on Sudoku, Countdown, and MATH500 under zero-shot evaluation show that ERILS improves multi-sample performance across all three tasks, with the largest gains on Sudoku. On Sudoku, ERILS achieves 98.4% best-of-4 completion accuracy, compared with 40.3% for the strongest baseline. ERILS also maintains approximately 90% deterministic single-completion accuracy on Sudoku across generation lengths of 128, 256, and 512 tokens. Our component analysis further shows that length-controlled external rollouts are more effective than uncontrolled external rollouts, and that source-specific reward processing avoids the training collapse observed with joint reward processing. These results show that rollout construction and reward processing are important design dimensions when integrating external rollouts into dLLM reinforcement learning.

In on-policy distillation (OPD), the student determines which states receive teacher supervision. As its policy evolves, earlier response prefixes become less likely even though teacher-student disagreement on them persists. Under matched trajectory and optimization budgets, neither more queries nor more frequent rollout resampling is uniformly beneficial. Current-policy rollouts outperform initial-policy rollouts at shorter response budgets, but this ranking reverses at longer budgets. Replaying initial-policy rollouts after current-policy training improves accuracy, whereas replaying fixed recent rollouts does not reproduce the gain. We propose R-OPD, a gradient-triggered curriculum that adaptively selects when to revisit initial-student trajectories. When changes in mean gradients fall within minibatch-level variation for two consecutive comparisons, training switches from the next iteration onward to initial-policy replay. Across eight mathematics benchmarks and three training-data orders, R-OPD improves average accuracy over continued current-policy sampling by 2.25/4.44 percentage points at 16K/32K for a 0.6B student and 2.81/6.15 points for a 1.7B student. With a 30B-A3B teacher, it improves 8B accuracy by 4.05 points at 32K. At 32K, R-OPD exceeds a fixed schedule of 40 current-policy updates followed by 20 replay updates by 1.39/1.66/1.85 points for 0.6B/1.7B/8B. At the same generation cap, R-OPD also produces longer responses, suggesting that well-timed revisits help students use more of their reasoning capacity.

Multimodal Large Language Models (MLLMs) still struggle with fine-grained visual understanding, where answers often depend on small but decisive evidence in the full image. We observe a regional-to-global perception gap: the same MLLM answers fine-grained questions more accurately when conditioned on evidence-centered crops than on the corresponding full images, suggesting that many failures stem from difficulty to focus on relevant evidence rather than insufficient local recognition ability. Motivated by this observation, we propose Vision-OPD (Vision On-Policy Distillation), a regional-to-global self-distillation framework that transfers the model's own privileged regional perception to its full-image policy. Vision-OPD instantiates two conditional policies from the same MLLM: a crop-conditioned teacher and a full-image-conditioned student. The student generates on-policy rollouts, and Vision-OPD minimizes token-level divergence between the teacher and student next-token distributions along these rollouts. This enables the model to internalize the benefit of visual zooming without external teacher models, ground-truth labels, reward verifiers, or inference-time tool use. Experiments on multiple fine-grained visual understanding benchmarks show that Vision-OPD models achieve competitive or superior performance against much larger open-source, closed-source, and "Thinking-with-Images" agentic models.

On-policy learning has been argued to reduce catastrophic forgetting, produce sparser parameter updates, and improve generalisation. However, existing comparisons between supervised fine-tuning and reinforcement learning vary many factors simultaneously, making the contribution of rollout policy difficult to isolate. We study the effect of rollout policy in a controlled strong-to-weak distillation setting, by independently varying rollout policy, token-level KL direction, and learning rate across the Llama3 and Qwen2.5 model families and reasoning tasks spanning scientific, medical, and arithmetic domains. Our analysis reveals a nuanced picture of distillation dynamics in which rollout policy does not necessarily play a central role. Instead, token-level KL direction more clearly shapes task performance and output coverage, while learning rate governs forgetting and update sparsity. Analysis of KL gradients and experiments along a continuous student-teacher rollout-policy spectrum explain this pattern: forward KL is remarkably robust to rollout policy, with its performance stable and strong despite changes to the rollout policy, whereas reverse KL is substantially more sensitive and favours student-generated rollouts. On-policy data nevertheless improves generalisation to harder variants of the Countdown arithmetic task under both KL directions, although this advantage does not reliably persist after subsequent RLVR. Our broader conclusions remain robust to removing gradient clipping, using sampled KL estimators, and training on tasks requiring longer reasoning chains. Overall, our results challenge the view that on-policy rollouts are inherently preferable and show that their value depends critically on the objective, evaluation setting, and optimisation hyperparameters.

While the shift from cascaded dialogue systems to end-to-end (E2E) speech Large Language Models (LLMs) improves latency and paralinguistic modeling, E2E models often exhibit a significant performance degradation compared to their text-based counterparts. The standard Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) training methods fail to close this gap. To address this, we propose X-OPD, a novel Cross-Modal On-Policy Distillation framework designed to systematically align the capabilities of Speech LLMs to their text-based counterparts. X-OPD enables the Speech LLM to explore its own distribution via on-policy rollouts, where a text-based teacher model evaluates these trajectories and provides token-level feedback, effectively distilling teacher's capabilities into student's multi-modal representations. Extensive experiments across multiple benchmarks demonstrate that X-OPD significantly narrows the gap in complex tasks while preserving the model's inherent capabilities.

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.

Reinforcement learning with verifiable rewards is typically performed on-policy, keeping training data close to the current policy but limiting learning to trajectories that the policy can discover itself. Off-policy methods such as supervised fine-tuning, on the other hand, can leverage external knowledge beyond the base model's capabilities, but may suffer from large distribution shift. The key challenge is thus to expand exploration without sacrificing learnability. In this work, we introduce Minimal Intervention Reinforcement Learning (MInTRL), which expands the exploration frontier through sparse, local interventions in otherwise on-policy rollouts. During generation, a judge-intervention policy periodically reviews the current policy's output, replaces erroneous suffixes with short corrections, and immediately returns control to the policy. During training, MInTRL adopts a sequence-level advantage-regression objective that eliminates the need for importance sampling. We show that sparse, local interventions can substantially improve coverage beyond finite-budget on-policy sampling while preserving the overall on-policy nature of the resulting trajectories. Across math and code benchmarks, MInTRL consistently outperforms standard on-policy and off-policy baselines. Ablations show that MInTRL remains effective with self-intervention and across different judge policies, while performance peaks at moderate intervention intensity, highlighting the importance of intervening minimally. These results establish minimal intervention as an effective paradigm for enhancing on-policy RL.

Off-policy and on-policy distillation have traditionally been formulated as separate paradigms, each favoring a different property of distillation trajectories. Teacher-generated (off-policy) traces are typically high-quality but lie far from the student's distribution, whereas student-generated (on-policy) rollouts are more learnable but often contain erroneous reasoning. We view these paradigms as the endpoints of a policy continuum and posit that a more effective rollout policy may lie in between. We introduce Interpolated Policy Distillation (IPD), which defines the next-token distribution at every decoding step as an explicit linear interpolation between the student and teacher distributions. The interpolation operates at the distribution level, token by token, and its coefficient provides direct control over the balance between trajectory quality and student learnability. Naively sampling from this policy would require sequentially querying the teacher at every token and is thus expensive. To make IPD practical, we accelerate it with a new speculative-decoding rule while exactly preserving the interpolated next-token distribution.At the trajectory level, the resulting rollouts naturally interleave student- and teacher-generated segments. Unlike recent heuristic segment-interleaving methods, however, this interleaving is induced by an exactly realized token-level interpolated policy rather than by hand-designed switching rules. Across text-only and multimodal reasoning benchmarks, IPD consistently outperforms both endpoint policies (SFT and OPD), their conventional two-stage combination (SFT-then-OPD), and recent heuristic segment-interleaving methods, demonstrating that token-level policy interpolation better balances trajectory quality and student learnability.

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 pass@1 nearly vanishes after compression, yet 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 \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 9times its unrecovered value and 1.6--4.4times 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.

Large reasoning models (LRMs) often suffer from overconfidence when expressing their uncertainty. Confidence-aware reinforcement learning (RL) offers a promising way to optimize calibration. However, it relies on on-policy rollouts and is thus constrained by the model's pre-RL confidence distribution, which we term confidence prior. In this work, we reveal that off-the-shelf LRMs exhibit a confidence prior heavily concentrated on a few high values, which persists throughout RL. Theoretically, we prove that this concentration suppresses policy gradient updates for rarely sampled confidence values and inflates the lower bound on expected Brier risk. To overcome this exploration bottleneck, we propose CalibSFT, a plug-and-play supervised fine-tuning stage that shapes a calibrated confidence prior with broad support before RL. For each question, CalibSFT constructs confidence targets combining its success rate with response-level correctness, which provably preserves proper-scoring optimality, and then balances training responses across the confidence spectrum to enable diverse confidence exploration during RL. To learn from incorrect responses without imitating their reasoning, CalibSFT introduces correctness-conditional supervision, guiding confidence across all responses while supervising reasoning only on correct ones. Across 16 mathematical and general reasoning benchmarks, incorporating CalibSFT reduces calibration errors and improves discrimination across five representative RL algorithms while preserving comparable accuracy. Furthermore, CalibSFT delivers practical benefits for downstream selective prediction and model routing. Our code is available at https://github.com/ml-stat-Sustech/verbalized-confidence-training.

Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning (RL) with simple rule-based rewards. However, existing zero-RL approaches are inherently ``on-policy'', limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. We introduce LUFFY (Learning to reason Under oFF-policY guidance), a framework that augments zero-RL with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Notably, we propose policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Remarkably, LUFFY achieves an over +7.0 average gain across six math benchmarks and an advantage of over +6.2 points in out-of-distribution tasks. It also substantially surpasses imitation-based supervised fine-tuning (SFT), particularly in generalization. Analysis shows LUFFY not only imitates effectively but also explores beyond demonstrations, offering a scalable path to train generalizable reasoning models with off-policy guidance.

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However, they exhibit limited exploration due to reliance on on-policy rollouts where confined to the current policy's distribution, resulting in narrow trajectory diversity. Recent approaches attempt to expand policy coverage by incorporating trajectories generated from stronger expert models, yet this reliance increases computational cost and such advaned models are often inaccessible. To address these issues, we propose In-Context Steered Policy Optimization (ICPO), a unified framework that leverages the inherent in-context learning capability of LRMs to provide expert guidance using existing datasets. ICPO introduces Mixed-Policy GRPO with Implicit Expert Forcing, which expands exploration beyond the current policy distribution without requiring advanced LRM trajectories. To further stabilize optimization, ICPO integrates Expert Region Reject Sampling to filter unreliable off-policy trajectories and Annealed Expert-Bonus Reward Shaping to balance early expert guidance with later autonomous improvement. Results demonstrate that ICPO consistently enhances reinforcement learning performance and training stability on mathematical reasoning benchmarks, revealing a scalable and effective RLVR paradigm for LRMs.

The evolution of Large Language Models (LLMs) has catalyzed a paradigm shift from superficial instruction following to rigorous long-horizon reasoning. While Group Relative Policy Optimization (GRPO) has emerged as a pivotal mechanism for eliciting such post-training reasoning capabilities due to its exceptional performance, it remains plagued by significant training instability and poor sample efficiency. We theoretically identify the root cause of these issues as the lack of distinctiveness within on-policy rollouts: for routine queries, highly homogeneous samples induce destructive gradient conflicts; whereas for hard queries, the scarcity of valid positive samples results in ineffective optimization. To bridge this gap, we propose Distinctiveness-aware Group Relative Policy Optimization (DaGRPO). DaGRPO incorporates two core mechanisms: (1) Sequence-level Gradient Rectification, which utilizes fine-grained scoring to dynamically mask sample pairs with low distinctiveness, thereby eradicating gradient conflicts at the source; and (2) Off-policy Data Augmentation, which introduces high-quality anchors to recover training signals for challenging tasks. Extensive experiments across 9 mathematical reasoning and out-of-distribution (OOD) generalization benchmarks demonstrate that DaGRPO significantly surpasses existing SFT, GRPO, and hybrid baselines, achieving new state-of-the-art performance (e.g., a +4.7% average accuracy gain on math benchmarks). Furthermore, in-depth analysis confirms that DaGRPO effectively mitigates gradient explosion and accelerates the emergence of long-chain reasoning capabilities.

Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse reasoning paths. In this work, we introduce TreePO, involving a self-guided rollout algorithm that views sequence generation as a tree-structured searching process. Composed of dynamic tree sampling policy and fixed-length segment decoding, TreePO leverages local uncertainty to warrant additional branches. By amortizing computation across common prefixes and pruning low-value paths early, TreePO essentially reduces the per-update compute burden while preserving or enhancing exploration diversity. Key contributions include: (1) a segment-wise sampling algorithm that alleviates the KV cache burden through contiguous segments and spawns new branches along with an early-stop mechanism; (2) a tree-based segment-level advantage estimation that considers both global and local proximal policy optimization. and (3) analysis on the effectiveness of probability and quality-driven dynamic divergence and fallback strategy. We empirically validate the performance gain of TreePO on a set reasoning benchmarks and the efficiency saving of GPU hours from 22\% up to 43\% of the sampling design for the trained models, meanwhile showing up to 40\% reduction at trajectory-level and 35\% at token-level sampling compute for the existing models. While offering a free lunch of inference efficiency, TreePO reveals a practical path toward scaling RL-based post-training with fewer samples and less compute. Home page locates at https://m-a-p.ai/TreePO.

