On-Policy Distillation

Mixture-of-Experts (MoE) language models route each token through a small subset of experts, making routing patterns useful for identifying task-relevant experts during downstream adaptation. Yet current approaches have two limitations: task experts are typically identified from aggregate routing statistics that reflect usage rather than association with successful task completion, and task-expert activations remain underexplored as signals for supervision allocation. We introduce Task-Expert-Aware Supervision (TEXAS), which combines correctness-conditioned task expert discovery with token-level supervision allocation. TEXAS compares expert activations on instances that the base model solves successfully and those it fails to solve, and retains experts more strongly activated on successful instances. During fine-tuning, it upweights answer tokens in failed instances when they activate these experts. TEXAS therefore leverages existing routing behavior without restricting adaptation to a fixed expert subset or imposing an explicit target routing distribution. Across three MoE models and six benchmarks, TEXAS achieves the best or tied-best performance in 17 of 18 settings and improves over the strongest baseline by 1.3--1.5 points on average. Ablations and further analyses validate both the discovered experts and the resulting supervision strategy.

Reinforcement learning with verifiable rewards (RLVR) broadcasts a single response-level reward to every token, while on-policy distillation (OPD) scores each token against a stronger teacher for a dense advantage but caps performance at teacher quality and discourages exploration beyond it. Their complementarity makes combining RLVR and OPD promising, but we find that fusing the two advantages with a fixed coefficient triggers entropy collapse from two miscalibrations: a magnitude mismatch, where token-level OPD advantages can spike far beyond the bounded RLVR advantage and erase its signal, and a temporal mismatch, where sustained full-strength OPD keeps pulling the student toward the teacher and limits exploration needed to surpass it. We propose SAF, a Stable Advantage Fusion framework that resolves both issues via a lightweight, four-stage pipeline applied only to the OPD advantage: a sparsify-then-compress mechanism for magnitude control paired with a warm-up-then-anneal mechanism for temporal control, with each stage independently switchable and adding negligible overhead. Instantiating RLVR with GRPO, we evaluate SAF across seven mathematical reasoning and code generation benchmarks with Qwen3-1.7B/4B/8B: SAF avoids entropy collapse and consistently outperforms fixed-coefficient GRPO+OPD fusion, improving the aggregate score by 0.51-2.70% across all six model-domain settings while achieving more stable training.

Autonomous Cyber Operations (ACO) are increasingly important for defending enterprise networks as cyber threats continue to evolve in sophistication. ACO applications commonly employ Reinforcement Learning (RL) agents to learn defensive behaviors through interaction with environments. However, RL agents typically require extensive exploration during training, often resulting in unstable behavior and poor initial decision-making before converging toward effective defense strategies. In this work, we investigate the use of a Large Language Model (LLM) to improve autonomous defensive decision-making within an ACO environment. Through prompt engineering rather than fine-tuning, we demonstrate that an 8-billion parameter LLM pretrained on cybersecurity data can outperform a baseline RL agent in a modified CybORG CAGE Challenge 2 environment. We then propose an online policy distillation framework that transfers the LLM's defensive policy into a lightweight RL agent containing only 64,910 parameters, reducing model size by several orders of magnitude while maintaining effective defensive capabilities. This provides a pathway toward operationalizing frontier cybersecurity models within lightweight, deployable agents. To evaluate transferability, we construct CybORG scenarios ranging from 4 to 12 hosts and assess the approach across varying network configurations. We also evaluate teacher-guided RL stabilization strategies and observe that none consistently surpass the optimized teacher policy, suggesting policy-alignment limitations between reward-driven RL optimization and teacher-guided defense strategies. Our results demonstrate the potential of cybersecurity-focused LLMs as sources of expertise for autonomous cyber defense, while policy distillation provides a practical path toward operationalizing frontier cybersecurity models within efficient, scalable agents.

Multimodal on-policy distillation (OPD) transfers fine-grained visual knowledge by supervising student-generated trajectories with a privileged-view teacher. Yet its next-token corrections are source-mixed, combining visual signals with linguistic priors and teacher-specific effects. The key challenge is to estimate which corrections are supported by visual evidence, not merely where or how strongly to distill. We introduce Visual Attribution Distillation (VAD), a counterfactual target-reconstruction algorithm that estimates the visually attributable part of a teacher correction. At each student-generated prefix, VAD evaluates the same fixed teacher with the relevant evidence present and removed. The corresponding change in centered log-probabilities defines ut, a signed proxy for the visual evidence direction that estimates how revealing the evidence supports or refutes candidate tokens. VAD projects the original correction onto this proxy to obtain an intervention-aligned component and a proxy-unexplained residual, then reconstructs a student-anchored target from the former. During training, this reconstructed target supplies the primary supervision signal, while the privileged teacher contributes a weak regularizer. Across six fine-grained visual benchmarks at 4B and 9B scales, VAD outperforms direct privileged-view distillation and visual-advantage weighting. Token- level and controlled-target analyses show that the proxy-aligned component is enriched in task-relevant visual corrections and yields stronger target shifts, especially when evidence refutes a mistaken answer. These results support counterfactual target reconstruction as an effective alternative to source-mixed supervision.

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the $β=1$ member of a broader policy-optimization family, where $β$ weights the KL penalty anchoring the student to a reference policy. This equivalence turns $β$ from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce $β$-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of $β$ selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that $β$-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.

On-policy distillation (OPD) provides dense token-level supervision from a teacher, but its effectiveness can depend on teacher consistency, meaning that the model providing OPD supervision should also have generated the demonstrations used to train the supervised fine-tuning (SFT) reference. However, this condition is frequently violated in practice when SFT data have mixed or unknown provenance or when different models are preferred for SFT data generation and subsequent distillation. In such cross-teacher settings, even a stronger OPD teacher can yield little improvement over the SFT reference. We find that raw teacher--reference disagreement contains potentially useful context-specific teacher evidence as well as a recurring component associated with differences in wording, formatting, and reasoning cadence. We introduce Lightning OPD 2.0 with cross-fitted style residualization, which uses rollout-level cross-fitting to estimate this recurring component as an operational proxy for style-token bias and subtracts it before constructing the token-level OPD update. Across mathematical reasoning and code generation benchmarks, Lightning OPD 2.0 consistently outperforms Lightning OPD in cross-teacher settings. Starting from Klear-Reasoner-8B-SFT, Lightning OPD 2.0 reaches 82.4% on AIME 2024 and 63.0% on LiveCodeBench v5. Together, these results establish Lightning OPD 2.0 as a practical approach to cross-teacher OPD, relaxing teacher consistency as a prerequisite and allowing the SFT data generator and distillation teacher to be selected independently. Code will be released soon.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language model agents. However, terminal rewards provide only coarse trajectory-level supervision, leaving successful behaviors, recurring mistakes, and incidental choices entangled in the same outcome signal. Existing agentic self-distillation methods enrich sparse supervision with natural-language skills, but skills retrieved externally or extracted from a single trajectory by stronger models may mismatch current experience, exceed the policy's capability, or remain path-specific. We propose Group-Reflective Self-Distillation (GRSD), which derives capability-aligned and outcome-discriminative guidance from the policy's own verified rollouts. For each prompt, the policy reflects on each verified trajectory in an on-policy group, and a stop-gradient snapshot contrasts the resulting reflections from successful and failed rollouts to construct group-level privileged guidance. Conditioned on this guidance, a self-teacher refines turn-level credit assignment by modulating outcome-based advantages while preserving the verifier-determined learning direction. Experiments across multiple agentic environments and model scales demonstrate that GRSD consistently outperforms competitive baselines and generalizes more effectively to unseen tasks.

