Language Model Distillation

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69 papers in the last four weeks, up 200% on the four weeks before. 0.7% of all new papers.

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Sep 27, 2026stat.ML

A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions

Knowledge Distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient ``student'' counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation of KD that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual roadmap and identifies critical open problems for the future of the field.

Luyang Fang, Haoran Lu, Jiazhang Cai +4

Department of Statistics, University of Georgia, Athens, Georgia 30602, USA · Department of Biostatistics, Boston University, Boston, Massachusetts 02118, USA

Language Model Distillation Knowledge Distillation

Sep 27, 2026cs.LG

DuoOPD: Learning from Joint Teacher-Student Outcomes for Multi-Task On-Policy Distillation

On-policy distillation (OPD) trains a student on its own responses with token-level feedback from a stronger teacher, yet the teacher can fail on questions the student already answers correctly, and how often each model succeeds varies across tasks. OPD ignores these outcomes and, on average, pushes down even the student's correct responses; gating feedback by student correctness fixes the direction but uses the teacher in the same way whether or not it succeeded. We introduce DuoOPD, in which the student's outcome sets the direction of feedback and the joint teacher-student outcome decides how the teacher supports it: when only the teacher succeeds, its verified answer becomes context for scoring the student's failed response, and when only the student succeeds, a weight shared within the task reinforces the whole response. A single rule covers all four outcome combinations without task-specific settings. Across Qwen3 and Llama, DuoOPD outperforms all five baselines in mean macro accuracy, improving over OPD by 2.58 and 5.98 percentage points, and it also leads on two further task mixtures spanning scientific calculation, instruction following, and code generation. Ablations show that outcome-based direction alone stays near the gated baseline, while the joint-outcome designs supply most of the gain.

Ao Yu, Weibo Gao, Heng Zhou +6

University of Science and Technology of China · The Hong Kong Polytechnic University · The University of Hong Kong +1

Language Model Distillation On-Policy Distillation Knowledge Distillation

Sep 27, 2026cs.CL

TeacherGRPO: Closing the Capacity Gap in Reasoning Distillation via Teacher Alignment

Reasoning distillation from powerful teacher models to smaller students faces the Gap Curse: as teachers grow more sophisticated, their complex distributions increasingly diverge from what students can approximate, causing performance degradation. Existing mitigation strategies either filter out challenging examples through data selection or introduce weaker intermediate assistant models, inherently compromising supervision coverage or quality. We propose Teacher Alignment, which directly adapts the teacher toward the student's distribution without discarding data or degrading reasoning quality. However, naive alignment through standard knowledge distillation triggers catastrophic collapse of the teacher's reasoning capabilities. To address this, we reformulate teacher alignment as reinforcement learning and introduce TeacherGRPO, built on Group Relative Policy Optimization with two key innovations: (i) Curriculum Selective Alignment applies dual token- and distribution-level curricula to focus rewards on high-signal reasoning gaps while filtering noise from trivial tokens and uncertain tail distributions, and (ii) Importance-Adaptive Length Regularization selectively penalizes verbose redundancy while preserving pedagogically critical reasoning steps. The aligned teacher then distills knowledge to students via standard pipelines. Extensive experiments show TeacherGRPO significantly outperforms baselines across diverse reasoning benchmarks and distillation methods. Our code is available at https://github.com/LzyFischer/TeacherGRPO.

Zhenyu Lei, Zihan Chen, Yaochen Zhu +5

University of Virginia · Netflix · University of Washington +2

Reasoning Distillation RL for Language Model Reasoning Language Model Distillation Teacher-Student Learning

Sep 27, 2026cs.CL

Calibration, Not Answer Selection: Distilling Internal Confidence in Reasoning Models

Reinforcement learning with binary correctness rewards trains correctness, not calibrated confidence. The confidence that reasoning models verbalize is systematically overconfident, and the problem is not merely one of scale: verbalized confidence tracks how willing a model is to commit to an answer, not how likely the answer is to be right. Post-hoc rescaling therefore fits one distribution but rarely transfers. We look inside the model instead. On factual question answering, a linear probe on the hidden state between the chain of thought and the answer is substantially better calibrated: its expected calibration error is 5 to 38 times lower than that of the verbalized score across four benchmarks and two model families. However, when used to pick among N sampled answers, that same probe nearly ties majority voting yet falls far short of the oracle. Internal states answer "how certain am I" well and "which answer is right" poorly, so the signal should be reported as a confidence rather than used to select answers. As a result, we introduce probe-guided self-distillation (Probe-SD): score a model's own sampled traces with the probe, overwrite the confidence each trace states, and finetune the base checkpoint of the same family, so nothing but the model itself remains at test time. On Qwen3-14B, Probe-SD cuts ECE from 0.178 to 0.024 in-domain and from 0.542 to 0.113 out-of-domain, where it also beats post-hoc recalibration and self-consistency distillation. The resulting confidence is well-calibrated and useful for weighted voting, behaviors previously attributed to online RL, here obtained with supervised finetuning alone.