Self-reflection is a powerful mechanism for credit assignment in human learning, converting sparse outcome feedback into actionable guidance. However, its potential for post-training Large Language Models (LLMs) remains underexplored. We propose Self-Reflective Policy Optimization (SRPO), a framework that internalizes this capability. SRPO enables LLMs to analyze their own completed trajectories, synthesize errors into concise "reflection patches," and use reflection-conditioned teacher scores on student on-policy rollouts as dense token-level training signals. This process effectively transforms sparse terminal supervision into dense, token-level learning signals without requiring external critics, separate reward models, or larger teacher models. We demonstrate that SRPO achieves state-of-the-art performance across mathematical reasoning and long-horizon agentic benchmarks with exceptional data efficiency. Using a Qwen3-8B base model, SRPO attains 73.3% on AIME'24 using only 8% (0.08x) of the training FLOPs required by scaled supervised fine-tuning, while significantly improving success rates on WebShop (64.7%), ALFWorld (76.8%), and SWE-Bench-Lite (31.2%). Code is available at https://github.com/Galleons2029/SRPO

While reinforcement learning (RL) has empowered multi-turn reasoning agents with retrieval and tools, existing successes largely depend on extensive on-policy rollouts in high-cost, high-accuracy regimes. Under realistic resource constraints that cannot support large models or dense explorations, however, small language model agents fall into a low-cost, low-accuracy regime, where limited rollout budgets lead to sparse exploration, sparse credit assignment, and unstable training. In this work, we challenge this trade-off and show that small language models can achieve strong multi-hop reasoning under resource constraints. We introduce DAVID-GRPO, a budget-efficient RL framework that (i) stabilizes early learning with minimal supervision, (ii) assigns retrieval credit based on evidence recall, and (iii) improves exploration by resampling truncated near-miss trajectories. Evaluated on agents up to 1.5B parameters trained on only four RTX 3090 GPUs, DAVID-GRPO consistently outperforms prior RL methods designed for large-scale settings on six multi-hop QA benchmarks. These results show that with the right inductive biases, small agents can achieve low training cost with high accuracy.

While modern video generative models achieve remarkable visual fidelity, they remain noticeably brittle when generating physically plausible dynamics and complex interactions. Targeted post-training is crucial, yet supervised fine-tuning suffers from offline state mismatch, and reinforcement learning is hindered by sparse, ill-defined physical reward functions. On-Policy (Self-)Distillation (OPSD) reconciles on-policy rollouts with dense corrective feedback, shifting the core challenge to designing effective privileged context. However, conventional modalities fall short: text prompts are inherently declarative, whereas real reference videos heavily entangle physical laws with visual appearance without parametric control. To this end, we propose PhysOPSD, introducing executable code as privileged physical context for video generation. Unlike static visual observations, executable code instantiates an editable physical world with intrinsic abstraction and controllability. Powered by PhysOPSD-Engine, we translate real-world physical scenarios into verifiable simulation programs. PhysOPSD then incorporates (i) dual-level physical privilege to bridge the information gap via an intermediate bottleneck, alongside (ii) controlled physical variations under shared rollout noise to expose causal dynamic shifts. Extensive experiments demonstrate that PhysOPSD substantially improves physical plausibility across diverse backbones, outperforming SFT and RL baselines with only 3K samples, while preserving general video generation quality.

The development of autonomous web agents, powered by Large Language Models (LLMs) and reinforcement learning (RL), represents a significant step towards general-purpose AI assistants. However, training these agents is severely hampered by the challenges of interacting with the live internet, which is inefficient, costly, and fraught with risks. Model-based reinforcement learning (MBRL) offers a promising solution by learning a world model of the environment to enable simulated interaction. This paper introduces DynaWeb, a novel MBRL framework that trains web agents through interacting with a web world model trained to predict naturalistic web page representations given agent actions. This model serves as a synthetic web environment where an agent policy can dream by generating vast quantities of rollout action trajectories for efficient online reinforcement learning. Beyond free policy rollouts, DynaWeb incorporates real expert trajectories from training data, which are randomly interleaved with on-policy rollouts during training to improve stability and sample efficiency. Experiments conducted on the challenging WebArena and WebVoyager benchmarks demonstrate that DynaWeb consistently and significantly improves the performance of state-of-the-art open-source web agent models. Our findings establish the viability of training web agents through imagination, offering a scalable and efficient way to scale up online agentic RL.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

While Large Language Models (LLMs) excel at code generation by learning from vast code corpora, a fundamental semantic gap remains between their training on textual patterns and the goal of functional correctness, which is governed by formal execution semantics. Reinforcement Learning with Verifiable Rewards (RLVR) approaches attempt to bridge this gap using outcome rewards from executing test cases. However, solely relying on binary pass/fail signals is inefficient for establishing a well-aligned connection between the textual representation of code and its execution semantics, especially for subtle logical errors within the code. In this paper, we propose CodeRL+, a novel approach that integrates execution semantics alignment into the RLVR training pipeline for code generation. CodeRL+ enables the model to infer variable-level execution trajectory, providing a direct learning signal of execution semantics. CodeRL+ can construct execution semantics alignment directly using existing on-policy rollouts and integrates seamlessly with various RL algorithms. Extensive experiments demonstrate that CodeRL+ outperforms post-training baselines (including RLVR and Distillation), achieving a 4.6% average relative improvement in pass@1. CodeRL+ generalizes effectively to other coding tasks, yielding 15.5% and 4.4% higher accuracy on code-reasoning and test-output-generation benchmarks, respectively. CodeRL+ shows strong applicability across diverse RL algorithms and LLMs. Furthermore, probe analyses provide compelling evidence that CodeRL+ strengthens the alignment between code's textual representations and its underlying execution semantics.

We introduce Kwai Keye-VL-2.0-30B-A3B, an open-source Mixture-of-Experts (MoE) multimodal foundation model designed to advance long-video understanding and agentic intelligence. To address the challenges of ultra-long contexts, information redundancy, and prohibitive computational costs inherent in hour-level videos, Keye-VL-2.0 is the first to adapt DeepSeek Sparse Attention (DSA) to GQA-based multimodal architectures, enabling lossless 256K context processing while capturing critical frames and long-range temporal dependencies. This architecture is underpinned by a highly optimized training and inference infrastructure, including scalable video I/O, heterogeneous ViT-LM parallelism, and custom DSA kernels that significantly maximize throughput and minimize computational overhead. Furthermore, to overcome the algorithmic dilemma of catastrophic forgetting during multi-task alignment, we introduce Cross-Modal Multi-Teacher On-Policy Distillation (MOPD) paired with Context-RL and Video-RL. By distilling dense token-level teacher feedback from on-policy rollouts back into the MoE backbone, which activates only 3B parameters, Keye-VL-2.0 natively empowers advanced agent collaboration across Code, Tool, and Search scenarios with multimodal self-correction. Extensive evaluations across video understanding, temporal grounding, reasoning, STEM, and agent benchmarks demonstrate that Keye-VL-2.0-30B-A3B achieves state-of-the-art performance among models of similar scale, particularly excelling in fine-grained temporal localization on TimeLens and long-video comprehension on Video-MME-v2 and LongVideoBench. We release our model checkpoints to accelerate community progress toward scalable and robust multimodal agentic applications.

Scaling interactive and verifiable environments is critical for training terminal agents. As frontier models become more capable, environments synthesized from scratch become less challenging and thus provide limited learning signals. Recent co-evolution methods iteratively synthesize environments near the model's learnable frontier based on weaknesses exposed during rollouts. However, their dependence on on-policy rollouts limits generalization and the continuous provision of learning signals as the model becomes stronger. In this paper, we propose environment evolution, which incrementally increases environment difficulty off-policy and schedules the evolved environments generation by generation during training to provide continuous learning signals. We derive three evolution directions that influence environment difficulty from the multi-turn learning objective and then implement evolution along these directions through a loop-engineered multi-agent harness. Quantitative rollout experiments with Hy4 preview, Claude Opus 5, and GPT-5.6 Sol show that environment evolution consistently produces more difficult environments. We validate its effectiveness on Qwen3.6-27B and Qwen3.6-35B-A3B through simple long-horizon RL training, improving their performance by 14.4 and 18.0 percentage points on Terminal-Bench 2.1, respectively.

Self-Distillation Policy Optimization (SDPO) provides dense token-level credit assignment for reinforcement learning with large language models by leveraging the model's own feedback-conditioned predictions as a self-teacher. Unlike GRPO, however, whose group-relative advantage naturally concentrates learning on a sweet spot of intermediate-difficulty questions, SDPO's KL-based advantage lacks an implicit notion of difficulty awareness. We analyze this gap through the lens of GRPO's advantage normalization. Extending the learnability framework to normalized rewards, we show that normalization absorbs the variance term p(1-p), equalizing leading-order learnability across questions and leaving p(1-p) as the sole residual scaling factor in the per-question gradient. This analysis yields a simple prescription: weight each question's SDPO loss by [p(1-p)]^{1/2}, resulting in SC-SDPO, a scale-consistent variant of SDPO. The proposed weights are obtained as a zero-cost byproduct of on-policy rollouts with batch-adaptive normalization, inducing an implicit curriculum that dynamically tracks the model's evolving competence. Experiments on scientific reasoning and tool-use benchmarks demonstrate that SC-SDPO consistently improves over SDPO, yielding gains of +3.2/+4.3 (mean@16/maj@16) on Qwen3-8B and +1.8/+3.0 on OLMo-3-7B, while preserving stable training dynamics throughout optimization.

Post-training for long-horizon agentic tasks has a tension between compute efficiency and generalization. While supervised fine-tuning (SFT) is compute efficient, it often suffers from out-of-domain (OOD) degradation. Conversely, end-to-end reinforcement learning (E2E RL) preserves OOD capabilities, but incurs high compute costs due to many turns of on-policy rollout. We introduce PivotRL, a novel framework that operates on existing SFT trajectories to combine the compute efficiency of SFT with the OOD accuracy of E2E RL. PivotRL relies on two key mechanisms: first, it executes local, on-policy rollouts and filters for pivots: informative intermediate turns where sampled actions exhibit high variance in outcomes; second, it utilizes rewards for functional-equivalent actions rather than demanding strict string matching with the SFT data demonstration. We theoretically show that these mechanisms incentivize strong learning signals with high natural gradient norm, while maximally preserving policy probability ordering on actions unrelated to training tasks. In comparison to standard SFT on identical data, we demonstrate that PivotRL achieves +4.17% higher in-domain accuracy on average across four agentic domains, and +10.04% higher OOD accuracy in non-agentic tasks. Notably, on agentic coding tasks, PivotRL achieves competitive accuracy with E2E RL with 4x fewer rollout turns. PivotRL is adopted by NVIDIA's Nemotron-3-Super-120B-A12B, acting as the workhorse in production-scale agentic post-training.

Real-world post-training of generalist robot policies faces two challenges: partial observability makes action selection ambiguous, while offline post-training methods delay feedback from deployment experience. We present Value as Memory (VaM), a framework that addresses these challenges through value caching and online real-world reinforcement learning (RL). Value caching conditions actions on recent value predictions as task-progress memory, while online updates enable timely policy improvement by combining offline demonstrations, off-policy interventions, and on-policy rollouts for sample-efficient adaptation. As a result, VaM transitions from offline RL warmup to online autonomous learning with sparse rewards. Across long-horizon tasks involving deformable objects and contact-rich manipulation, VaM yields a mean absolute success-rate gain of 29.4% with value caching, while achieving a 32.8% gain with online autonomous learning over matched offline training. The evaluated online schedule performs 8times as many policy iterations under the same gradient-step budget, with more than 2times lower recorded time per gradient step with concurrent data collection and training.

Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-policy rollouts via counterfactual reasoning on different ways of satisfying the LTL specification. Our experiments, conducted in both discrete and continuous state-action spaces, confirm the effectiveness of our counterfactual experience replay approach.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

Long-horizon tool-using agents must reason over user goals, domain policies, tool calls, simulator state, and delayed verifiable rewards. Reinforcement learning (RL) is a natural fit for this setting, but multi-turn on-policy rollouts create long contexts, while model-specific attention layers may require custom masks and learned sink normalization. We present SINKFLEX-RL, a modular training system for RL in dual-control tool-use environments. The system combines a Gymnasium-compatible environment wrapper, a VERL-style rollout dataflow, group-relative policy optimization without a separate value model, and a sink-aware FlexAttention path designed to preserve model-specific sink scaling under causal and sliding-window masks. In a preliminary Tau2Bench retail run, validation reward (mean@1) rises from 0.25 early in training to 0.44 later in the observed training window, while training-score and trajectory-reward proxies also trend upward. In a fixed-configuration memory benchmark, the optimized attention path reduces peak VRAM from 28.06GB to 22.52GB at 4096 tokens, a 19.7% reduction, and runs the measured 8192-token configuration using 25.53~GB where the eager baseline runs out of memory. These results illustrate the value of integrating environment interfaces, RL dataflow, and attention-kernel design for memory-feasible long-horizon agent training.

We present Miles v0.1, a full-stack, production-ready system for frontier post-training. Building upon the clean design of slime, Miles designs each stage of the reinforcement-learning (RL) training loop around a single principle: components should be verified, clean, and customizable. With accuracy, efficiency, reliability, and scalability as first-class goals, Miles aims to make frontier-scale RL accessible to researchers and enterprises alike. This report walks through the system end to end: rollout engines built on SGLang, a trainer with a choice of two backends (NVIDIA Megatron-LM and PyTorch FSDP), and three weight-synchronization transports for different deployment topologies. Beyond full-parameter RL, Miles also supports LoRA RL, on-policy distillation, supervised fine-tuning, and true-on-policy rollout-training alignment, and extends the same architecture to diffusion models. We close with an end-to-end case study: fully asynchronous agentic RL on a GLM-5.2 744B-A40B model over terminal-use coding tasks, running on 64 NVIDIA GB300 GPUs with a median step time of 263 seconds over the first 30 measured steps. Miles is open-sourced at https://github.com/radixark/miles, with the project website at https://miles.radixark.com.