Recent advances in post-training Large Language Models (LLMs) increasingly rely on Reinforcement Learning with Verifiable Rewards (RLVR) or On-Policy Self-Distillation (OPSD). While OPSD provides dense, logit-level supervision, it inherently suffers from exposure bias due to the privileged information of the self-teacher. In multi-turn agentic settings, this leads to reasoning route convergence and the loss of clear optimization directions. To tackle these challenges, we introduce Contrastive Reinforced Policy Optimization (CRPO), which reformulates agentic OPSD from a contrastive learning perspective. By leveraging predictive entropy to distinguish between positive positions (reflective exploration) and negative positions (exposure bias), CRPO conducts group-wise contrast to preserve reliable, fine-grained optimization signals. Extensive evaluations across 13 challenging reasoning and deep-search benchmarks demonstrate that CRPO consistently outperforms existing reinforcement learning and self-distillation baselines, significantly enhancing training stability and generalization in long-horizon interactions.

Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.

Recent work on LLM agents is shifting from external capability elicitation to capability internalization, enabling agents to retain useful skills without retrieval at inference time. On-policy self-distillation (OPSD) offers a promising direction, but many existing methods typically supervise students by scoring actions along student-generated trajectories. Such supervision has two limitations: teacher preferences are not validated by environment outcomes, and action-level scores underuse information from student rollouts, teacher rollouts, and their behavioral relationship. We therefore advocate outcome-verified teacher supervision and comparative learning over teacher-student trajectories. Based on this view, we propose Outcome-Verified Comparative Self-Distillation (OVCSD). OVCSD organizes failed student rollouts into a prefix tree, adaptively invokes a skill-conditioned teacher from student-reached states, and retains only outcome-verified successful continuations. It then applies localized comparative learning at the first state-aligned divergence and distills the post-divergence teacher suffix to transfer completion behavior. Experiments on ALFWorld and WebShop across three model scales show that OVCSD consistently outperforms skill-free RL and existing self-distillation baselines, achieving up to 29.7 and 5.4 absolute success-rate gains over the strongest baselines on ALFWorld and WebShop, respectively, while adding less than 3% privileged interaction during training.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

A single reinforcement-learning run can produce a strong reasoner yet an incomplete teacher: it often amplifies only a subset of the valid solution modes. We argue that reinforcement learning (RL)-trained policies should therefore be viewed as local probes of a multi-basin reasoning solution manifold, rather than as globally reliable supervisors. Based on this view, we propose an expand-then-compress framework that couples teacher construction with multi-teacher policy distillation. In the expansion stage, Residual Group Relative Policy Optimization (RGRPO) trains a sequence of teachers from a common initialization and redirects each later round toward examples not yet covered by the accumulated teacher union. In the compression stage, reliability-gated Teacher-Union On-policy Distillation (TU-OPD) lets the student learn from its own response prefixes. For each example, only reliable teachers contribute, and their sampled-token OPD losses are weighted by their per-example quality. We further introduce Consensus-Residual Decomposition, which preserves a winner teacher's excess token preferences over its reliable peers, preventing specialist behavior from being suppressed during teacher aggregation. Experiments on mathematical reasoning, code generation, and instruction following show that the resulting Qwen3-1.7B student consistently outperforms the strongest individual teacher across all three domains, yielding relative improvements of 2.0%, 8.3%, and 6.9%, respectively, while retaining single-model inference. These results establish a simple but powerful principle: stronger students can be obtained not by selecting a single better teacher, but by deliberately constructing and compressing a complementary teacher union.

Deep neural networks (DNNs) have achieved remarkable success in classical machine learning problems. However, they are known to be vulnerable to adversarial attacks. Countermeasures proposed in the literature, notably Information Bottleneck Distillation (IBD) introduced by Kuang et al., degrade the classification accuracy on clean inputs while improving the robustness to adversarial inputs. In this work, we extend the IBD framework by introducing an extra teacher model (clean teacher) trained with only clean inputs, into the distillation process from a robust teacher model trained by adversarial training. The features of both clean and robust teachers are transferred to the student through a cross-layer attention matrix. Experimental results on the CIFAR-10 and CIFAR-100 datasets show that the proposed method improves classification accuracy on clean samples compared to the original IBD, while maintaining similar accuracy on adversarial samples. Furthermore, our methods are competitive with state-of-the-art approaches, including the recent dual-teacher distillation framework B-MTARD, particularly in terms of the harmonic mean between clean and robust accuracy. We also analyze the impact of different training settings that have different influences on the attention module.

Comparative feedback, asking people which of two behaviors they prefer, has become a standard way to align robot and agent behavior with human intent when the reward itself cannot be specified directly. Preference-based reward learning typically casts the human teacher as a passive oracle answering learner-generated queries. We argue this forfeits the teacher's defining advantage: knowledge of the objective. A teacher who knows the target can construct training examples more efficiently than any learner-driven acquisition strategy, an advantage that widens as the reward's feature dimension grows. However, exploiting this advantage requires an accurate model of what the learner currently knows. We therefore recast preference learning as a human-autonomy team problem coupling two behavioral models: the teacher maintains a model of the learner to design an informative curriculum, and the learner maintains a second-order model of the teacher's model, emitting structured preference constraints (understanding statements) that keep the teacher's model of the learner synchronized. In simulation, an informed teacher outperforms learner-led selection; teacher-model drift under alternating teachers erodes this advantage; and understanding statements repair it, with second-order (ToM-2) statements outperforming mean-belief statements when the teacher's error about the learner is concentrated in a particular direction rather than spread evenly.