Yadong Xi, Rongsheng Zhang, Tangjie Lv +2

NetEase · Amazon · Singapore University of Technology and Design

Confidence Estimation in Language Models Language Model Calibration Language Model Distillation LLM Uncertainty Estimation

Sep 26, 2026cs.AI

Train4Merge: A Controlled Single-Teacher Study of RL vs. SFT Teachers for OPD-Based Model Merging

Domain experts trained from a shared checkpoint can transfer their specialized capabilities to a single student through on-policy distillation (OPD). Existing research primarily focuses on improving this merging process, while the algorithms used to train the experts have received limited systematic comparison. We investigate which training algorithm produces teachers better suited to OPD through controlled single-teacher comparisons of supervised fine-tuning (SFT) and reinforcement learning (RL) across Agentic, Reasoning, and Perception. Teachers and students share the same Qwen3.5-9B initialization, and the two teacher types are compared at similar task performance. Our experiments show that RL teachers yield stronger students and higher recovery of teacher performance gains across all three domains. At their best checkpoints, RL-guided students outperform SFT-guided students by 4.27, 1.50, and 0.86 percentage points, respectively. In Agentic, the best SFT-guided student recovers only 44.44% of its teacher's performance gain over the base model, whereas the best RL-guided student recovers 115.00%, surpassing its teacher. Our further analysis shows that RL teachers undergo smaller parameter displacements from the shared initialization than SFT teachers. These findings support the hypothesis that RL teachers' smaller departures from the student's starting point facilitate learning through OPD, resulting in stronger students.

Jingyuan Huang, Zuming Huang, Yucheng Shi +4

University of Georgia · INF Tech · Tencent +1

Language Model Merging Language Model Distillation On-Policy Distillation Supervised Fine-Tuning RL Fine-Tuning

Sep 24, 2026cs.CL

Post-Training Leaves Behavioral Shadows on Unrelated Decisions

We find that language models can transfer capabilities through task-unrelated text. Post-training typically improves language models using task-specific data. Prior work on subliminal learning shows that information about these updates can pass through unrelated generations, but has largely focused on traits or preferences using extensive teacher outputs. We introduce Active Taskless Distillation (ATD), which achieves capability transfer using only a single word from the teacher per prompt. ATD probes the behavioral shadow of post-training by selecting prompts where the teacher and student's shared public ancestor is nearly indifferent between two ordinary words. A student initialized from this ancestor learns solely from the resulting prompt-word pairs, without target-task examples, teacher logits, or teacher parameters. In the primary coding experiment with Qwen2.5-1.5B, 5,664nses yield a 5.34 pp gain on HumanEval+ over an exact nuisance-matched control thadisrupts prompt-resperiments showtransfer in scientific knowledge, commonsense reasoning, and reading comprehensins across additional model generations, sizes, and families. Functional analyses show that the learned sid composable, andthat its strength tracks the teacher's update strength.