Training prompts in online reinforcement learning (RL) differ substantially in how informative they are for the current policy: some are already saturated while others are too difficult to yield reliable learning signals, yet both receive equal rollout budget under standard training. We propose an exploration-guided prompt scaffolding framework that adapts the training prompt distribution dynamically throughout RL post-training of multimodal large language models (MLLMs). Central to our approach is the Exploration Potential Score (EPS), a lightweight rollout-based proxy for prompt utility derived from KL-regularized policy improvement theory, computable directly from on-policy rollout statistics without additional overhead. Rather than discarding low-utility prompts, we use a teacher model to generate scaffolded rewrites that preserve the original task intent while making subsequent training more informative, reframing teacher supervision as training-data refinement rather than output imitation. Integrated with GRPO on Geo3K and MMK12, our method consistently outperforms the baseline on both in-domain and out-of-distribution benchmarks, achieving up to 9.7\% relative improvement in-domain and gains of 11.5\% on MathVision and 11.1\% on MMMU-Pro.

Long-horizon LM agents learn from multi-turn interaction, where a single early mistake can alter the subsequent state distribution and derail the whole trajectory. Existing recipes fall short in complementary ways: supervised fine-tuning provides dense teacher supervision but suffers from covariate shift because it is trained on off-policy teacher trajectories; while reinforcement learning with verifiable rewards avoids this off-policy mismatch by learning from on-policy rollouts but with only sparse outcome feedback. We address this dilemma by revisiting Dataset Aggregation (DAgger) for multi-turn LM agents: the algorithm collects trajectories through a turn-level interpolation of student and teacher policies, and the student is then trained on these trajectories using supervised labels provided by the teacher. By directly interacting with environments, we expose the model to realistic states likely to be encountered during deployment, thereby effectively mitigating covariate shift. Besides, since the student is learned by mimicking the teacher's behavior, it receives rich feedback during learning. To demonstrate DAgger enjoys the benefits of both worlds, we tested the algorithm to train a software-engineering agent with 4B- and 8B-scale student models. On SWE-bench Verified, our DAgger-style training improves over the strongest post-training baseline by +3.9 points at 4B and +3.6 points at 8B. The resulting 4B agent reaches 27.3%, outperforming representative published 8B SWE-agent systems, while the 8B agent achieves 29.8%, surpassing SWE-Gym-32B and coming within 5 points of stronger 32B-scale agents. Together with consistent gains on the held-out SWE-Gym split, these results suggest the effectiveness of DAgger for modern long-horizon LM agents.

Activation Oracles (AOs) are promising methods for interpreting residual stream activations. However, current AOs face important issues, such as hallucinations and vagueness. Additionally, text-inversion confounds make them hard to evaluate. To this end, we improve the Activation Oracle (AO) training regime in four ways: training on on-policy rollouts, improving the conversational dataset, feeding more layers and an improvement to the injection formula. The capability improvements are marginal, but quality of life improvements are quite substantial. In addition, we open source the first comprehensive evaluation suite for AO quality, which we call AObench. Overall, we hope that our work sets a foundation that helps improve AOs and other models in the paradigm of scalable, end-to-end interpretability.

Rubrics have emerged as an alternative to RLVR in open-ended domains where a single ground-truth final answer is not available. Existing rubric-based training methods rely on an LLM verifier that scores each rollout against rubrics. This introduces substantial training-time overhead, exposes optimization to verifier-specific biases, and reduces rubric feedback to a sparse end-of-trajectory signal. We propose Rubric-Guided Self-Distillation (RGSD), a verifier-free training method in which the base policy, conditioned on the rubric, serves as the teacher for the unconditioned student. RGSD distills the rubric-conditioned teacher distribution into the student token-by-token, replacing sparse trajectory-level rewards with dense per-token learning signals and removing the LLM judge from the training loop entirely. Across Qwen-2.5 (3B, 7B) and Qwen3-Thinking (4B, 8B) models on medical and science domains, RGSD achieves rubric satisfaction comparable to judge-based GRPO while using one on-policy rollout per prompt and no training-time verifier calls. Ablations show that raw rubrics provide a stronger teacher enrichment signal than self-generated reference responses, while a stronger GRPO judge can outperform RGSD in some settings, positioning RGSD as a complementary verifier-free alternative when verifier cost or reliability is the bottleneck.

Humanoid control requires natural whole-body coordination, precise real-time responses to control signals, and robust generalization across diverse environmental contexts, making it a cornerstone for generalist embodied agents. Behavior Foundation Models (BFMs) have recently emerged as a promising solution to address these challenges by leveraging large-scale behavioral data to achieve superior expressiveness, versatility and generalization. However, despite growing interest in scaling BFMs to further improve their capabilities, it remains unclear how key factors, including the learning paradigm, behavioral data and model architecture should be coordinated to enable effective scaling. In this work, we revisit the scaling recipe for BFMs and demonstrate that substantial performance gains can be achieved through the coordination of three core components: 1) the learning paradigm of motion tracking that reformulates diverse humanoid control problems as the reproduction of integrated whole-body behaviors in the global frame; 2) the strategic synergy between on-policy rollout quantity and reference motion diversity; and 3) the expressive and scalable model architecture termed Humanoid Transformer that facilitates the natural emergence of structured behavioral representations. Through extensive experiments in both simulation and real-world deployment, we demonstrate that our approach yields significant improvements in control fidelity and task generalization, reducing Mean Per-Keypoint Position Error (MPKPE) on the test set by over 10% in local mode and 82% in global mode compared with existing humanoid controllers. These results establish BFM as a principled and effective foundation for scalable and general-purpose humanoid control.

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

Reinforcement learning (RL) improves large language model (LLM) agents by teaching them which actions lead to high rewards, but provides little supervision on what those actions do to the environment. World modeling (WM) can fill this gap, yet existing approaches often require separate simulators, extra training stages, or additional inference-time computation. We observe that on-policy RL rollouts already contain the needed signal: each transition pairs an action with its resulting next observation. Based on this observation, we propose PaW, a Policy and World modeling co-training framework that adds auxiliary WM supervision to the same policy during RL, without changing the inference paradigm. To make auxiliary WM supervision informative and stable, PaW introduces three components: action-entropy-based WM data selection, noise-tolerant WM loss, and reward-adaptive loss balancing. Experiments on three agentic task benchmarks show consistent improvements over strong RL baselines across models and RL algorithms. These results suggest that standard RL rollouts are a practical source of WM supervision for language-agent training.

Reinforcement learning (RL) is a natural fit for agentic knowledge base question answering (KBQA), where a model must issue executable actions, observe knowledge-base feedback, and eventually return an answer. However, current RL-based KBQA systems mainly optimize sparse rewards from the final answer, leaving intermediate action errors weakly supervised. This is especially limiting for logical-form annotated KBQA benchmarks: gold logical forms can be converted into executable action sequences, but existing pipelines use them mainly for warm-start data construction rather than for on-policy RL updates. We propose GAPD, a training-time Gold-Action Policy Distillation framework that adds dense token-level guidance to outcome-based RL. To align gold actions with on-policy student rollouts, GAPD uses MID-ANCHOR MATCHING: it treats the intermediate entities reached during student exploration and gold execution as state anchors, and matches student states to gold states through these explored entity sets. The current policy conditioned on this aligned gold action serves as a stop-gradient teacher, whose token distribution is distilled back to the ordinary student policy over generated action-token spans. GAPD consistently surpasses the current state of the art on WebQSP, GrailQA, and GraphQ.

Deploying multimodal foundation models as closed-loop policies increasingly requires conditioning actions on observations that are no longer visible. However, existing benchmarks either expose the full state, conflate hidden-state reconstruction with other agent skills, or test recall only after an episode has ended. We introduce RNG-Bench (Reconstructive Non-Markov Games), a benchmark suite designed to isolate a base model's ability to reconstruct past observations and act on them during multi-step interaction. RNG-Bench includes two complementary games: Matching Pairs, where card identities briefly revealed at specific locations must later be recalled, and 3D Maze, where egocentric views must be integrated into a spatial map. Both games are evaluated under a unified harness with three controlled difficulty axes: grid size, visual pattern, and observation modality. The benchmark further introduces a head-to-head duel protocol to control for instance-level variance and a Memory Gap metric that disentangles forgetting from poor action selection. The hardest configurations require contexts of roughly 128K tokens and 350 image inputs per episode, and remain far from saturated by frontier MLLMs. Memory Gap analysis shows that most residual errors stem from forgetting earlier observations rather than from suboptimal decision making. Finally, fine-tuning Qwen3.5-9B on optimal-policy rollouts and filtered model demonstrations improves performance on RNG-Bench and transfers to existing benchmarks without degrading general multimodal capability.

Perceptive locomotion policies typically observe a dense robot-centric elevation map, although only the terrain beneath and around the next footsteps informs the control decision. Learned encoders compress the whole visual input, leaving the policy to work out which inputs matter while learning the baseline locomotion task. Learning both at once slows training and, without computationally expensive attention mechanisms, makes generalization to new terrain harder. We instead remove redundant inputs from the elevation map before the policy sees it. A lightweight foothold prediction model (FPM) predicts future footholds from proprioception and the velocity command alone, and we sample the elevation map only in small patches around these predicted footholds. We train the prediction model alongside the locomotion policy, periodically retraining it on new policy rollouts as the robot's gait matures. This allows the perception to anticipate where the policy will step, while the policy learns to leverage terrain information around those steps. With the proposed lightweight preprocessing, the policy reaches a given terrain difficulty in roughly a third of the training iterations required with the complete map. It outperforms policies that observe the complete map where footholds are sparse, including in narrow walled corridors, and on unseen terrain, and it matches an attention-based encoder trained at several times the cost. The policy transfers zero-shot to a Unitree G1 humanoid traversing various obstacles, stairs, gaps, and step-downs beyond the training distribution in both indoor and outdoor environments.

Strong single-turn editing performance does not guarantee reliable multi-turn interaction: as edited outputs are repeatedly reused, small unintended changes can accumulate into severe visual drift. This long-term drift is often mitigated through training on multi-turn data or cross-turn rollouts, potentially altering pretrained priors, or through specialized inference-time mechanisms that are difficult to scale to foundation models. We introduce TailSteer, a final-stage training framework that improves multi-turn robustness while retaining the generative and editing capabilities acquired through earlier training. TailSteer follows a simple principle: keep early denoising dynamics close to those of the base model and concentrate preservation corrections near the trajectory tail, where fine-grained deviations can be suppressed. These corrections are learned from the editor's own on-policy denoising rollouts, using unchanged source content as a preservation reference without requiring curated ground-truth editing pairs. Experiments across the FLUX, SenseNova, and Qwen families show that TailSteer substantially reduces cumulative drift over 15-20 editing turns while largely preserving base-model performance on extensive text-to-image and single-image editing benchmarks. These results demonstrate that long-horizon editing robustness can be unlocked in foundation models after TailSteer, rather than by relearning their existing capabilities.

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 same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD^2 and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.

Agentic reinforcement learning (RL) has become a critical stage in the post-training of large language models. Existing critic-free, group-relative methods estimate policy advantages from multiple rollouts, avoiding the substantial memory overhead of conventional proximal policy optimization (PPO) and achieving strong performance on long-horizon interactive tasks. Despite their success, recent studies revealed three limitations: (1) Lack explicit value generalization and effective temporal credit assignment; (2) Suffer from potential advantage collapse in long-horizon complex tasks; (3) Require a costly trade-off between sampling budget and policy performance. In this work, we propose Single-rollout Autoregressive Policy Optimization (SAPO), a low-memory and compute-efficient framework in which the policy and value functions share a single autoregressive backbone. SAPO exploits the autoregressive structure of LLMs to produce policy and value predictions at distinct causal boundaries with shared parameters, while independently optimizing the PPO objectives and auxiliary on-policy SARSA objectives. To robustly estimate the contribution of each turn, we further introduce a trajectory-level generalized advantage estimator that combines lambda-returns with batch normalization. Experiments across ALFWorld and WebShop with Qwen2.5-1.5B/7B show that SAPO trains stably and outperforms PPO and GRPO by mean +15.1 and +12.1 percentage points, respectively, while eliminating the memory cost of a separate critic model and reducing per-iteration runtime by 33.2% over PPO.

Weak-to-strong generalization asks whether stronger models can learn from weaker supervisors and surpass them. This question is particularly important for successive model generations and multi-domain consolidation, where repeating frontier-scale post-training from scratch can be prohibitively expensive. Yet conventional distillation treats the weak teacher as an optimization target, potentially imposing its capacity ceiling on the student. We introduce On-Policy Reverse Distillation (OPRD), which evaluates the teacher's policy shift relative to its reference policy on student rollouts and amplifies the component of the student's verifier-driven policy gradient along that direction. By rescaling only verifier-supported updates, OPRD preserves the stationary points of policy optimization while accelerating learning beyond the teacher. In both successive model transfer and multi-teacher distillation, OPRD achieves higher performance with fewer student updates than existing RL and distillation approaches. Response-style analysis shows that OPRD students remain closer to models trained with verifier-based RL alone than to their weak teachers, suggesting that teacher guidance accelerates rather than redirects the student's own optimization. Results in conventional strong-to-weak distillation further demonstrate that OPRD effectively combines verifier-driven policy optimization with teacher guidance regardless of capacity ordering.

Visuomotor policies trained via behavior cloning are vulnerable to covariate shift, where small deviations from expert trajectories can compound into failure. Common strategies to mitigate this issue involve expanding the training distribution through human-in-the-loop corrections or synthetic data augmentation. However, these approaches are often labor-intensive, rely on strong task assumptions, or compromise the quality of imitation. We introduce Latent Policy Barrier, a framework for robust visuomotor policy learning. Inspired by Control Barrier Functions, LPB treats the latent embeddings of expert demonstrations as an implicit barrier separating safe, in-distribution states from unsafe, out-of-distribution (OOD) ones. Our approach decouples the role of precise expert imitation and OOD recovery into two separate modules: a base diffusion policy solely on expert data, and a dynamics model trained on both expert and suboptimal policy rollout data. At inference time, the dynamics model predicts future latent states and optimizes them to stay within the expert distribution. Both simulated and real-world experiments show that LPB improves both policy robustness and data efficiency, enabling reliable manipulation from limited expert data and without additional human correction or annotation.