The growing capability of image generation models has made synthetic images a routine presence in open media, making robust and generalizable AI-Generated Image (AIGI) detection increasingly essential. While multi-modal large language models (MLLMs) offer a transparent alternative to black-box binary scoring, we observe that current MLLM-based detectors still exhibit notable perception bottlenecks in capturing fine-grained anomalies. They primarily focus on how visual evidence is organized and synthesized, leaving the intrinsic perception less optimized. To mitigate this gap, we present Veritas++, a perception-enhanced reasoning framework that establishes reliable perception as the foundation of authenticity reasoning. Rather than directly optimizing the model's explanatory ability, we ground AIGI detection on three basic perception abilities, i.e., capturing fine-grained visual details, semantic anomalies and pixel-level differences. Building on this insight, we introduce Perception-oriented Learning (PoRL), which replaces open-ended description supervision with verifiable rewards to explicitly strengthen these capacities. To further integrate enhanced perception with reasoning, we introduce Value-aware On-Policy Distillation (VaOPD), an adaptive distillation mechanism that prioritizes high-value distillation signals over uniform supervision, internalizing perception-aware reasoning through a privileged self-teacher. Extensive experiments across standard, in-the-wild and emerging benchmarks demonstrate that Veritas++ achieves promising generalization. The perception learning effectively bridges the perception gap and yields seamless gains on detection, while VaOPD further enables efficient capability evolvement without sacrificing existing performance. Code and checkpoints are available at https://github.com/EricTan7/VeritasPP.

Fine-tuning is the dominant paradigm for specializing large language models (LLMs), yet it exposes a critical vulnerability: malicious data providers can embed harmful behaviors into downstream corpora, creating models that retain professional skills while violating human values on demand. Existing safety-realignment defenses often fail in practice due to three key limitations: they frequently cause catastrophic forgetting of specialized skills; their effectiveness collapses when the defender cannot observe the attacker's prompt template; and successfully realigned models remain susceptible to re-jailbreaking via simple system prompt switches. To address these challenges, we propose Routing-based On-Policy Distillation (ROPD), a novel realignment framework that models the divergence between aligned and compromised output probability distributions rather than fitting specific prompt templates. We conduct extensive experiments comparing ROPD against four state-of-the-art baselines across three datasets and three base models with varying alignment strengths. Our results demonstrate that when baseline defenses face template mismatches, often accompanied by severe degradation in downstream task performance. In contrast, ROPD substantially mitigates template-mismatch risks, maintaining superior robustness in both defense effectiveness and capability preservation. While our analysis indicates ROPD is not entirely immune to template shifts, its performance degradation is negligible compared to existing methods, establishing a new standard for robust LLM realignment.

Knowledge distillation (KD) enables a compact student model to learn from a powerful teacher and has become an effective paradigm for model compression. The emergence of diverse model architectures has extended KD from homogeneous to heterogeneous settings. However, differences in architectural inductive biases between the teacher and student models often result in substantial representation discrepancies, limiting the effectiveness of direct knowledge transfer. Recently, redundancy suppression has offered a new perspective on heterogeneous KD by preserving cross-architecture invariance and reducing feature redundancy through decorrelation of teacher-student feature correlations. Nevertheless, this formulation may weaken useful structural information through uniform decorrelation, while a fixed coefficient may make the effective contribution of redundancy suppression sensitive to teacher-student pairs and training stages. To address these problems, Correlation Calibration-based Redundancy Suppression (CoCaRS) is proposed to better retain structural information while suppressing redundancy and reduce sensitivity to coefficient settings across teacher-student pairs and training stages. Specifically, CoCaRS calibrates feature decorrelation through Confusion Evidence Estimation (CEE) and Strength Allocation Control (SAC), which respectively capture reliable semantic relations for correlation estimation and preserve discriminative structure during decorrelation. Adaptive Coefficient Regulation (ACR) further regulates the contribution of the calibrated redundancy suppression objective according to its relative loss scale, reducing sensitivity to coefficient settings. Extensive experiments on CIFAR-100 and ImageNet-1K validate the effectiveness of CoCaRS in improving distillation performance and reducing sensitivity to coefficient settings. Code will be released soon.

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.

On-policy distillation (OPD) grounds token-level supervision in the student's own trajectory, yet suffers from prefix failure: once the student commits to a wrong reasoning direction, all subsequent generation builds on this deviation, producing misdirected continuations that elicit unreliable supervision and waste compute. We identify a teacher-student continuation asymmetry on failed prefixes, where the teacher tends to redirect while the student continues along the original direction, and convert it into a label-free handoff trigger in Relay On-Policy Distillation (Relay-OPD). During training, Relay-OPD constructs relay trajectories by letting the teacher briefly take over at detected trigger points to produce a teacher leg, after which the student resumes and is optimized on the resulting trajectory. A limited relay budget concentrates intervention on critical early positions while limiting departure from the student policy. With a Qwen3-4B-Instruct-2507 teacher and Qwen3-0.6B/1.7B-Non-Thinking students on eight mathematical reasoning benchmarks, Relay-OPD achieves the best or second-best results on every benchmark, outperforming standard OPD by +5.73% and the strongest baseline FastOPD by +1.49% on average for 1.7B, with consistent gains at 0.6B. Training trajectory length is reduced by over 50%.

Deploying diabetic retinopathy (DR) screening models in primary care requires edge-efficient systems that remain accurate, safe, and reliable under domain shift. Multi-teacher knowledge distillation (KD) is a natural compression strategy, but existing approaches largely assume that all teachers provide equally trustworthy supervision. In our setting, this assumption fails: a strong CNN teacher (EfficientNet-B3, 0.876 QWK) and a weaker Transformer teacher (Swin-Base, 0.830 QWK) are complementary, yet the Transformer's logits can still mislead the student. We therefore propose OrthKD, a selective-trust distillation framework that transfers full supervision from the strong CNN, uses feature-only distillation from the weak ViT, and enforces orthogonality between teacher-specific student projections to encourage complementary rather than redundant evidence. This design preserves local lesion precision, injects global structural context, and improves robustness to distribution shift. On 132,049 retinal images, a 5.4M-parameter MobileNetV3 student reaches 0.885 QWK on EyePACS and improves zero-shot Messidor-2 performance from 0.507 to 0.728 QWK, while also achieving strong referral AUC and calibration. These results show that selectively distilling heterogeneous teachers can enable practical DR screening on resource-constrained devices.