Ziyang Zhang, Yubin Jing, Yuanhao Zeng +3

Peking University · Georgia Institute of Technology · ShanghaiTech University +2

Subliminal Learning Language Model Distillation Language Model Post-Training

Sep 23, 2026cs.LG

LastOPD: Taming Collapse in Latent On-Policy Distillation

On-policy distillation (OPD) corrects a student on the responses it writes, but its signal is the teacher's next-token distribution: it tells the student what the teacher says but misses how it thinks. Latent supervision promises the missing part by aligning the student's latent states to the teacher's. Recent methods such as OPRD bring this signal into on-policy distillation. However, we observe two failures of this recipe when distilling Qwen3-4B and Qwen3-8B into Qwen3-1.7B-Base. Early gain, late collapse: latent supervision alone lifts MATH-500 accuracy from 25 to 46 in 10 steps, but subsequent training degrades performance down to 11 with no recovery. Better alignment, worse behavior: although the alignment metric steadily improves throughout this collapse, the most aligned model turns out to be the worst performing. Further analysis suggests a mismatch in how the latent signal is applied: layers paired by depth play different roles in the two models, so continued alignment may pull the student toward teacher states it cannot understand. To address this, we propose LastOPD, which applies the latent signal only at the last-layer state, the common interface both LM heads read, and only during a 10-step crossfade into token-level OPD. This keeps the useful part of the latent signal and hands the student to token-level supervision before the collapse sets in. Extensive experiments show that LastOPD improves MATH-500 over token-only OPD by 5.55 and 4.02 points with the 4B and 8B teachers, leads on most held-out datasets, and reaches the final score of token-only OPD in about half the steps. Code is available at https://github.com/Muyiiiii/LastOPD.

Jie Yang, Zhengyu Fang, Zelin Xu +7

University of Illinois at Chicago · Visa Research · Case Western Reserve University +2

Language Model Distillation On-Policy Distillation

Sep 23, 2026cs.SD

Reward-Tilted On-Policy Distillation for Acoustic Grounding in Audio-Language Models

Audio-language models (ALMs) can exploit textual shortcuts to answer questions while overlooking acoustic evidence, weakening audio understanding. On-policy distillation (OPD) trains compact ALMs by supervising student-generated responses with teacher predictions, but does not explicitly distinguish acoustic support from linguistic predictability. We propose Reward-Tilted On-Policy Distillation (RT-OPD) to strengthen acoustic grounding. Given the same question and student-generated text, a frozen teacher predicts the next token with and without audio inputs. Their log-probability contrast defines a reward that reshapes the teacher distribution for reverse-KL distillation, emphasizing the additional evidence provided by audio. Across two compact students and three benchmarks, RT-OPD consistently outperforms Vanilla OPD. Experiments with silenced and replacement audio further suggest that RT-OPD strengthens the student's reliance on acoustic evidence. Our 3B model achieves 72.72% accuracy on MMAU, the highest among the compared 3B models and competitive with several 7B and 8B models. Code and model checkpoints are available at https://github.com/KaiyangLi1992/RT-OPD.

Kaiyang Li, Shaobo Han, Yue Tian +1

NEC Laboratories America, Inc., USA · School of Computing, University of Connecticut, USA

Audio-Language Models Language Model Distillation On-Policy Distillation

Sep 23, 2026cs.LG

Counterfactual Constraint-Conditioned On-Policy Distillation for Multi-Constraint Instruction Following

Multi-constraint instruction following requires a model to respond to a query under many simultaneously active constraints. Even strong instruction-tuned models still routinely violate some of them. Existing approaches either augment supervision with sequence- or token-level RL rewards from external verifiers or learned graders, or use on-policy distillation (OPD) against a single full-context teacher whose probability mass becomes diluted as more constraints become simultaneously active. We propose CC-OPD (Counterfactual Constraint-Conditioned On-Policy Distillation), which inverts the standard supervision-generation direction in distillation. Rather than enriching the teacher with information beyond what the student sees, CC-OPD ablates each constraint from the teacher's conditioning in turn, and constructs the per-constraint signal from the resulting per-token probability differentials. The resulting per-token leave-one-out log-likelihood shifts are summed, clipped, and added to the vanilla OPD reward as a token-level shaping term. All shaping terms are obtained from the frozen teacher, without an external verifier during distillation, and the reward equals vanilla OPD wherever the aggregate shift is zero. Across two Qwen model pairs and seven benchmarks, CC-OPD achieves the highest average among all evaluated student-training methods. A 1.5B student trained with CC-OPD surpasses its own 7B RL-trained teacher on the MulDimIF benchmark.

Yanzhao Zheng, Yuanqiang Yu, Tianze Xu +6

Alibaba Group, Hangzhou, China

Reward Shaping Instruction Following Language Model Distillation On-Policy Distillation

Sep 21, 2026cs.LG

iSDFT: Information-Proximal Self-Distillation for Continual Learning in LLMs

On-policy self-distillation fine-tuning (SDFT) learns new skills from demonstrations while reducing forgetting, but it always distils toward the full demonstration-conditioned teacher. This fixes teacher influence at the full-teacher endpoint, providing no control over how much demonstration information should be transferred at each prediction state. We introduce Information-Proximal SDFT (iSDFT), which instead treats the teacher as a budgeted source of information. At each token, iSDFT selects the distribution closest to the current student that satisfies a prescribed teacher-information constraint, yielding a closed-form exponential target with a locally determined tilt. To control cumulative drift, we further anchor the student to its frozen base policy. Across four heterogeneous LLM backbones and two specialisation tasks, iSDFT improves vanilla SDFT in 7 of 8 model-task settings and matches it in the remaining one. It also provides tighter retention on the original SDFT benchmark suite, with 73% of evaluations remaining within 0.5 points of the base model versus 52% for the strongest baseline, while achieving the largest mean improvement on all ten additional mathematics, coding, and competition-mathematics benchmarks. These results show that controlling how much and when teacher information is introduced improves specialisation while preserving broader capability.