MLLM-based GUI agents have demonstrated strong capabilities in complex user interface interaction tasks. However, long-horizon scenarios remain challenging, as these agents are burdened with tasks beyond their intrinsic capabilities, suffering from memory degradation, progress confusion, and math hallucination. To address these challenges, we present UI-Copilot, a collaborative framework where the GUI agent focuses on task execution while a lightweight copilot provides on-demand assistance for memory retrieval and numerical computation. We introduce memory decoupling to separate persistent observations from transient execution context, and train the policy agent to selectively invoke the copilot as Retriever or Calculator based on task demands. To enable effective tool invocation learning, we propose Tool-Integrated Policy Optimization (TIPO), which separately optimizes tool selection through single-turn prediction and task execution through on-policy multi-turn rollouts. Experimental results show that UI-Copilot-7B achieves state-of-the-art performance on challenging MemGUI-Bench, outperforming strong 7B-scale GUI agents such as GUI-Owl-7B and UI-TARS-1.5-7B. Moreover, UI-Copilot-7B delivers a 17.1% absolute improvement on AndroidWorld over the base Qwen model, highlighting UI-Copilot's strong generalization to real-world GUI tasks.

Reinforcement learning from verifiable rewards (RLVR) is an emerging paradigm for improving the reasoning ability of large language models. However, standard on-policy training discards rollout experiences after a single update, leading to computational inefficiency and instability. While prior work on RL has highlighted the benefits of reusing past experience, the role of experience characteristics in shaping learning dynamics of large reasoning models remains underexplored. In this paper, we are the first to investigate what makes a reasoning experience valuable and identify rollout correctness and entropy as effective indicators of experience value. Based on these insights, we propose ExGRPO (Experiential Group Relative Policy Optimization), a framework that organizes and prioritizes valuable experiences, and employs a mixed-policy objective to balance exploration with experience exploitation. Experiments on five backbone models (1.5B-8B parameters) show that ExGRPO consistently improves reasoning performance on mathematical/general benchmarks, with an average gain of +3.5/7.6 points over on-policy RLVR. Moreover, ExGRPO stabilizes training on both stronger and weaker models where on-policy methods fail. These results highlight principled experience management as a key ingredient for efficient and scalable RLVR.

Aligning diffusion models with human preferences usually relies on a sparse terminal reward evaluated on the final generated samples, which creates a severe temporal credit-assignment problem across the denoising process. We propose Latent Reward Registers, a mechanism that estimates terminal preference directly from intermediate noisy latents. Learnable, position-free register tokens are appended as an auxiliary read path to a frozen Diffusion Transformer (DiT), extracting preference signals without altering the generator's hidden states or velocity field. The resulting dense, differentiable reward field spans the full denoising trajectory and supports two alignment strategies. For training, Reward-Gradient On-Policy Distillation (RG-OPD) converts this dense reward field into per-step targets at states visited by the current generator, replacing rollout-intensive policy gradients with direct on-policy distillation. For inference, Reward-Guided Sampling (RGS) steers trajectories with magnitude-matched reward-gradient corrections and no parameter updates. Empirically, at high noise levels (t=0.8) the registers reach the highest pairwise accuracy among the evaluated latent reward models. RG-OPD outperforms online reinforcement learning baselines while reducing GPU hours by up to 33x. RGS achieves significant reward improvement with a favorable reward-quality balance against training-free baselines. Code and weights are to be available at https://github.com/Guanys-dar/latent-reward-register

Vision-language-action (VLA) models adapted through supervised fine-tuning (SFT) inherit a structural asymmetry: expert demonstrations teach the policy where success behavior lies, but provide no signal about where it ceases to be reliable. We argue that robust VLA adaptation should therefore be viewed not as further demonstration fitting, but as **Failure-Boundary Learning**---the problem of *Discovering*, *Localizing*, and *Shaping* the boundary between recoverable deviations and task failure. To instantiate this view, we propose **DLS**: built on a **real-grounded behavioral prior** from few real demonstrations and simulated co-training, DLS *discovers* failure boundaries at scale through on-policy digital twin rollouts. Rather than reducing each rollout to a binary label, **semantic progress localization** uses privileged simulator states to assign progress-aware signals that capture *where* the failure boundary is crossed, not merely *whether*. These signals drive **directional boundary shaping** in the flow dynamics---reinforcing success-producing denoising directions and suppressing failure-producing ones, without action likelihoods or auxiliary critics. Across real-robot manipulation tasks, DLS improves robustness over SFT and online RL baselines, especially under randomized initial states and unseen visual conditions.

LLM agents are increasingly evaluated on multi-week decision tasks in which the state that drives cost is never directly observed. On such tasks the final cost cannot say why an agent failed: it may have misread the world, or read it correctly and still failed to act (the knowing-doing gap). Existing evaluations cannot separate these two failures; their reference policies either read privileged information the agent never sees, or are missing altogether. We introduce STOCKTAKE, a 26-week supply-chain replenishment benchmark built as a factored partially observable Markov decision process with six hidden factor processes, designed so that a fair reference policy is computable: an exact Bayes filter per factor drives a rollout policy on the identical observation stream the agent receives. Scoring each run between a symptom-blind base-stock floor (0) and this oracle (1) yields a skill score, and grading each week's written rationale yields a stated-belief detection lag and a knowing-doing rate, so state estimation and control are measured separately. On fifty seeds with curated stress profiles, Claude Sonnet 5, GPT-5.4, DeepSeek-V4-Pro, and Grok 4.5 detect 84-88% of hidden failures, typically within a week of onset, yet span skill scores from 0.62 to -0.23: two of the four end below the symptom-blind floor while naming factors slightly faster than the two that beat it. The failure has two faces. Where stress persists, 34-43% of correctly diagnosed stress weeks still end in stockout for every model, a rate that partly reflects the severity of the weeks models notice. That rate also runs opposite to skill: the two models under the floor stock out least on diagnosed weeks, so under-response is only one face of the gap, and their traces point to the other, responses whose cost exceeds what they protect. STOCKTAKE measures both directions of that failure.

On-policy distillation has recently emerged as a promising alternative to standard sequence-level imitation, training a student by scoring its own rollouts with a teacher model. However, we observe ``Off-policy Teacher Decay'' problem in this paradigm: for the later tokens, with student's earlier trajectory as context that is off-policy to the teacher, the teacher's ability to produce a corrective score would decay, and may fall back to token-completion behavior learned in the pre-training stage. We empirically verify this problem, and we propose Early Stopping Rollout (ESR) to fix it: a simple yet effective distillation strategy that simply restricts the rollout generation to the first response tokens. We show that ESR both surpasses the full rollout OPD performance across model size, family, tasks and training regime, and exhibit much higher GPU efficiency and training stability, especially under cross model family scenarios. We further investigate the mechanism behind this surprising performance and discovered "Cascading Alignment" and "Sub-mode Commitment" effect of ESR that may explain why it works effectively and even sometimes exceeding the teacher model performance. Besides, we show that this position-based token selection strategy cannot be fully explainable by KL divergence and entropy signals.

On-policy distillation (OPD), which supervises a student on its own sampled trajectories, has emerged as a data-efficient post-training method for improving reasoning while avoiding the reward dependence of reinforcement learning and the catastrophic forgetting often observed in standard supervised fine-tuning. However, standard OPD typically computes teacher supervision under noisy student-generated contexts and often relies on a single stochastic teacher rollout per prompt. As a result, the supervision signal can be high-variance: the sampled teacher trajectory can be incorrect, uninformative, or poorly matched to the student's current reasoning behavior. To address this limitation, we propose BRTS, a Best-of-N Rollout Teacher Selection framework for on-policy distillation. BRTS augments standard student-context OPD with a teacher-context supervision branch constructed from the curated teacher trajectory. Rather than distilling from the first sampled teacher rollout, BRTS samples a small pool of teacher trajectories and selects the auxiliary trajectory using a simple priority rule: correctness first, student alignment second. When multiple correct teacher trajectories are available, BRTS chooses the one most aligned with the student's current behavior; when unconditioned teacher samples fail on harder prompts, it invokes a ground-truth-conditioned recovery step to elicit a natural derivation. The selected trajectory is then used to provide reliable teacher-context supervision inside the OPD loop, augmented with an auxiliary loss on the teacher trajectory. Experiments on AIME 2024, AIME 2025, and AMC 2023 show that BRTS improves over standard OPD on challenging reasoning benchmarks, with the largest gains on harder datasets. Our code is available at https://github.com/BWGZK-keke/BRTS.

On-policy distillation (OPD) transfers teacher knowledge to a student through feedback on student-generated rollouts, but generating complete rollouts and computing per-token teacher feedback are computationally expensive. Existing truncation methods save computation by stopping rollouts early. However, they do not compensate for truncated token gradients, which biases the gradient estimates and changes Vanilla OPD's original training objective. Furthermore, their truncation decisions rely on assumptions about supervision quality or criteria that may not generalize across settings. We introduce Stochastic Truncated On-Policy Distillation (STOPD), which accelerates OPD by randomly truncating student rollouts and correcting the resulting sampling bias with blockwise inverse-probability weighting (IPW). At each training step, we sample a stopping position for each rollout before generation and let the student generate until that position or natural termination. We obtain teacher feedback on every generated token and use blockwise IPW to compensate for the lower probability of retaining later tokens while controlling the weights. We prove that this weighting preserves Vanilla OPD's gradient sum in expectation and derive one-step update-error bounds for SGD, Adam, and Muon. We evaluate STOPD across multiple teacher-student model pairs, task domains, and optimizers. STOPD reduces generated tokens by 25-48% while maintaining accuracy comparable to Vanilla OPD, achieving 1.3-2.2x training speedups.

On-policy distillation (OPD) improves reasoning models by applying dense teacher supervision on student-sampled trajectories. However, scaling OPD to long-horizon reasoning exposes a reliability and efficiency problem: standard OPD assigns every candidate the same long rollout budget, even though some trajectories may quickly become weakly aligned with the teacher and provide less useful supervision. Prior analyses suggest that teacher--student compatibility is important for OPD success, motivating early-prefix top-k overlap as a proxy for continuation value. Continuing low-overlap trajectories to the full rollout length may cause them to drift further from the teacher as generation proceeds, increasing computational cost while providing limited distillation benefit. To address this, we introduce Prefix-Guided On-Policy Distillation (PG-OPD), a rollout-allocation framework that estimates continuation value from fixed-length prefixes. PG-OPD computes teacher-student top-k overlap in an early probe window and allocates long rollouts only to high-overlap candidates, while stopping the rest at the prefix length. Across teacher--student combinations on AMC, AIME, and HMMT benchmarks, PG-OPD achieves up to a 4.80-point accuracy gain and up to a 2.46x wall-clock speedup across configurations. These results demonstrate that using early-prefix compatibility to guide candidate pruning can improve both training efficiency and reasoning performance.

Large Language Models (LLMs) increasingly rely on reinforcement learning with verifiable rewards (RLVR) to elicit reliable chain-of-thought reasoning. However, the training process remains bottlenecked by the computationally expensive rollout stage. Existing acceleration methods-such as parallelization, objective- and data-driven modifications, and replay buffers-either incur diminishing returns, introduce bias, or overlook redundancy across iterations. We identify that rollouts from consecutive training epochs frequently share a large portion of overlapping segments, wasting computation. To address this, we propose SPEC-RL, a novel framework that integrates SPECulative decoding with the RL rollout process. SPEC-RL reuses prior trajectory segments as speculative prefixes and extends them via a draft-and-verify mechanism, avoiding redundant generation while ensuring policy consistency. Experiments on diverse math reasoning and generalization benchmarks, including GSM8K, MATH-500, OlympiadBench, MMLU-STEM, and others, demonstrate that SPEC-RL reduces rollout time by 2-3x without compromising policy quality. As a purely rollout-stage enhancement, SPEC-RL integrates seamlessly with mainstream algorithms (e.g., PPO, GRPO, DAPO), offering a general and practical path to scale RLVR for large reasoning models. Our code is available at https://github.com/ShopeeLLM/Spec-RL

On-policy distillation (OPD) has become increasingly popular for transferring teacher capabilities to student models. In this work, we ask a critical research question: Is on-policy sampling always beneficial for distilling arbitrary teacher-student pairs? We show that a simple alternative, Semi-OPD, which distills from offline rollouts generated by the initial student, can often outperform OPD in both accuracy and training efficiency. Across 17 teacher-student pairs ranging from 1.5B to 235B parameters, Semi-OPD outperforms OPD in 14 cases, with up to +13.6% accuracy and 11.4x training speedup. We further find that the choice between OPD and Semi-OPD depends on the alignment between the initial teacher and student, quantified by an output-token overlap ratio: OPD is beneficial only when the two are highly aligned with high overlap ratios. Our deeper investigation suggests that effective distillation requires on-policyness w.r.t. both the student and the teacher. For misaligned pairs, student rollouts can become increasingly off-policy w.r.t. the teacher as context length grows, weakening the distillation signal. In contrast, Semi-OPD is often more stable, as it distills on shorter contexts while covering full trajectories and exposing the student to more teacher-preferred tokens. Beyond proposing Semi-OPD as an efficient alternative, our work motivates the community to rethink when to use OPD and to study stronger OPD variants with meaningful teacher-student pairs.