Training large language models (LLMs) to act in long-horizon games is a promising step toward generalist decision-making, yet reinforcement learning with verifiable rewards (RLVR) relies on sparse final rewards that reveal little about which decisions determine success. Denser process signals could supply this missing turn-level credit, but existing sources are hard to keep both cheap and accurate. We observe that changes in a game solver's state value reveal whether an action advances the state toward success. Building on this insight, we propose CAST (Credit Assignment from Solver Teachers), which converts these value changes into solver advantages and injects them into RLVR as turn-level signals. We further show that, under a soft-optimal solver assumption, maximizing the solver advantage is equivalent to on-policy distillation from the solver, requiring only scalar values rather than teacher logits. Across Sokoban, Minesweeper, and Rush Hour, CAST outperforms all trained baselines on every game under both in-domain and unseen-difficulty evaluation and achieves the highest average zero-shot performance on ALFWorld and WebShop. Our code is available at https://github.com/Wloner0809/CAST.

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model's native CFG schema retains privileged information in the teacher's negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive--Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

On-Policy Self-Distillation (OPSD) uses privileged information available only to the teacher to provide dense token-level supervision on trajectories generated by the student. However, existing methods often rely on verified solution traces, explanations generated by external models, or manually localized visual evidence, which limits their scalable application to multimodal large language models. To address this issue, we exploit the information gap between high- and low-resolution views of the same image and propose RP-OPSD (Resolution-Privileged On-Policy Self-Distillation for Multimodal Large Language Models). During training, the student policy generates on-policy trajectories from images at one-quarter of the original resolution, while the teacher policy provides supervision using the original-resolution images. By minimizing the divergence between their output distributions along the student trajectories, the student learns the predictive behavior of the teacher under high-resolution inputs, thereby strengthening its low-resolution capability and transferring the learned improvement to original-resolution inference. RP-OPSD requires neither additional human annotations nor external models to generate solution traces but only image--question pairs. Experiments on Qwen3.5-9B show that RP-OPSD achieves a 5.45% relative improvement in average performance at the original resolution and a $1.78\times$ training speedup over OPSD. These results demonstrate that resolution differences can serve as a simple and scalable source of privileged information, providing an effective and efficient approach to on-policy self-distillation for multimodal large language models.

Reinforcement learning enables Agentic RAG systems to learn multi-turn search from verifiable outcome rewards, but all- zero rollout groups provide no comparative signal and may hide useful search behavior. We present EviBack, an evidence- constrained Teacher backoff that supplies auxiliary super- vision to such groups while preserving verifiable Actor re- wards. It separates evidence assessment from answer refine- ment, preventing reference answers from overriding evidence- insufficiency judgments. A fully automated, end-to-end GPT- 5.5-assisted APE pipeline starts from a manually authored single-prompt dual-task Teacher, automatically partitions and labels rollout data, and performs ablation, task decomposition, evaluation, and selection to produce a gated two-stage Teacher. Compared with the manual design, the resulting Teacher im- proves downstream F1 and valid-answer rate while reduc- ing search, duplicate queries, and forced termination. Across seven open-domain QA benchmarks and three Qwen3 scales, EviBack improves F1 over Search-R1 and raises both single- and multi-hop macro F1. We guarantee that the code will be made publicly available at a later stage.

In many real-world scenarios, encountering continual shifts in domain during inference is very common. Consequently, continual test-time adaptation (CTTA) techniques leveraging a teacher-student framework have gained prominence, allowing models to adapt continuously even after deployment. In such a framework, a weight-averaged mean teacher is used to produce pseudo-labels from test data for self-training. The mean teacher gets updated as an exponential moving average of the student parameters using a high value of momentum that is kept fixed even if different distributions of test data are encountered. To combat the resulting drift of the model, we propose a novel controlled teacher adaptation methodology that dynamically sets a proper momentum value depending on the quality of the incoming data. Additionally, we estimate class prototypes from the source pretrained model to help align the target data as they come in. Importantly, our method does not require access to source data or its statistics at any stage of the pipeline, making it truly source-free. We perform extensive experiments on benchmark datasets to demonstrate that our approach outperforms different state-of-the-art adaptation frameworks, many of which require access to source data.

On-policy distillation (OPD) trains a student on its own trajectories while a teacher supplies dense token-level likelihoods at student-visited prefixes. These likelihoods are often read locally: agreement appears safe to imitate, whereas disagreement appears to identify an error. We show that both readings are confounded by the outcome of the completed trajectory. We introduce an outcome-resolved diagnostic that crosses pointwise teacher-student divergence with final-answer correctness, separating safe imitation, productive divergence, harmful divergence, and agreement-on-failure. In an eight-seed mathematical-reasoning study with a Qwen3-8B student and Qwen3-32B teacher, agreement-on-failure constitutes 67.84% of pooled response-token mass; with a Qwen2.5-7B/32B pair it remains 67.68%. The result persists across threshold, sequence-level, format, and truncation audits. Even on prompts that the Qwen3 teacher solves in all four independent attempts, student accuracy rises to 86.91% but agreement-on-failure remains 14.76%. We then run three matched training probes that use the available signals to imitate, mask, or contrast whole trajectories; none consistently reduces agreement-on-failure. The result points to a localization limitation: local divergence paired with a trajectory-level outcome does not identify where a failed trajectory became unrecoverable. Addressing this limitation requires additional positional information, such as process labels, teacher continuations from student prefixes, or token-level alignment across rollouts. Our contribution is therefore diagnostic rather than a new training method.

Post-training enables vision-language models (VLMs) to understand human instructions and perform various downstream tasks. Current post-training methods usually rely on human-annotated data, distillation from external models, reinforcement learning with human feedback, or verifiable answers. This limits their ability to improve without external supervision. To tackle this, we propose NOPD (Noisy Student On-Policy Self-Distillation), a simple yet effective self-distillation approach that improves VLMs without any external models or ground-truth answers. Our key insight is that prediction discrepancies between clean and corrupted inputs naturally induce a self-supervision signal. In NOPD, the model learns from corrupted inputs while using its own predictions under clean inputs as token-level supervision. We show the effectiveness of NOPD on five visual reasoning tasks; it can match and even outperform reinforcement learning approaches or distillation from external models. Notably, when trained with 2.1K samples from Geometry3K, NOPD improves Qwen2.5-VL-7B by 20 points on its validation set. It also shows generalization on out-of-distribution test sets and achieves 7.4 point gains on MathVista. Furthermore, we demonstrate that NOPD is a general approach to enhance VLMs, achieving improvements across three models on 12 benchmarks.

Open-weight language models from different families exhibit complementary capabilities, motivating their consolidation into a compact student through on-policy distillation (OPD). However, full-vocabulary OPD typically assumes a shared tokenizer, while existing cross-tokenizer methods may discard teacher probability mass or assign it to student tokens with unrelated content. We introduce Byte-Prefix Marginalization (BPM), which re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space. Specifically, BPM assigns each teacher token's probability to the longest student token whose byte representation is a prefix of the teacher token's bytes, aggregates mass mapped to the same student token, and places otherwise unmatched mass in an explicit residual category. This produces a vocabulary-complete, byte-aligned, and mass-preserving target for dense OPD. The target exactly recovers the teacher-induced byte-prefix marginal when the relevant prefix does not span multiple teacher tokens (a condition satisfied at more than 99% of training positions) and uses a mass-preserving, chain-factorized lower bound otherwise. Across Qwen3-32B, GLM-Z1-9B-0414, and MiniMax-M2.7 as teachers, BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks, improving six-benchmark avg@8 by 3.7-6.6 points over the strongest baselines.

Test-time scaling through iterative self-evolution with environment feedback, as demonstrated by AlphaEvolve, shows remarkable performance gains. We hypothesize that the success of such evolution frameworks hinges on meta-skills, such as self-reflection with environment feedback, that enable effective multi-round refinement, yet are largely neglected by traditional post-training. To bridge this gap, we present MetaEvolve, a framework designed to develop these meta-skills via a data synthesis pipeline, evolution-aware reinforcement learning (RL), and inference-time evolutionary search. Concretely, we ground MetaEvolve in coding, where program execution provides natural, continuous reward signals beyond binary correctness. Building on these signals, we synthesize evolution trajectories as training data, each containing a current program, its fitness score (combining correctness and efficiency), and a history of prior attempts, and train the model via RL with verifiable rewards derived from test case execution. By training on large-scale code data, we aim to inspire generalizable domain-agnostic meta-skills that can transfer broadly to open-ended problems where such rich training signals are scarce. Across seven coding benchmarks, MetaEvolve outperforms the strongest baseline by 10.01% absolute on in-distribution tasks and 24.12% on out-of-distribution tasks. On open-ended algorithm optimization problems entirely outside the training domain, it further achieves a 46.9% relative improvement. These results demonstrate that explicitly cultivating self-evolution meta-skills offers a principled path toward more capable and autonomously self-evolving AI.

On-policy self-distillation (OPSD) is promising as it removes the external teacher required by on-policy distillation (OPD), yet it still needs asymmetric information between teacher and student to ensure that the self-teacher provides a stronger learning signal than the student. Existing methods create this asymmetry either through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. For this purpose, we propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix -- one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. Using ViRL39K dataset, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. For example, on Qwen3-VL, it improves the seven-benchmark aggregate from $62.27\% \rightarrow 67.04\%$ at 2B, $71.30\% \rightarrow 73.16\%$ at 4B, and $72.51\% \rightarrow 76.26\%$ at 8B. Furthermore, VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.

While large audio-language models have achieved remarkable progress in auditory perception, they still lag behind text-based large language models in deep logical reasoning, primarily due to the scarcity of high-quality audio reasoning data. To bridge this gap, we propose X$^3$-OPD, a cross-modal on-policy distillation framework that transfers reasoning capabilities from a powerful text teacher to an audio-language student. During training, the student generates reasoning trajectories conditioned on its own acoustic perception, while the teacher provides token-level guidance using matched textual inputs and verified answers. We further construct a three-tier symmetric corpus covering textual reasoning rendered into speech, audio-event reasoning grounded in complex acoustic scenes, and spoken-dialogue reasoning involving paralinguistic cues. This design extends cross-modal distillation beyond textually recoverable content to reasoning grounded in non-linguistic events, prosody, and conversational context. Experiments on MMSU, MMAU, BIG Bench Audio, and MMAR demonstrate that X$^3$-OPD substantially improves audio-grounded reasoning and chain-of-thought quality while largely preserving the model's existing capabilities under domain shift.

Omni-modal models provide a unified interface for text, images, and audio. However, improving these abilities together remains difficult, as post-training on pooled multimodal data often fails to preserve the strengths of modality teachers. On-policy distillation (OPD) has recently become popular in model post-training. It samples responses from the current student and compares the teacher's and student's next-token distributions along those responses, yielding dense supervision while reducing the mismatch between training and inference. Despite these advantages, standard OPD does not readily extend to several modality teachers. Their guidance may favor conflicting changes to the shared model, while matching each teacher's next-token distribution can prevent the student from moving beyond that teacher. To address these challenges, we propose On-Policy Omni Distillation (OPOD), which consolidates text, image, and audio teachers into one omni model. OPOD routes each response to the corresponding teacher, controls the teachers independently, and applies guidance only when the teacher assigns a higher probability to the generated token. The selected teacher also evaluates answer confidence and whether the reasoning increases support for the answer. Extensive experiments on twelve benchmarks show that OPOD achieves the best average at three model scales, reaching 70.8, 51.7, and 46.2 and outperforming the strongest comparator by 2.1, 1.8, and 1.7 points. At 30B, it surpasses the base model and pooled RL training on all twelve benchmarks, and ranks first or second on eleven even when the teachers are included. Only the student is retained for deployment.

Vision-language models have shown strong potential for social robot navigation by leveraging rich semantic understanding of complex environments and human behaviors. However, large scale VLMs are difficult to deploy on resource-constrained robotic platforms, while lightweight VLMs often lack sufficient social reasoning capability. To address this problem, we propose SOPD-SocialNav, a selective on-policy distillation (SOPD) method that transfers social navigation knowledge from a large teacher VLM to a lightweight student VLM. SOPD introduces an entropy-based token selection mechanism that uses teacher uncertainty to identify socially informative decision tokens, while suppressing gradients from low-entropy tokens corresponding to trivial navigation states. A temperature-controlled Jensen-Shannon divergence objective is then used to align the student and teacher distributions on the selected tokens. Experiments on the SNEI and MUSON benchmarks demonstrate that SOPD consistently outperforms supervised fine-tuning, off-policy distillation, and standard on-policy distillation baselines in action prediction, perception consistency, and reasoning consistency. Real-world deployment on a Scout Mini robot further shows that the distilled model can generate more socially appropriate navigation behaviors in conversational and queuing scenarios. These results suggest that SOPD is an effective strategy for building lightweight yet socially aware VLM-based navigation systems.