Reinforcement learning (RL) is essential for enhancing the complex reasoning capabilities of large language models (LLMs). However, existing RL training pipelines are computationally inefficient and resource-intensive, with the rollout phase accounting for over 70% of total training time. Quantized RL training, particularly using FP8 precision, offers a promising approach to mitigating this bottleneck. A commonly adopted strategy applies FP8 precision during rollout while retaining BF16 precision for training. In this work, we present the first comprehensive study of FP8 RL training and demonstrate that the widely used BF16-training + FP8-rollout strategy suffers from severe training instability and catastrophic accuracy collapse under long-horizon rollouts and challenging tasks. Our analysis shows that these failures stem from the off-policy nature of the approach, which introduces substantial numerical mismatch between training and inference. Motivated by these observations, we propose Jet-RL, an FP8 RL training framework that enables robust and stable RL optimization. The key idea is to adopt a unified FP8 precision flow for both training and rollout, thereby minimizing numerical discrepancies and eliminating the need for inefficient inter-step calibration. Extensive experiments validate the effectiveness of Jet-RL: our method achieves up to 33% speedup in the rollout phase, up to 41% speedup in the training phase, and a 16% end-to-end speedup over BF16 training, while maintaining stable convergence across all settings and incurring negligible accuracy degradation.

On-policy (Self-)Distillation (OPD / OPSD) has shown strong potential for post-training large language models (LLMs). However, existing methods still rely heavily on external supervision, including ground-truth signals, environmental feedback, or guidance from larger models, and therefore fall short of genuine "self"-distillation. In this study, we show that on-policy self-distillation can be achieved using only a model's own generations via internal consistency. We propose unsupervised on-policy self-distillation (U-OPSD). U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold. It then conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong. Across diverse benchmarks, base models, and training settings, U-OPSD consistently improves over the base models and matches or surpasses supervised methods with ground truth (GT) such as OPSD and GRPO. On five mathematical reasoning benchmarks, i.e., AIME24, AIME25, HMMT25, MATH500, and AMC23, U-OPSD improves over the base model by 8.5% and 10.7% on Qwen3 non-thinking mode at 4B and 8B scales, and outperforms OPSD by 3.2% and 2.3% on average, respectively. In thinking mode, U-OPSD stays on par with OPSD, ahead by 0.9% at 4B and level at 8B and surpassing GRPO by 0.7% and 1.1%, respectively. Code is available at [https://github.com/williamium3000/u-opsd](https://github.com/williamium3000/u-opsd).

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches \(71.5\%\), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach \(98.9\%\) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

On-policy distillation (OPD) provides teacher supervision on student-generated trajectories, but a single trajectory realizes only one continuation at each decision, limiting supervision coverage under a finite sampling budget. We propose BranchOPD (Branching On-Policy Distillation), which selects informative decision points using student uncertainty and teacher-student disagreement, resamples student-policy continuations from shared prefixes, and applies token-level teacher supervision to both main trajectories and branches. BranchOPD operates at token-level decisions in mathematics and within-turn decisions in agent tasks. Shared-prefix reuse reduces student-generated token costs by approximately 19% on ALFWorld and 31% on WebShop relative to seven independent trajectories. We also introduce protocol-boundary repair (PBR), which uses targeted supervision under protocol constraints to mitigate repetition and wasted generation. BranchOPD outperforms Vanilla OPD and Multi-Rollout OPD (n=7) across all evaluated benchmarks, with gains over Vanilla OPD of 18.55 percentage points in mean mathematics accuracy over 16 sampled answers (avg@16) and 13.8 points in mean ALFWorld ID/OOD success. Mechanistic analyses and selection ablations show that branching at uncertain decisions expands subsequent behavior coverage and outperforms random selection and turn-initial branching.

On-policy knowledge distillation (OPD) trains a student on its own rollouts under token-level supervision from a teacher. Not all token positions matter equally, but existing views of token importance are incomplete. We ask a direct question: which tokens carry the most useful learning signal in OPD? Our answer is that informative tokens come from two regions: positions with high student entropy, and positions with low student entropy plus high teacher--student divergence, where the student is overconfident and wrong. Empirically, student entropy is a strong first-order proxy: retaining 50% of tokens with entropy-based sampling matches or exceeds all-token training while reducing peak memory by up to 47%. But entropy alone misses a second important region. When we isolate low-entropy, high-divergence tokens, training on fewer than 10% of all tokens nearly matches full-token baselines, showing that overconfident tokens carry dense corrective signal despite being nearly invisible to entropy-only rules. We organize these findings with TIP (Token Importance in on-Policy distillation), a two-axis taxonomy over student entropy and teacher--student divergence, and give a theoretical explanation for why entropy is useful yet structurally incomplete. This view motivates type-aware token selection rules that combine uncertainty and disagreement. We validate this picture across three teacher--student pairs spanning Qwen3, Llama, and Qwen2.5 on MATH-500 and AIME 2024/2025, and on the DeepPlanning benchmark for long-horizon agentic planning, where Q3-only training on <20% of tokens surpasses full-token OPD. Our experiments are implemented by extending the OPD repository https://github.com/HJSang/OPSD_OnPolicyDistillation, which supports memory-efficient distillation of larger models under limited GPU budgets.

On-policy distillation (OPD) trains a student on its own rollouts with token-level teacher supervision. Recent selective OPD methods exploit the non-uniformity of OPD signals by prioritizing high-entropy or high-disagreement tokens. We revisit this principle and ask: which token-level teacher signals are actually learnable? Using a fixed-context diagnostic that measures same-context teacher-student KL reduction, we show that raw KL disagreement is a coarse proxy for learning value. It conflates learnable disagreement, where the teacher assigns corrective mass to the student's top-K candidates, with incompatible disagreement, where the teacher places mass mostly off the student's current support. We formalize this local compatibility as token teachability and show that it better predicts fixed-context improvement than raw KL alone. Motivated by this finding, we propose Teachability-Aware OPD (TA-OPD), a lightweight token-position selection method that applies OPD loss to high-teachability positions without reward models or verifiers. Across Qwen2.5 and Qwen 3 teacher-student settings, TA-OPD often surpasses full-token OPD with only 5% retained tokens and improves over entropy- and divergence-based baselines. Our results reframe selective OPD as selecting learnable teacher signals rather than merely salient tokens.

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.

On-policy self-distillation (OPSD) trains a model on its own rollouts and uses a frozen copy to provide dense token-level targets conditioned on a reference target. This works well for LLM reasoning, but a direct extension to multimodal large language models (MLLMs) can create a shortcut: the privileged target may guide tokens mainly based on the text reference target rather than the image. We propose ViGOS, a visually grounded OPSD framework for MLLM post-training. The student first writes a visual description and then reasons toward the final answer. For valid rollouts, an image-only perception teacher supervises the description, while a privileged reasoning teacher supervises the reasoning and final answer on the same student prefix. A reference teacher is used only for invalid rollouts to recover the output format. Across general vision-language, expert reasoning, visual math, spatial grounding, and visual-language-prior benchmarks, ViGOS keeps the main benefits of OPSD and improves image-grounded behavior in shortcut-prone settings.

On-policy distillation (OPD) trains a student on its own rollouts guided by teacher feedback and is becoming increasingly important for large language model (LLM) post-training. Like reinforcement learning (RL), however, OPD faces an on-policy systems bottleneck, as rollouts can dominate training time for reasoning workloads. Asynchronous training pipelines can alleviate this bottleneck by decoupling rollout generation from learner updates, but doing so introduces stale-policy data. While prior work has studied stale data in asynchronous RL, its effects in OPD remain underexplored. We present the first systematic study of staleness in asynchronous OPD, focusing on a practical setting where teacher feedback is implemented through local KL losses and full-vocabulary teacher logits are too expensive to store or transfer, necessitating finite teacher-score caches. We first show that KL direction changes the stale-data problem: teacher-weighted forward KL is more robust to stale rollouts, whereas student-weighted reverse KL is vulnerable. Second, for this vulnerable reverse-KL case, we study whether methods designed to stabilize asynchronous RL can mitigate OPD staleness. In our experiments, they do not improve over a simpler OPD-specific surrogate: recomputing the reverse-KL signal under the current student at learner time. Third, we analyze how finite teacher-score caches create a bias-variance tradeoff for sparse and sampled reverse-KL OPD estimators. This motivates multi-sample Monte Carlo (MC), which preserves MC correctability while reducing one-sample variance. Finally, we present and open-source AsyncOPD, a fully asynchronous OPD training pipeline built from these estimator choices. Experiments show that AsyncOPD improves training throughput by 1.6times to 3.8times over strict synchronous training while reaching comparable accuracy.

Flow-matching models are now a mainstream method to image generation, but its adaptation to diverse downstream scenarios typically relies on post-training, which may cause conflicts among task-specific optimization objectives. Reinforcement learning enables direct optimization of task-specific rewards beyond the original models, yet trajectory-level optimization may incur high-variance gradients and cross-task interference. On-policy distillation (OPD) offers dense and stable supervision on student rollouts, but conventional teacher matching remains imitation-based. We propose DreOPD, a Degraded-reference extrapolative OPD method for flow-matching models that bridges these two paradigms. Our DreOPD converts implicit reward extrapolation into closed-form velocity regression, enabling extrapolative post-training with the stability of OPD. It further uses a mildly degraded reference to strengthen the teacher-reference contrast, yielding a clearer extrapolation direction. Experiments on single- and multi-teacher settings show that DreOPD outperforms OPD and multi-task RL baselines in average performance, while surpassing specialized teachers on most metrics.

On-policy distillation (OPD) trains a student on its own rollouts with token-level supervision from teacher models, but its effectiveness can depend strongly on the warm-up stage before OPD. In this paper, we demystify warm-up for OPD from both data and training perspectives. For data, we find that effective warm-up relies on teacher-compatible chain-of-thought supervision, and that even incorrect teacher rollouts can provide comparable benefits to correct ones. This suggests that warm-up primarily transfers a teacher-compatible thinking pattern rather than merely correct answers. For training, we show that low-rank adaptation (LoRA) with a near-saturation training duration better balances in-domain adaptation and out-of-distribution generalization than full-parameter SFT. Based on these findings, we propose Simple-OPD, a plug-and-play initialization method that warms up the student on teacher-generated CoT with LoRA before OPD. Experiments across diverse settings demonstrate the effectiveness and robustness of Simple-OPD.

On-policy distillation (OPD) trains a student on its own rollouts using dense supervision from a teacher. In multi-turn environments, a mistake at a critical decision step can redirect the subsequent rollout toward poor outcomes. We use low teacher confidence on student actions to select high-uncertainty steps for correction. In a controlled ALFWorld study, a single teacher correction at a low-confidence step improves subsequent student behavior and task success, motivating selective intervention during distillation. We propose UOPD, an uncertainty-aware intervention method for on-policy distillation. At low-uncertainty turns, UOPD executes student actions and applies the standard OPD loss. At high-uncertainty turns, it samples and executes teacher actions and trains the student to imitate them through supervised fine-tuning, which minimizes forward Kullback-Leibler divergence in expectation. UOPD utilizes adaptive uncertainty thresholds to target a scheduled intervention rate. Empirically, we evaluate UOPD across a broad range of agentic tasks, including ALFWorld, WebShop, and Search, demonstrating its superior performance over OPD methods and their variants. UOPD improves WebShop score by up to 15.8% relative to standard OPD.

On-policy distillation (OPD) trains a target policy on its own rollouts using token-level supervision from a stronger teacher, but typically relies on the teacher being substantially more capable than the target. Recent work relaxes this requirement by transferring the relative policy difference between an expert and a reference policy rather than the expert's absolute distribution. Yet it remains unclear which differences provide useful supervision and which targets can benefit from them. We develop a unified view in which the log-probability ratio between a proxy expert and a proxy reference defines an implicit reward for KL-regularized policy optimization. This formulation induces an on-policy update for the target, recovers conventional OPD as a special case, and enables any-to-any transfer across models that differ in scale, training stage or generation. Our systematic experiments yield three findings. First, a stronger expert is not necessarily a better source of supervision: differences induced by task-specific training, including reinforcement learning and supervised fine-tuning, transfer consistently, whereas those arising from model scale alone transfer weakly or not at all. Second, the expert and reference serve complementary roles: the expert provides the capability to be transferred, while the reference filters out shared behavior and isolates the relevant residual. Third, even a useful difference does not transfer to every target: success requires the induced update to move the target toward the expert and generalize beyond sampled rollouts. Raw policy distance does not predict transferability, whereas an appropriate reference can rescue otherwise unsuccessful transfer. These results characterize when relative policy differences provide effective supervision for OPD.

On-policy distillation (OPD) trains a student model on its own rollouts with token-level supervision from a teacher, assuming that the teacher can reach a correct answer from any prefix the student writes. We call this property the recoverability of the teacher and show it fails on incorrect rollouts: the teacher follows student errors, although it recognizes them. We propose CriticOPD, using error recognition to restore recoverability. The teacher critiques an incorrect rollout, allowing the student to rewrite its solution following the error. The resulting output, including the critique as privileged information, is scored by the teacher while the student uses the revision without the critique for training. On two Qwen3 students and six mathematical reasoning benchmarks, CriticOPD improves OPD, with the largest gains on competition problems.

On-policy distillation (OPD) provides dense token-level supervision on student rollouts, but this supervision can become unreliable when the student and teacher diverge, either because of a large initial policy gap or compounding errors in long-horizon reasoning and tool use. We introduce Divergence-Triggered Dynamic Distillation (DTDD), an adaptive OPD framework that uses segment-level student-teacher divergence to trigger teacher takeover during training. When divergence triggers an intervention during reasoning, the student prefix continues to receive standard OPD supervision. The teacher then generates a recovery suffix, which the student learns through behavior cloning, using cross-entropy on the teacher-generated tokens. We evaluate DTDD in three regimes: long-horizon reasoning, distillation from a base initialization without offline supervised fine-tuning (SFT), and multi-turn agents. We also compare alternative trigger designs and teacher-intervention rates. DTDD reduces the post-warmup peak gradient norm by 8.6times and, from a base initialization, reaches 21.3% held-out math accuracy in 2.6times fewer optimizer updates than OPD; both methods finish near 22%. It improves best-observed performance by 4.8 and 4.1 percentage points on ALFWorld with LoRA and agentic code, respectively. Ablations show that segment-averaged triggers outperform token-spike triggers. Behavior cloning is also more effective than the tested OPD surrogate for training teacher-generated recoveries. Across 23 experimental arms, takeover tends to help when the teacher substantially outperforms the OPD-trained student, provided that the teacher can recover from student-visited states, the student can learn those recoveries, and teacher intervention is neither excessive nor insufficient.

On-policy distillation (OPD) trains a student language model on its own responses, guided by a fixed teacher. Generating these responses is expensive, so systems use quantized inference and asynchronous rollouts to reduce the cost. Both, however, introduce training-inference mismatch between the rollout engine and the model being trained. Such mismatch can destabilize reinforcement learning (RL), but its effects on OPD remain unclear. This paper investigates how much mismatch OPD tolerates, where its effects arise, and how training systems can use this tolerance. Measuring all mismatch sources on one scale, we examine quantization across three student-teacher pairs, with additional tests of weight staleness and injected noise on one pair. OPD tolerates substantial mismatch without meaningful loss of training quality but degrades at higher levels, revealing an empirical mismatch budget. Both the quality cost of mismatch and the mismatch introduced by quantization depend on the model, with some layers particularly sensitive to reduced precision. In controlled comparisons, OPD remains stable under rollout configurations that destabilize RL methods. Under weight noise, mismatch also shifts the prefixes reached during generation, introducing errors that per-token corrections cannot address. To put these findings into practice, we introduce a lightweight admission check that screens rollout configurations against a calibrated budget without requiring a full training run for each candidate. Model-specific FP8 recipes preserve training quality while providing capacity for at least 1.93times as many KV-cache tokens as BF16. Combining FP8 with asynchronous rollouts reaches the same training quality 1.62times sooner than synchronous BF16 training. Code is available at https://github.com/benyucong/train-inference-mismatch-opd

Self-distillation is a promising recipe for self-improvement in language models. In this setting, a model can serve as its own teacher when given privileged information, such as a solution to a math problem. This seems especially appealing for thinking models, which can use test-time reasoning to absorb the privileged information. Surprisingly, we show that privileged self-distillation degrades thinking models on long reasoning traces: across five Qwen3 and OLMo thinking models evaluated on AIME24, AIME25, and HMMT25, privileged-context distillation causes a relative drop of up to 17% in avg@16 accuracy. The degradation scales with the amount of privileged context withheld from the student and is most pronounced at long rollout budgets, where thinking models otherwise obtain their largest gains. This failure mode is not specific to self-distillation: on-policy distillation (OPD) improves thinking models, but privileged OPD reverses these gains. Our diagnostics link this failure mode to how privileged teacher context reshapes learning at high-entropy forking positions, where multiple continuations remain plausible and may lead to different reasoning paths. Privileged context lowers fork rates in thinking-model rollouts but not in instruction-model rollouts. This leads to an interesting dichotomy, where privileged context can help instruction-tuned models but hurts stronger thinking models. The effect is visible when the student begins a self-correction branch, where privileged OPD penalizes sampled reconsideration tokens that vanilla OPD supports. Thinking models trained with a privileged teacher produce fewer verification, backtracking, and hedging markers, even after length normalization. These findings indicate that self-distillation for strong thinking models requires attention to token-level signal, especially around correction and reasoning steps.

On-policy distillation can transfer the reasoning capabilities of a strong teacher to a smaller student. However, distillation from a stronger teacher model faces two mismatches: its solutions may be difficult for a smaller student to imitate, and its token-level probabilities may be incompatible with, or even unavailable to, the student. Existing methods handle these settings through different forms of supervision. To this end, we propose Bridged Self-Distillation (BSD), a unified framework for distilling from any teacher that provides reasoning traces. The model to be distilled from, termed the external teacher, first provides a reasoning trace as privileged context, which can be generated in an offline fashion. The student generates rollouts without this context, while a copy of the student conditioned on it, serving as the self-teacher, scores the same rollouts in the student's own token space. BSD uses the resulting token-level guidance to adjust updates on unsuccessful rollouts, with a verifier providing the outcome signal. As the external teacher is queried only to produce text, the same training procedure applies to all teacher scenarios: shared-tokenizer, cross-tokenizer, and closed API teachers. Across these scenarios, BSD improves over the base model and outperforms baselines tailored to each scenario, offering a novel and unified pathway for distillation. Code is available: https://github.com/TUMLegalTech/Bridged-Self-Distillation

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Reinforcement learning for multimodal large language models (MLLMs) is often hindered by severe reward sparsity in complex reasoning tasks. This challenge is particularly pronounced in human-centered scenarios involving states, emotions, intentions, and behaviors, where heterogeneous multimodal signals and subjective human factors make high-quality chain-of-thought (CoT) annotations expensive and difficult to obtain. Although many multimodal datasets provide expert-annotated ground-truth labels, directly using these labels for supervised fine-tuning may encourage shortcut learning in multimodal perception and provides limited transparency for safety-critical human--AI interaction. To address these limitations, we propose OmniOPSD, a Rationale-Privileged On-Policy Self-Distillation framework that uses frontier-generated rationales as teacher-side privileged evidence rather than student imitation targets. OmniOPSD uses frontier-generated evidence-aware rationales only as training-time privileged evidence context for a local teacher. The student samples its own rollout from the original multimodal input, while the rationale-privileged teacher scores the same tokens and provides dense token-level supervision. Thus, the student learns on its own trajectory distribution without directly imitating frontier-model completions, and inference requires no labels, rationales, CoT annotations, or closed-source model access. Experiments on MER-UniBench show that OmniOPSD achieves state-of-the-art performance with an average score of 84.19, and ablations further support the value of rationale-privileged teacher guidance.

Search-augmented reasoning agents interleave internal reasoning with calls to an external retriever, and their performance relies on the quality of each issued query. However, under outcome-reward reinforcement learning, every search decision in a rollout shares the same trajectory-level reward, leaving individual queries without step-specific credit. Recent process-supervision approaches address this gap by drawing step-level signals from outside the policy, relying either on a much larger teacher model, or on sub-question annotations produced by a stronger external system. In contrast, we propose SD-Search, which derives step-level supervision from the policy itself through on-policy hindsight self-distillation, requiring neither an external teacher nor additional annotations. In SD-Search, a single model plays two roles that differ only in conditioning: a student that sees only the context available at inference time, and a teacher that additionally conditions on a compact hindsight block summarizing the search queries and final outcomes of a group of rollouts sampled from the same question. Since the teacher knows how each rollout unfolded and which ones succeeded, its query distribution implicitly marks which decisions were worth making, and the student is trained to recover this behavior by minimizing the token-level Jensen--Shannon divergence to the teacher at search-query positions. This layers a dense, step-level signal on top of GRPO's coarse trajectory reward. Crucially, this signal is produced by the policy itself within the standard RL training loop, without external model inference, auxiliary annotation pipeline, or additional training stage.

On-policy distillation (OPD) consolidates expert capabilities into a single student by matching teacher and student final-layer distributions on student-generated rollouts. We investigate whether depthwise prediction transitions, the changes in predictions between layers, can provide additional task-relevant supervision. Our diagnostic study finds that stronger teacher--student agreement in intermediate transitions is associated with higher answer correctness within questions, with correct responses exhibiting lower mean transition KL across all measured intermediate layer pairs. These observations motivate On-Policy Transition Distillation (OPTD), which augments final-layer distribution matching by aligning teacher and student layer-to-layer log-probability increments on student-generated rollouts. Evaluations across three backbones and eight benchmarks spanning mathematics, coding, and instruction following show that OPTD achieves the best or tied-best overall performance in both dual- and three-domain distillation. In the three-domain setting, OPTD recovers approx 90% of the overall teacher--student capability gap, compared with approx 75% for OPD.

Aligning large language models (LLMs) on domain-specific data remains a fundamental challenge. Supervised fine-tuning (SFT) offers a straightforward way to inject domain knowledge but often degrades the model's generality. In contrast, on-policy reinforcement learning (RL) preserves generality but fails to effectively assimilate hard samples that exceed the model's current reasoning level. Recent off-policy RL attempts improve hard sample utilization, yet they suffer from severe training instability due to the forced distribution shift toward off-policy knowledge. To reconcile effective off-policy knowledge absorption with the stability of on-policy RL, we propose Rephrasing Policy Optimization (RePO). In RePO, the policy model is prompted to first comprehend off-policy knowledge and then rephrase it into trajectories that conform to its own stylistic and parametric distribution. RePO dynamically replaces low-reward rollouts with these rephrased, high-quality trajectories. This strategy guides the model toward correct reasoning paths while strictly preserving on-policy training dynamics. Experiments on several benchmarks demonstrate that RePO improves hard-sample utilization and outperforms existing baselines, achieving state-of-the-art performance.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Industrial anomaly detection (IAD) requires identifying fine-grained deviations from normal visual patterns. Multimodal large language models (MLLMs) can improve recognition accuracy by comparing query images with references at inference time, but these benefits rely on additional retrieval and processing. We investigate whether the benefits of reference comparison can instead be internalized in the model parameters. Access to references during training allows a reference-aware teacher to supervise a query-only student. However, the teacher may favor plausible responses based on query cues or language priors rather than valid visual information. We propose ADOPD, a reference-privileged on-policy distillation framework. The teacher evaluates student-generated rollouts under matched and mismatched references. The matched-reference teacher-to-student log-ratio defines the token-level learning direction, specifying what the student should learn. The likelihood gap between the two reference views estimates reference-specific support and calibrates the sequence-level weight. ADOPD achieves 77.31% average accuracy on the MMAD benchmark under zero-shot inference, improving the Qwen3-VL-4B backbone by 6.14 points and outperforming its one-shot setting by 2.64 points. Experiments show that ADOPD learns a fine-grained anomaly inspection strategy from reference comparison. The project will be available at https://github.com/withTai/ADOPD.

On-policy self-distillation (OPSD) uses a privileged teacher to supervise a reasoning model on prefixes sampled from its own rollouts. Yet each rollout also reveals how the student's response unfolds and whether it succeeds, student-specific hindsight that standard OPSD does not use to form the teacher. We introduce Privileged Adaptation from Student Trajectories (PAST), which treats each completed student trajectory as additional privileged information for the OPSD teacher while leaving the student's distillation prefixes unchanged. PAST preserves the student's next-token distribution on correct trajectories and uses failed trajectories to adapt the teacher toward verified success under student-proximity regularization. We characterize what such a trajectory-conditioned teacher can transfer to a prefix-only student. Forward-KL distillation projects the teacher distributions to their conditional arithmetic mean given the prefix. This projection separates trajectory-specific variation that remains privileged from the mean policy shift available to the student. For correct trajectories, the unclipped population objective also has the frozen student as an ideal distributional fixed point. Across three mathematical reasoning benchmarks, PAST improves the Avg@12 macro average over Vanilla OPSD by 5.6 percentage points. A 2times2 factorial study shows gains from both complete-trajectory access and teacher adaptation, while trajectory removal and shuffling confirm that the adapted teacher uses the matching hindsight context.

On-policy self-distillation (OPSD) provides dense teacher targets, but evaluates them only along student-sampled rollouts. When the privileged teacher favors an alternative action at a visited prefix, OPSD can provide a target for the branch decision but cannot supervise the successor contexts induced by that action unless the student samples it. This creates a training-time data-collection bottleneck and suggests a different role for teacher-student disagreement: proposing a trajectory branch rather than identifying a sufficient local repair. Our diagnostic framework using controlled token interventions reveals that a teacher-preferred token at peak disagreement can improve student continuation success, while its local corrective value is limited. Motivated by this finding, we introduce a simple branch-regenerate-distill algorithm, Trajectory-Intervention Self-Distillation (TISD). TISD forces a teacher-selected branch action, returns suffix generation to the student, and distills the full trajectory under the privileged-context-conditioned teacher. Across the coding models, TISD improves average Avg@4 over SDPO by 1.2 percentage points. Across the science domains, it improves average Avg@128 by 0.8 points under an equal-step budget and by 0.3 points under an equal-time budget. These results support teacher-guided branching as a way to expose useful successor contexts for self-distillation.

On-policy distillation (OPD) transfers reasoning behavior by training a student on teacher feedback along student-generated trajectories, but standard full-rollout training ties every update to a costly completion and can over-allocate supervision to late positions with low marginal value for the current student. We revisit this assumption through the useful supervision horizon: student-induced rollouts can drift from teacher-preferred continuations, while aligned prefixes may already preserve the long-horizon OPD update direction. We propose ADWIN, an adaptive-window framework for OPD that treats rollout length as an online admissibility decision, training on short teacher-anchored prefixes while using delayed full-rollout probes to audit prefix--full alignment and adapt the next horizon with staleness control. Across math and code reasoning benchmarks in single-task, multi-task, and strong-to-weak settings, ADWIN improves the accuracy--compute trade-off over full-rollout OPD and prefix-based baselines, reducing end-to-end training cost by up to 4.1 times while achieving comparable or better accuracy.

On-policy distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.