This paper introduces Sentence Splitter, a self-supervised framework built upon a T5-based encoder--decoder architecture for uncovering the latent factual structure of natural language sentences. The proposed method identifies the semantic boundary between a descriptive prefix (head) and its factual completion (tail) by formulating sentence splitting as a discrete segmentation problem, where a sentence of length $N$ admits $N$ possible split points but only one recovers the intended head--tail structure. Rather than explicitly searching over all candidate boundaries, the model learns to recover the factual completion through probabilistic sequence generation. To eliminate the need for manual annotation, symbolic head--tail pairs are first verbalized into natural-language templates that provide supervision for training the Sentence Splitter. The trained splitter is then applied to raw text to extract aligned prefix--tail pairs, which are subsequently used to train a generative model that proposes additional plausible completions through a lightweight bootstrapping process. This unified pipeline provides a scalable and structure-aware approach to constructing self-supervised training data while bridging symbolic knowledge and natural language. Experiments on both structured and naturally occurring text demonstrate that the proposed splitter generalizes beyond synthetic templates and that the resulting structure-aware supervision consistently improves downstream performance on knowledge graph completion and commonsense question answering, highlighting the effectiveness of recovering latent factual structure for knowledge-centric NLP.

On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.

Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but a scalar trajectory reward offers limited token-level guidance. Existing self-distillation methods add a privileged teacher but typically assign it a fixed role: direct distribution matching may destabilize successful behavior, while magnitude-only modulation offers little corrective guidance after failure. We observe that successful and failed trajectories require different forms of hindsight supervision. A successful response already contains a valid student-generated reasoning path and can therefore serve as privileged context rather than being replaced by an external rationale. A failed response, however, requires corrective reference information. We introduce Hybrid Hindsight Self-Distillation ($\mathrm{H}^{2}\mathrm{SD}$), which jointly adapts teacher context and update strategy to trajectory correctness. For successful trajectories, we construct the teacher context from the verified response and a rephrasing instruction, and use the teacher only to re-evaluate the original response tokens. The resulting probabilities refine token credit assignment without changing the direction determined by the reward. For failed trajectories, a verified reference hint provides corrective guidance through reverse-KL distillation. Experiments on challenging reasoning benchmarks show that H$^2$SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.

Large vision-language models (LVLMs) have recently shown strong potential for industrial anomaly detection (IAD) by providing image-level anomaly judgments and interpretable defect reasoning. However, current LVLM-based IAD methods still struggle to produce precise pixel-level anomaly maps from generated language judgments. We aim to achieve precise pixel-level localization while using language as guidance rather than letting it dominate the visual response. Specifically, we propose \textbf{OPD-IAD}, an evidence-privileged dense on-policy self-distillation framework for LVLM-based IAD. OPD-IAD distills privileged defect evidence onto the model's own on-policy judgment trajectory, enabling the final generated judgment to be learned under dense supervision rather than treated only as a textual answer. The resulting judgment serves as a semantic condition for dense anomaly perception. To turn this condition into dense visual evidence, we introduce \textbf{Language-guided Visual Anchoring}, which uses a judgment reforward to re-encode the image and question under the final-judgment condition into semantic anchors and contrasts them with dense visual features through a contrastive heatmap head to generate anomaly maps. The language judgment therefore provides compact semantic guidance, while dense visual features remain the basis for pixel-level scoring, allowing language to guide anomaly localization without letting language quality directly dictate the pixel-level response. Extensive experiments show that OPD-IAD achieves the best overall performance among LVLM-based IAD methods, leading on most image-level, pixel-level, and QA metrics.

Antibodies are essential therapeutic molecules, and their complementarity-determining regions (CDRs) form the primary antigen-recognition interface. Recent protein generative models have demonstrated broad capabilities in biomolecular design, yet post-training strategies for downstream objectives remain limited. Standard denoising training operates on noisy states obtained by perturbing native structures, whereas recursive generation proceeds through model-generated intermediate states. For flexible antibody CDR loops such as CDR-H3, this mismatch can allow backbone deviations to accumulate along the denoising trajectory and compromise antigen-facing loop geometry. We introduce ABOPD, an antibody design framework based on on-policy distillation that leverages privileged native geometry during training to supervise states visited along the model's own denoising trajectories. With this fine-grained structural supervision, ABOPD substantially improves structural recovery on RAbD CDR-H3 generation, reducing RMSD by 0.42 Å (from 2.37 Å to 1.95 Å) and outperforming supervised fine-tuning and offline distillation controls, offering a path to higher-fidelity protein design.

Rubric-based RL has recently shown promise in improving LLMs on open-ended tasks. A widely recognized limitation of rubric-based RL is limited exploration: criteria that no rollout manages to satisfy (Unexplored Criteria, UC) receive no optimization signal. Recent methods address this by incorporating rubric information as external guidance during rollout, yet they introduce a train-inference mismatch: the policy is optimized on rollouts produced under external guidance while this guidance is absent at inference time, causing error accumulation through autoregressive decoding. Moreover, these exploration-focused approaches overlook a fundamentally different failure mode that we term Suppressed Criteria (SC) -- criteria that are satisfied by some rollouts yet whose learning signals are lost during optimization because scalar reward aggregation assigns them non-positive aggregate advantages. Our analysis reveals that SC are remarkably prevalent: over 57% of samples exhibit this failure mode throughout training, with an average of 1.8 SC per sample. To simultaneously address both UC and SC without introducing training-inference mismatch, we propose Criterion-Distilled Policy Optimization (CriPO), which enhances rubric-based RL via on-policy self-distillation. For UC, CriPO constructs a criterion-injection self-teacher and computes a localized forward-KL loss to inject missing behaviors into the policy. For SC, CriPO employs a counterfactual self-teacher to locate criterion-relevant tokens in negative-advantage rollouts and flips their token-level advantages to positive values, preserving useful patterns that would otherwise be suppressed. Experiments on medicine and science benchmarks demonstrate that CriPO consistently outperforms rubric-based RL, achieving stronger final performance with approximately $2\times$ fewer optimization steps.

On-policy self-distillation (OPSD) offers a promising approach for training large language models without relying on a separate teacher model. However, its effectiveness on complex agentic tasks remains largely unexplored. In this work, we instantiate Feedback-Augmented Self-Distillation (FA-SD), a self-distillation algorithm for agentic search that leverages successful demonstrations as privileged information. We identify that models can rely on recurring reasoning-and-search output templates, producing trajectories that appear diverse but are largely agnostic to the input question, making the KL-based self-distillation signal uninformative. We term this phenomenon decoding collapse, a failure mode that can be missed by existing evaluation metrics. To understand its underlying cause, we show that although the self-teacher achieves stronger performance, learning remains inherently unstable due to inconsistent supervision signals. We further decompose this inconsistency into model inconsistency and prompt inconsistency, and show that the latter can significantly degrade the quality of the supervision signal, limiting the effectiveness of self-teacher learning. To mitigate this inconsistency, we introduce an exponential moving average (EMA) teacher to stabilize the self-teacher and provide more consistent supervision signals. Although the EMA teacher requires a warm-up phase during which performance may temporarily regress, it ultimately improves model performance by providing more stable supervision.

We propose Token-Level Off-Policy Labeling (TOPL), an off-policy training paradigm that reframes post-training as a token-level correctness prediction task. Our key intuition is that by training the model to distinguish good and bad tokens in a response, we naturally guide the model towards generating good tokens, while avoiding the pitfalls that come with directly training the model to generate off-policy tokens. Experiments on document summarization tasks show that TOPL achieves strong out-of-distribution generalization across 11 datasets against a diverse set of sequence-level and token-level baselines. We further demonstrate that TOPL transfers effectively to machine translation, suggesting that its benefits generalize across different faithful generation tasks. Through ablation studies, we confirm that our token-level learning signal is critical to good performance; sequence-level analogues do not confer similar benefits. Finally, we show that TOPL induces interpretable model updates: the LoRA adapters learned through TOPL function as linear classification heads and steering vectors.

We present a practical recipe for building a compact Hindi text-to-speech (TTS) model by distilling a large flow-matching teacher (IndicF5, 337M-parameter DiT) under a severe data budget (~17.6 hours). Training a small model from scratch on this much data fails outright. Instead we warm-start the student from the teacher by pruning depth only: keeping the teacher's width, text dimension, attention heads, and mel/text I/O fixed so all non-block tensors copy one-to-one, and retaining an evenly-spaced subset of transformer blocks. We first measure how much depth the teacher tolerates (it remains near-functional at -27% blocks but collapses past -50%), then descend gradually (22 -> 16 -> 12 -> 8 -> 6 blocks), re-fine-tuning after each prune, with each step gated by an objective ASR word-error-rate (WER) check. The resulting students reach WER 0.00 on unseen sentences at 249M and 190M parameters, and remain robust down to 131M; at 102M we observe a clear capacity cliff that we attribute to the data budget rather than the recipe. We also document two train/inference feature- and library-parity failures (mel filterbank and rotary-embedding library versions) that silently degrade audio, and a version-independent fix. The method yields a high-quality Hindi voice that runs in real time on a 6 GB laptop GPU. An independent 50-sentence FLEURS benchmark compares the released 190M student against its teacher and MMS-TTS-hin.

On-policy knowledge distillation transfers reasoning from large teachers to compact students, but existing approaches suffer three compounding failure modes: (i) cold-start collapse, where a fresh student assigns near-zero mass to teacher-preferred tokens; (ii) state-agnostic divergence scheduling, where time-only forward/reverse-KL interpolation ignores the student's coverage state; and (iii) binary reward sparsity, where pass/fail signals discard information from partially correct traces. We present CADENCE, a unified framework with a targeted fix for each. Its DRIFT mechanism schedules a per-token convex mixture of forward-KL and reverse-KL surrogate objectives on student-sampled trajectories (per-token surrogates, not sequence-level KL gradient estimators). Six components extend it: (A) COVA, a coverage-adaptive $β$ schedule accelerating the forward-to-reverse transition; (B) FTB, a forking-token boost concentrating gradient at high-entropy positions via a globally-normalized entropy reference; (C) CCD, a dense reward adding numerical-proximity partial credit for incorrect-but-close traces; (D) LAP, brevity-preferential correct-rollout reinforcement; (E) EMR, an entropy-matching calibration regularizer; (F) BSD, a bootstrapped self-distillation phase. On GSM8K and MATH-500 (corrected 512-token protocol, 5 seeds, reported std), CADENCE distills a 0.5B student from a 1.5B teacher to 69.8 $\pm$ 0.5% GSM8K pass@1 (from 48.7% pretrained; 63.2% of the teacher gap closed) and to 72.1 $\pm$ 0.4% with a 3B teacher (76.2% closed), beating the strongest matched-compute label-using baseline (DRIFT+binary reward) by +4.4 $\pm$ 0.7 points. All experiments run on a single Apple Mac Studio (M-series, 64GB unified memory), showing principled distillation reaches strong reasoning quality without datacenter-scale hardware.

Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes \textbf{trace-based on-policy distillation (TOPD)}, a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4$\times$ fewer rollout rounds, corresponding to an estimated 96.0$\times$ to-accuracy model-compute speedup.

Deploying LLM agents typically requires a compact test-time student, even if a stronger teacher is available during training. We study knowledge brewing: distilling a teacher's interactive experience into a persistent external memory for the student. Crucially, this requires no weight updates, expert demonstrations, ground-truth labels, or test-time teacher access. This setting poses two challenges: environments provide only sparse, binary feedback, and teacher-authored notes must be inherently tailored to be concretely executable by a substantially weaker student. To address these hurdles, we propose AgentBrew, comprising two coupled components. First, a failure-triggered teacher--Ralph Loop mitigates sparse feedback by transforming student failures into environment-validated notes. Second, student-aware synthesis calibrates teacher knowledge to the weak executor's operational granularity, yielding model-specific, actionable guidance. Extensive evaluations and comprehensive ablations across coding, math, and tool-use tasks demonstrate that this asymmetric, training-free brewing paradigm produces highly capable yet deployable LLM agents.

Animal re-identification (Re-ID) relies on fine-grained identity cues that can be disrupted by blur, noise, compression, and other visual degradations. Existing robustness strategies based on degradation-augmented training or pixel-level restoration improve robustness indirectly, but do not explicitly repair shifts in the identity retrieval space. We study corruption-robust animal Re-ID as input-conditioned feature-space repair and introduce DARA, a lightweight retrofit for compact Re-ID models. DARA freezes the fine-tuned backbone and learns routed low-rank residual experts to adapt degraded-input embeddings without corruption-type annotations. To stabilize this adaptive repair, original-to-corrupted distillation uses an original-image teacher to preserve individual embeddings and retrieval relations. Experiments on ATRW, FriesianCattle2017, MPDD, and SeaStarReID2023 show that DARA improves corrupted-query retrieval over standard and augmentation-based fine-tuning, generalizes to unseen corruptions and cross-domain evaluation, and recovers 77.0% of the corrupted-query mAP gap to full corrupted fine-tuning while adding only 0.49% parameters and 0.05% FLOPs.