On-Policy Self-Distillation (OPSD) has emerged as a promising paradigm for safety alignment, delivering dense, token-level supervision by distilling from a teacher conditioned on refusal-oriented privileged prompts. However, we reveal that this paradigm suffers from critical inefficiencies that degrade both training efficiency and general reasoning capabilities. Specifically, we diagnose two fundamental bottlenecks: (1) supervisory collapse over extended rollouts, where the teacher's corrective efficacy degrades precipitously as the student's generation prefix lengthens, injecting noisy gradients into late-stage tokens; and (2) gradient dilution from stylistic shifts, where the distillation objective is dominated by safety-irrelevant stylistic discrepancies induced by privileged prompting, washing out genuine safety signals and impairing base reasoning. To resolve these issues, we propose Efficient On-Policy Self-Distilled Safety Alignment (EOPSA), which concentrates computational and gradient budgets exclusively on reliably supervised, safety-critical tokens. EOPSA incorporates two coordinated mechanisms: (i) Adaptive Rollout Scheduling, which dynamically bounds the generation horizon guided by a novel Teacher Rescue Rate (TRR) metric to operate strictly within reliable supervision regimes; and (ii) Selective Distillation, which filters out safety-neutral tokens to restrict gradient updates exclusively to safety-pivotal transitions. Extensive evaluations across reasoning models up to 32B parameters demonstrate that EOPSA slashes rollout computation by sim50% and backpropagates through merely sim2% of tokens, consistently outperforming full-token distillation baselines in both safety compliance and reasoning retention.

Decision models target structured tasks by directly predicting choices or scores, avoiding autoregressive decoding latency. However, transferring a generative LLM's ranking knowledge to a decision model remains challenging: the teacher expresses preferences through a ranked list of document ID sequences, while the student determines the ranking using scores from the first-token position. To bridge this gap, we introduce DecisionRank, a decision model trained through item-space on-policy distillation (OPD). Item-space OPD constructs the student's rollout by sorting its document scores into a ranked sequence. A generative teacher takes the resulting ranking list as inputs and provides conditional feedback to directly supervise those scores. Combined with offline ranking supervision, DecisionRank achieves state-of-the-art performance on both general and reasoning-intensive retrieval benchmarks such as TREC DL, BEIR, and BRIGHT. Across four benchmarks, item-space OPD consistently outperforms alternative training objectives. Even at 1.7B parameters, DecisionRank surpasses its 27B generative teacher on TREC DL19--23. At 8B, it outperforms its generative listwise counterpart while running 24.5times faster on TREC DL and 16.7times faster on BRIGHT.

Reasoning models think out loud, but much of what they say is noise. We introduce OPSDC (On-Policy Self-Distillation for Reasoning Compression), a method that teaches models to reason more concisely by distilling their own concise behavior back into themselves. The entire approach reduces to one idea: condition the same model on a "be concise" instruction to obtain teacher logits, and minimize per-token reverse KL on the student's own rollouts. No ground-truth answers, no token budgets, no difficulty estimators. Just self-distillation. Yet this simplicity belies surprising sophistication: OPSDC automatically compresses easy problems aggressively while preserving the deliberation needed for hard ones. On Qwen3-8B and Qwen3-14B, we achieve 57-59% token reduction on MATH-500 while improving accuracy by 9-16 points absolute. On AIME 2024, the 14B model gains 10 points with 41% compression. The secret? Much of what reasoning models produce is not just redundant-it is actively harmful, compounding errors with every unnecessary token.

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.

On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.

Multilingual reasoning transfer is crucial for extending reasoning capabilities of large language models (LLMs) beyond high-resource languages. On-policy self-distillation (OPSD) and its variants have emerged as a promising paradigm, providing dense token-level supervision on student-generated rollouts, yet their objectives do not explicitly prioritize reasoning signals most critical to cross-lingual transfer. We characterize that target-language reasoning comprises the generation of both surface text and reasoning pivots, which are decisions that advance or redirect the reasoning process and shape subsequent inference. This motivates concentrating privileged distillation around such pivots. We therefore propose RP-OPSD, Reasoning-Pivot-guided On-Policy Self-Distillation, using the distributional shift between matched teacher views with and without an English reference solution as an operational proxy to guide privileged distillation and reference anchoring. Experiments on mathematical reasoning benchmarks covering 17 languages and multiple difficulty levels show that our method outperforms strong multilingual reasoning baselines and OPSD variants. Further analysis reveals that RP-OPSD concentrates privileged distillation on reasoning-control and problem-condistioned state-update tokens, while downweighting it for tokens that mainly support surface realization. Our code is available at https://github.com/NJUNLP/RP-OPSD.

On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.

On-policy self-distillation (OPSD) trains a student to match a privileged teacher distribution along its own sampled trajectory. Standard OPSD applies this supervision to unverified student rollouts while conditioning the teacher on privileged context, typically a reference solution. We separate these roles in a factorial analysis and find that scaffold correctness has a stronger effect on downstream accuracy than context correctness. Unverified scaffolds create an imitation gap because the teacher can use information unavailable to the student. This gap shrinks with model scale, yet OPSD continues to supervise mostly unverified trajectories. In contrast, verified scaffolds remain effective even when the teacher is conditioned on the student's own unsuccessful rollout. Based on this finding, we introduce OASIS, which retains the OPSD objective but supervises mostly verified by label on-policy trajectories and replaces written solutions with unverified model-generated attempts as the teacher context. OASIS therefore requires only final-answer labels. Across Qwen3-1.7B, 4B, and 8B on AIME 2024, AIME 2025, and HMMT 2025, OASIS improves over the base model by 3.2--3.8 points on average, while OPSD's gain falls from 3.05 points at 1.7B to 0.14 at 8B. At 8B, OASIS improves over OPSD by 3.05 points, showing that verified on-policy scaffolds preserve the effectiveness of self-distillation as models scale.

On-policy distillation (OPD) strengthens language-model reasoning, yet whether students acquire new factual knowledge or compositional skill for multi-step reasoning remains unknown. We separate these capabilities using a controlled synthetic framework that measures the student's initial capabilities and independently controls the teacher's additional facts, compositional skill, or both. Across four models from three families, reverse-KL OPD reliably transfers compositional skill across unseen reasoning structures, but transfers minimal factual knowledge. Decoupling the distillation recipe reveals the source of this asymmetry: replacing reverse KL with forward KL restores factual transfer, whereas student rollouts specifically improve the execution of multi-step reasoning. Experiments on recent factual QA and competition mathematics show a similar asymmetry under reverse-KL OPD, yielding notable reasoning gains without factual memory expansion. Together, these results demonstrate that on-policy distillation does not expand a model's parametric knowledge, but instead teaches it to organize and compose the knowledge it already possesses.

On-policy self-distillation (OPSD) teaches large language models new skills through a teacher that shares the student's backbone and supervises its own rollouts. Existing teachers either inject privileged context at the input -- inducing post-hoc rationalization -- or fine-tune weights, accumulating drift and forgetting across tasks. We propose \method, whose teacher differs from the student only by a learnable soft prompt: trained on (x, y_gold) pairs with the backbone frozen, the prompt yields a task-specific teacher that preserves the student's exact representational geometry. \method\ extends naturally to multi-task settings by routing each example in a merged corpus to its corresponding soft-prompt teacher, allowing a single student to absorb knowledge from K teachers in parallel; at inference, all prompts are discarded. On Qwen3-1.7B-Base and Phi-4-mini-instruct across four tasks (Science, Tool Use, Biology, Math), the single-task variant (OPD with a PT teacher) matches or exceeds full fine-tuning while training orders of magnitude fewer parameters, and the multi-task variant achieves the best overall average (56.2 on Qwen3-1.7B-Base) while preserving general-capability benchmarks -- in contrast to sequential SFT, which degrades both.

On-Policy Self-Distillation (OPSD), which aligns a student model's token-level distribution with that of its self-teacher prompted by privileged context, has emerged as a promising direction to mitigate reward sparsity in sequence-level post-training paradigms. However, OPSD often fails to achieve continuous performance gains during training. In this paper, we find that the model's limited self-teaching capability underlies this phenomenon by generating unreliable guidance on certain samples. To address this problem, we propose Teacher-Evolution Self-Distillation (TESD), which enables the self-teacher to generate rollouts and receive environmental feedback based on task correctness and context independence. First, using these rewards as training objectives, we perform teacher-oriented optimization to continuously enhance the model's self-teaching capability during distillation. Second, by estimating teacher guidance reliability from these rewards, we apply adaptive student-oriented optimization to down-weight samples with unreliable guidance. Extensive experiments across multiple datasets and model scales show that TESD consistently outperforms representative token-level and sequence-level methods, highlighting the necessity of improving supervision quality in OPSD.

Speculative decoding (SD) accelerates large language model inference by reducing the sequential cost of token-by-token generation. Advanced SD methods reduce proposal cost with parallel drafters that predict entire blocks in one forward pass, but overall speedup still depends on acceptance length. On-policy distillation (OPD) can push well-trained drafters beyond acceptance-length plateaus, yet conventional pipelines collect supervision through sequential draft-and-verify rollouts. Our key insight is that on-policy supervision need not inherit these dependencies: a draft block can be supervised using only its reference prefix and draft-sampled history. We propose SpecOPD, a branch-parallel OPD framework that parallelizes draft sampling and target supervision across independent branches drawn from the evolving drafter policy at reference anchors. We pack these branches into proposal trees to share target-prefix computation, using tree masks for full attention, branch-consistent indexer groups for sparse attention, and indexed state replay for linear attention to preserve each branch's history. We train the drafter with an E2E-TV surrogate that directly targets acceptance length. Our study spans 8B full-attention (GQA), 27B full-linear (GQA--GDN), and 125B sparse-linear (QSA--GDN) targets, three parallel draft architectures (DFlash, DSpark, and DFlash V2), and four task domains (dialogue, coding, mathematics, and agentic). SpecOPD achieves up to 41.45% higher mean acceptance length, 16.09times supervised-token throughput over sequential-rollout OPD under native configurations, and up to 3.56times generation speedup over autoregressive decoding.

Supervised fine-tuning (SFT) is the predominant method for adapting large language models (LLMs), yet it often struggles with generalization compared to reinforcement learning (RL). In this work, we posit that this performance disparity stems not just from the loss function, but from a more fundamental difference: SFT learns from a fixed, pre-collected dataset, whereas RL utilizes on-policy data sampled from the current policy. Building on this hypothesis, we introduce one-token rollout (OTR), a novel fine-tuning algorithm that guides SFT with the policy gradient method. OTR reframes the autoregressive learning process by treating each token generation as a single-step reinforcement learning trajectory. At each step, it performs a Monte Carlo ``rollout'' by sampling multiple candidate tokens from the current policy's distribution. The ground-truth token from the supervised data is then used to provide a reward signal to these samples. Guided by policy gradient, our algorithm repurposes static, off-policy supervised data into a dynamic, on-policy signal at the token level, capturing the generalization benefits of on-policy learning while bypassing the costly overhead of full sentence generation. Through extensive experiments on a diverse suite of challenging benchmarks spanning mathematical reasoning, code generation, and general domain reasoning, we demonstrate that OTR consistently outperforms standard SFT. Our findings establish OTR as a powerful and practical alternative for fine-tuning LLMs and provide compelling evidence that the on-policy nature of data is a critical driver of generalization, offering a promising new direction for fine-tuning LLMs.

On-policy distillation (OPD) reduces train-test state mismatch by training a student on its own generated trajectories, but weak students may visit teacher-misaligned prefixes where supervision is less representative. We introduce SAKI (Supervision Allocation with KL-constrained Interpolation), which combines a KL-constrained teacher-guided rollout with maximal coupling and reuses realized accept/correction events to route token-level supervision. Accepted positions retain sampled-token reverse-KL supervision, while correction positions receive direct supervision on the teacher's highest-probability token. Under maximal coupling, the correction probability is exactly TV(p_t, q_t), so the same trust-region radius controls rollout deviation and upper-bounds intervention and specialized-supervision frequency. We further implement an engine-resident speculative verifier that preserves the exact-q trajectory distribution and coupling semantics while improving matched-workload rollout throughput by 4.22x. Across seven mathematical reasoning benchmarks, SAKI improves the matched teacher-guided baseline in Mean@8 and Pass@8 for both 1.7B and 0.6B students. Placement controls and fixed-prefix analysis further support correction-triggered routing as a conflict-adaptive supervision signal.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for improving large language models (LLMs) on various tasks, yet its sparse outcome rewards lack token-level credit assignment for intermediate steps. To address this, on-policy self-distillation (OPSD) leverages a self-teacher with privileged context to provide additional dense learning signals. However, because the self-teacher is often overconfident and imposes excessive penalties on long reasoning trajectories, OPSD frequently struggles in practice. To mitigate this, we propose self-instructing policy optimization (SIPO) with a contrastive self-teacher to provide dense credit. At each iteration, SIPO samples multiple rollouts per prompt from the current policy, scores them with environment rewards, and constructs two teacher contexts for each rollout by pairing the reference answer with mistakes made within the group. The model then re-evaluates its own responses under both contexts, using the difference between the two teacher log-probabilities as token-level feedback, so that biases shared by both contexts are expected to largely cancel. The resulting objective yields a token-level advantage for every rollout: the reward still sets the main direction of each update while the self-teacher redistributes credit across tokens. Even in groups where every rollout fails and group-relative advantages vanish, SIPO still provides a learning signal. By preserving direct optimization of the task reward while providing dense, token-level feedback, this approach bridges reinforcement learning and on-policy self-distillation. Extensive experiments across multiple reasoning and code-generation benchmarks demonstrate that SIPO outperforms both RLVR and OPSD baselines without an external teacher or additional generation.

A deployable text-to-image diffusion model must hold several capabilities at once, such as instruction following, text rendering and human preference, and must sample in a few steps. Capabilities and few-step sampling are built in separate stages: a full-step model first consolidates capabilities through multi-teacher on-policy distillation, then serves as a fixed teacher for step distillation. Every full-step model we evaluate scores lower once compressed, and the second stage cannot begin until the first finishes. We introduce StepX-OPD, which merges the two stages: one student acquires every capability while learning to sample in a few steps, so frozen specialists supervise it on the states its own rollout visits rather than on a longer trajectory it never runs. Because a decomposition of the rollout's KL weights velocity mismatch most heavily near the clean end, we also regress the student's velocity on the low-noise part of the rollout. Separately, we find that capability integration makes models write prompt words into images on prompts that never asked for text, and we give a variant that lowers it. We evaluate on SD3.5-Medium and FLUX.1-dev across instruction following, text rendering, image quality and human preference. On both architectures, StepX-OPD attains the highest normalized average score among the four-step methods compared and exceeds the forty-step Flow-OPD model, and on SD3.5-Medium it trains with about 37% fewer GPU-hours than sequential DiffusionOPD followed by step distillation.

Multimodal deep search requires an agent to solve open-world problems by chaining search, tool use, and visual reasoning over evolving textual and visual context. Two bottlenecks limit current systems. First, existing tool-use harnesses treat images returned by search, browsing, or transformation as transient outputs, so intermediate visual evidence cannot be re-consumed by later tools. Second, training data is usually built by fixed curation recipes that cannot track the target agent's evolving capability. To address these challenges, we first introduce a visual-native agent harness centered on an image bank reference protocol, which registers every tool-returned image as an addressable reference and makes intermediate visual evidence reusable by later tools. On top of this harness, On-policy Data Evolution (ODE) runs a closed-loop data generator that refines itself across rounds from rollouts of the policy being trained. This per-round refinement makes each round's data target what the current policy still needs to learn. The same framework supports both diverse supervised fine-tuning data and policy-aware reinforcement learning data curation, covering the full training lifecycle of the target agent. Across 8 multimodal deep search benchmarks, ODE improves the Qwen3-VL-8B agent from 24.9% to 39.0% on average, surpassing Gemini-2.5 Pro in standard agent-workflow setting (37.9%). At 30B, ODE raises the average score from 30.6% to 41.5%. Further analyses validate the effectiveness of image-bank reuse, especially on complex tasks requiring iterative visual refinement, while rollout-feedback evolution yields more grounded SFT traces and better policy-matched RL tasks than static synthesis.

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated carefully. The standard practice is to use this data directly on the model that will be deployed, for example by running GRPO on the deployment student. We argue that this is often an inefficient allocation because it overlooks a reward-density principle: sparse sequence-level reward should train models where exploration is productive, while dense token-level teacher reward should be used where the aim is to compress behavior into a smaller model. In this view, GRPO-style sparse RL and OPD-style dense teacher supervision are not separate recipes; they are different reward-density regimes. The allocation rule is simple: use scarce labeled training data upstream on the strongest model that can turn it into reward-shaped behavior, then transfer that behavior downstream as dense supervision. We evaluate this rule on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student, while transfer from the same teacher before RL underperforms. The bridge is important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts is consistently strongest on MATH before any post-bridge student-side sparse RL, and also gives the best pre-Stage~3 AIME endpoints for the canonical 8B/14B teachers. The bridge also makes later student-side sparse RL effective: GRPO that is weak on a cold student lifts MATH from 75.4% to 78.5% after the bridge and outperforms a matched replay control by 2.8 points. The operational principal is to avoid using scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

On-policy distillation (OPD) is a widely adopted post-training technique for LLM reasoning. It is commonly believed to transfer knowledge from a stronger teacher, yet what OPD actually distills into the student's internal representations remains unclear. We study this question with sparse crosscoders, which learn one feature dictionary shared by the student before and after OPD and the teacher. Standard crosscoder analyses, however, identify model-specific features but cannot tell how a model's use of its features changes, since all models are encoded into one set of feature activations. We therefore propose the swap readout, which reads each student checkpoint's feature activations on its own, measuring how training changes the student's use of each feature, even for checkpoints unseen by the crosscoder. Across three OPD settings, we find that OPD neither creates features nor passes on the teacher's own, and leaves the firing rates of over 98% of the student's frequently used features within 20%. We further examine the SFT warm-up on the teacher's rollouts that commonly precedes OPD and makes it more effective. Rather than adding features, the warm-up reweights the shared ones in two ways. First, it already raises and lowers many of the features that OPD later raises and lowers, doing part of OPD's work in advance. Second, it changes features that OPD alone would not, notably those for conversation format, reasoning style, and mathematical notation, and these changes persist through OPD. Imposing this reweighting on a directly distilled student's features, without changing its weights, brings its accuracy close to that of the warmed-up student, whereas the same change on shuffled features does not. Together, these findings suggest that OPD reweights existing features rather than acquiring new ones: the student learns from the teacher how to use the features they already share.

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to 0.715 while keeping UTMOS. With 10-NFE training rollouts and 32-NFE evaluation, GROW retains comparable performance while training 2.9x faster than 32-NFE DiTAR-GRPO. We will open-source complete GROW codes, faithful DiTAR reproduction, and all model checkpoints.

Pretrained world action models (WAMs) provide generalist capabilities across diverse robotic manipulation tasks, yet improving target-task performance to an expert level without degrading pretrained skills remains challenging. We explore on-policy distillation (OPD) for WAMs and introduce WAM-OPD. WAM-OPD inherits the advantage of OPD methods that transfer task-specific teacher knowledge under the student's own induced distribution, rather than directly fitting the student to a narrow task-specific data distribution. However, in closed-loop manipulation, the observation histories change as the student policy evolves, requiring fresh environment rollouts to remain on-policy. Applying OPD to WAMs entails repeated data collection, which is costly even in simulation and often impractical on real robots. To avoid repeated environment rollouts during distillation, we introduce prefix-weighted trajectory replay (PWTR). PWTR uses a fixed trajectory pool composed primarily of initial-student rollouts, supplemented with task-specific teacher rollouts to broaden trajectory coverage. For each trajectory replayed from this pool, PWTR conditions the current policy on successive stored histories to generate fresh denoising paths, along which the task-specific teacher provides supervision. Although these denoising paths are refreshed as the policy evolves, the replayed environment trajectories remain fixed. PWTR therefore reweights per-decision distillation losses using proxy importance weights derived from path scores accumulated over the trajectory prefix preceding each decision to mitigate the resulting shift in the history distribution. Simulated and real-world experiments demonstrate task adaptation without additional environment interaction during distillation. In both settings, WAM-OPD improves target-task performance while retaining near-initial performance on tasks excluded from adaptation.

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

We propose OPSD-V, an on-policy self-distillation paradigm for post-training few-step autoregressive (AR) video diffusion models. Existing few-step AR video generators can produce long videos with low latency, but still suffer from error accumulation and weakened motion dynamics during long autoregressive rollout. OPSD-V reduces long-horizon degradation while preserving the original few-step inference path. The key idea is to introduce real long-video data as temporal context during training and use it to provide dense trajectory-level supervision. Specifically, the student follows the exact inference-time rollout, generating each chunk conditioned on its own previously generated KV cache. In parallel, the teacher is evaluated at the same student-visited denoising states, but uses a cleaner AR-consistent temporal cache in which older history can be replaced by real-video context. This provides dense denoising-level corrective targets under on-policy AR cache dynamics, without changing the sampler, number of denoising steps, or inference-time cache mechanism. We apply OPSD-V to representative few-step AR video models, including Self-Forcing and LongLive. Experiments show consistent improvements in visual quality, motion dynamics, and VBenchLong scores. A user study with 10 participants comparing 20 video pairs shows that OPSD-V is preferred over the base models in 66.0% of overall-preference judgments (82.5% excluding ties).

Prompt injection is listed as the \#1 threat to AI agents. When an agent accesses external data from websites, files, or emails, an attacker may inject a prompt into the data, saying, "Ignore all prior instructions and perform <an attacker's task>." To prevent arbitrary manipulation of agents, defenders try to train secure LLMs, which, however, still suffer from near 100% attack success rates (ASRs) against adaptive prompt injections. We note that this is because existing defensive finetuning recipes rely on sequence-level feedback signals (in DPO or GRPO). Treating an entire output equally prevents the model from learning precisely which output tokens are insecure. In this paper, we propose Secure On-Policy Distillation (SecOPD) that provides token-level feedback to guide defensive fine-tuning. The LLM receives an injected sample and produces a rollout, whose tokens are scored by the initialization model given the corresponding clean input. With more fine-grained training signals, our defended Qwen3.6-27B achieves a 9.0% ASR against the SoTA PISmith adaptive prompt injections, compared to 94.0% for the prior SoTA, Meta-SecAlign. The obtained security generalizes to domains completely unseen in training: in agentic tool calling, SecOPD achieves a 4.7% ASR compared to 5.5% for Meta-SecAlign. Code and the model are available at https://github.com/pppyb/SecOPD and https://huggingface.co/pybbb/Qwen3.6-27B-SecOPD.

On-policy distillation (OPD) trains a student model on its own trajectories using dense token-level feedback from a stronger teacher model. Since each update is conditioned on the reasoning prefix already generated by the student, the prefix also shapes how effectively teacher feedback is converted into learning. We find that shared prefixes can lead to weak token-level updates, a phenomenon we call Prefix-Induced Supervision Attenuation (PISA). This attenuation arises in two common cases. (i) High student confidence can weaken corrective gradients even when the teacher disagrees. (ii) Tokens that rely on earlier reasoning can receive learning signals as weak as those for simple local continuations. To solve this problem, we propose Trajectory Dropout, a simple training-time intervention that exposes these weakened signals. The student first performs a standard full-context rollout to generate a complete trajectory. During training, we randomly drop a certain proportion of the student's reasoning trajectory, while the teacher continues to observe the complete trajectory for token-level supervision. This intervention strengthens corrections for overconfident predictions and introduces additional supervision at prefix-sensitive positions. Trajectory Dropout consistently improves average performance across teacher--student model pairs of different scales and six mathematical reasoning benchmarks, while also yielding gains on two out-of-domain benchmarks. It can also be flexibly integrated into existing OPD variants with negligible computational overhead, further improving their performance. These results demonstrate that Trajectory Dropout provides a simple mechanism for strengthening token-level supervision across model scales and OPD objectives.

Since the introduction of the GRPO algorithm, reinforcement learning~(RL) has attracted increasing attention for LLM post-training, yet training efficiency remains a critical challenge. In mainstream RL frameworks, inference and training are co-located on the same devices, and their synchronous execution prevents concurrent inference and training. In this work, we revisit the strategy of separating inference and training deployment, and propose a periodically asynchronous framework that transforms synchronous RL training into an asynchronous producer--consumer pipeline. By synchronising model weights at the beginning of each training iteration and generating all rollouts from the same policy, the proposed framework remains inherently on-policy, avoiding the off-policy bias introduced by existing asynchronous approaches without any modification to standard RL algorithms. We further introduce a unified tri-model architecture and a shared-prompt attention mechanism to support efficient asynchronous execution and reduce redundant computation. Experiments on NPU platforms show that the proposed framework achieves around 2times throughput improvement from asynchronous execution, with additional gains from system-level optimisations, substantially outperforming mainstream RL frameworks in end-to-end training throughput while maintaining comparable accuracy. Further validation on GPU platforms confirms that the proposed framework generalises effectively across hardware architectures, indicating its potential for widespread application.

Reinforcement learning with verifiable rewards (RLVR) plays a crucial role in expanding the capacities of LLM reasoning, but GRPO-style training is dominated by expensive rollouts and wastes compute on unusable prompts. We propose Prompt Replay, an overhead-free online data selection method for GRPO that reuses prompts only (not trajectories), to preserve on-policy optimization. After each step, we insert prompts with medium difficulty into a buffer, and prioritize prompts closer to a pass rate of 0.5 (half answers correct, half wrong) to maximize the advantage, thus learning signal. Training batches are formed by mixing reused prompts with fresh samples, with cooldown steps and max reuse times controlling aggressiveness vs risk of overfitting. Across multiple model families (Llama-3.2- 3B, Qwen3-8B) and training datasets (Dolci, Polaris), evaluated using average accuracy on six standard math benchmarks, Prompt Replay reduces zero-variance prompts, increases mean absolute advantage and shows faster initial accuracy gains. Yet, it plateaus and converges with the baseline, as too aggressive configuration was used. The method is most efficient when the rollouts are the primary bottleneck and the dataset is difficult for the model. We additionally observe that Qwen2.5-Math can exhibit spurious-reward effects that invalidates ablations, raising a warning signal for using it as a sole testbed for GRPO method research.

On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: https://github.com/ShenzhiYang2000/OPRD.

On-policy distillation (OPD) improves LLM reasoning by training a student model on its own generated outputs, but standard OPD treats all student-generated outputs (SGOs) equally regardless of their informativeness. We observe a consistent asymmetry in controlled filtering experiments: in both OPD and on-policy self distillation (OPSD), training only on incorrect SGOs outperforms training only on correct ones. Our further analysis suggests that models trained on correct-only SGOs tend to generate shorter reasoning traces and show weaker reflection behavior, while incorrect SGOs better preserve exploratory reasoning near the model's capability boundary. To exploit this signal without requiring full answer-containing rollouts, we introduce ReNIO, which Reweights Negative trajectory Importance for LLM On-policy distillation. By using the student-to-teacher probability ratio, ReNIO identifies pivotal tokens leading to wrong reasoning traces and aggregates their information into a normalized sample weight, inherently assigning larger weights to likely negative trajectories without observing the correctness of final-answer. Since Re-NIO only uses prefix-conditioned token probabilities, it preserves OPD's prefix training advantage over full-rollout reinforcement learning. Across both mathematical reasoning and code generation tasks, ReNIO improves both OPD and OPSD, with representative relative gains of up to 8.90% for Qwen3-1.7B and 10.00% for R1-Distill-Qwen-7B on mathematical reasoning benchmarks. Code repo: https://github.com/BDML-lab/ReNIO.