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

Large language models have made strong reasoning gains through supervised fine-tuning, reinforcement learning, and on-policy distillation, yet these post-training methods are usually evaluated only by final-answer accuracy. We study how they reshape confidence during reasoning. We introduce a three-stage calibration framework that evaluates confidence before, during, and after chain-of-thought generation, corresponding to difficulty estimation, early termination, and answer aggregation. Through a controlled comparison on mathematical reasoning benchmarks, we find that OPD provides the most useful pre-reasoning confidence, SFT gives the strongest online signal for early stopping, and RL produces the most reliable trace-level signal for aggregation. We further show that confidence reliability is position-dependent: RL confidence becomes informative after a path-commitment phase, while OPD confidence is useful early but can become inversely calibrated later. Based on this observation, we propose PosConf, a position-aware confidence strategy that uses confidence only from reliable relative-position intervals. PosConf improves RL answer aggregation by 6.1 points over majority voting and consistently improves OPD early stopping under tight token budgets, with gains up to 4.3 points by avoiding its later inverse-calibration region, showing that \emph{confidence in reasoning models should be used both stage-wise and position-awarely}. Our code is available at https://github.com/EIT-NLP/Post-Training-Calibration.

Sampling multiple solutions and returning the majority answer is among the most reliable ways to improve the reasoning accuracy of large language models without labels, and a growing family of methods converts this consensus signal into training supervision. However, existing approaches use consensus only in restricted forms: as a filter that selects solutions for fine-tuning, as a preference between answers, or as a scalar reward for reinforcement learning, discarding most of the information that the agreeing solutions contain. We present CANON (Consensus-ANchored self-distillatiON), a label-free training method that turns consensus into dense, token-level supervision. For each unlabeled prompt, CANON samples multiple solutions, extracts the majority answer, and conditions a frozen snapshot of the model on a solution that reaches it; this consensus-anchored teacher then supervises the model on its own rollouts at every token. Experiments on mathematical and scientific reasoning benchmarks show that CANON improves pass@1 by up to 12 points, outperforming label-free reinforcement learning by 6 points at a seventh of its compute and approaching a teacher conditioned on gold solutions; trained on pooled unlabeled data, it transfers to held-out benchmarks, matching training methods that use gold labels. Analysis suggests that the improvements are not pure distribution sharpening: after training, the model solves problems it previously never solved in 32 attempts, and its majority vote itself becomes more accurate.

On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.

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

A theoretical understanding of Transformers is crucial to better understand the capacities and limitations of large language models (LLMs). There is much work analyzing the expressivity of attention-based models. By proposing handcrafted weights or using computational complexity arguments, a large amount of past theoretical works have sought to characterize which tasks are and which are not in the hypothesis class of Transformer models. However, little work investigates the learnability of such solutions. In this work, we make progress towards this goal. Inspired by recent loss landscape analysis work, we propose preliminary sample complexity bounds for learning C-RASP constructions with Transformers.

Conventional language-model distillation often relies on fixed teacher-generated data, which may not cover the states encountered by an evolving student policy. On-policy distillation (OPD) instead collects teacher or evaluator supervision on student-generated rollouts. However, existing OPD methods differ substantially in supervision form, tokenizer compatibility, teacher access, and supervision granularity, leading to fragmented implementations that are difficult to reproduce and extend. We present \textsc{EasyOPD}, an on-policy distillation framework built on verl, a distributed reinforcement-learning framework for large language models. \textsc{EasyOPD} separates user-side configuration, method-specific supervision logic, and verl-based execution. Its method modules connect to the shared backend through extension boundaries for loss construction, rollout metadata, reward processing, tokenizer alignment, and teacher-side computation. We instantiate representative methods for three OPD settings -- cross-tokenizer OPD, on-policy self-distillation, and step-wise OPD. Experiments on reasoning, code-generation, scientific-knowledge, and tool-use benchmarks show that these implementations can be executed through the same verl-based backend while retaining their method-specific objectives and task-dependent performance profiles. We release \textsc{EasyOPD} with runnable YAML configurations, documentation, and an installable demonstration package and video.

On-Policy Self-Distillation (OPSD) has emerged as a crucial paradigm for enhancing and aligning Large Language Models (LLMs). However, in complex reasoning tasks, OPSD paradoxically degrades downstream performance. In this paper, we systematically investigate this pathology and identify a severe optimization trap we define as \textbf{Thinking Collapse} -- a sharp decline in the model's native intermediate reasoning behavior, measured by epistemic-token density (ET per 1k). Through entropy-based gradient masking and token-level target analysis, we show that this collapse is triggered by aggressive teacher gradients at high-student-entropy decision forks, where student epistemic tokens are frequently suppressed into teacher non-epistemic targets and are highly concentrated in high pointwise student-teacher divergence regions. To resolve this optimization pathology, we propose \textbf{Adaptive Dual-Perspective OPSD (AD-OPSD)}, a robust control framework that dynamically moderates the self-distillation objective. AD-OPSD selectively anchors high-suppression-risk sandboxed tokens to a reference prior derived from the frozen base model via an asymmetrical pointwise divergence gate, preserving native thinking capacity while retaining OPSD's error-correcting power. Extensive experiments across competitive mathematical benchmarks show that AD-OPSD improves over standard OPSD by up to \textbf{+4.1%} absolute average accuracy across diverse model scales and datasets. Further analysis demonstrates that AD-OPSD mitigates thinking collapse and generalizes robustly to different post-training paradigms.

Vision-Language Models (VLMs) have achieved success using homogeneous Transformers to process multimedia data. Recent studies show that heterogeneous structures interleaving efficient mechanisms, like linear attention, improve both performance and inference latency over homogeneous designs. However, these efforts rely on handcrafted static mixing patterns, which are sub-optimal and difficult to adapt to specific hardware. To bridge this gap, we propose Multi-Objective Search for Adaptive Inter-layer Composition (MOSAIC), a hardware-aware search method that automatically transforms homogeneous models into optimized heterogeneous architectures. MOSAIC integrates diverse efficiency mechanisms--including linear, sparse, and low-rank operators--into a unified search space. By formulating the selection as a multi-objective Mixed Integer Programming (MIP) problem, our method identifies optimal configurations that maximize downstream performance under strict hardware latency constraints. To mitigate performance degradation from structural transitions, we introduce a two-stage parameter recovery process: global off-policy distillation to stabilize internal representations, followed by a dual-teacher on-policy distillation leveraging a 235B oracle for knowledge expansion and the original 4B teacher for distributional stability. We validate MOSAIC through MOSAIC-4B, derived from Qwen3-VL-4B-Instruct. Results demonstrate that MOSAIC-4B matches the baseline's performance across multiple benchmarks while requiring less than 2% of the original training cost. Furthermore, it substantially improves inference efficiency, achieving 1.76x prefilling and 2.54x decoding speedups.

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).