Ahmed Khaled Khamis, Xiaotong Ji, Hassan Jaber +4

Imperial College London · Politecnico di Torino · UCL Centre for AI

Continual Learning for LLMs Language Model Distillation On-Policy Distillation Knowledge Distillation

Sep 21, 2026cs.CL

Efficient LLM Distillation for Bangladesh Legal Context: A Smartphone-Compatible Retrieval-Augmented Generation Model

Legal information in Bangladesh is inaccessible to most citizens. Statutory text is English-only, trained lawyers are concentrated in urban centres, and cloud-dependent AI fails where mobile connectivity is unreliable, a setting in which hallucinated legal text causes direct harm. The system addresses statutory interpretation only; queries that require judicial precedent or case-law reasoning fall outside its scope. We target the statutory access gap by compressing a 9-billion-parameter Gemma-2 teacher into a 2-billion-parameter student through two-phase progressive knowledge distillation. Phase 1 performs supervised fine-tuning on 9,429 quality-gated legal question-answer pairs (65% acceptance from 14,514 generated queries); Phase 2 minimises sparse Kullback-Leibler divergence against the teacher's top-50 per-token logits at temperature tau = 4.0, implemented via QLoRA (4-bit NF4, rank-32 LoRA adapters). Prior legal language models target general legal English; this system specialises in Bangladeshi statutory law. Every response is grounded through hybrid retrieval combining dense semantic search (60%) and BM25 (40%) across 36,029 statutory passages from the Bangladesh Constitution and national legislation. On a 50-query English benchmark, the distilled model reaches ROUGE-L 0.4715 and BERTScore F1 0.5679, a 103% ROUGE-L and 143% BERTScore gain over the retrieval-augmented undistilled baseline (ROUGE-L 0.2323, BERTScore 0.2340). The adapter quantises to 1.6 GB (GGUF Q4_K_M) and runs at 4-8 tokens per second on a Pixel 6 with no network access. Cross-lingual evaluation on 50 Bangla queries yields ROUGE-L 0.4083 and BERTScore 0.8133, showing effective retrieval from Bangla input against an English-only corpus. In a single-evaluator pilot, a practising lawyer rated 50 responses at a weighted mean of 4.16/5 (90% rated 4 or 5), supporting utility beyond text-overlap metrics.

MD. Nafis Kamal, Mahadi Hasan Fahim, Talha Ridwan +4

Computer Science and Engineering BRAC University Dhaka, Bangladesh

Retrieval-Augmented Generation Legal NLP On-Device Language Model Inference Language Model Distillation Legal QA

Sep 21, 2026cs.LG

CLOOPD: Closing the Learner Loop in On-Policy Distillation

On-policy distillation (OPD) pays twice for each fresh batch: the student generates trajectories and a stronger teacher scores them. Existing methods improve which trajectories are scored and how the teacher signal is constructed, but usually consume it with one actor update. We introduce CLOOPD, a closed-loop framework separating teacher-signal acquisition from student-side realization. CLOOPD selects an adaptive

α

waypoint inside a KL envelope, freezes the scored batch and its advantages, re-forwards the student after each actor pass, measures realization, and allocates actor work under a separate token budget. The framework includes deterministic two- and three-pass policies, token-priced CLOOPD-TPMR, and a budget-matched control. Across six 300-step runs on an 8-H20 node, every CLOOPD policy improves the one-pass TOP-D anchor at comparable teacher-token scale: macro accuracy rises from 15.41 to 17.78 with CLOOPD-Fixed2 and 19.36 with CLOOPD-Fixed3. At step 100, CLOOPD-Fixed3 reaches 15.35, nearly matching TOP-D at step 300 while using 67.2% fewer teacher-scored tokens and 28.0% fewer GPU-hours. Earlier 8-A100 ablations show adaptive

α

eliminates observed trust-envelope violations; a third pass adds headroom. These results position CLOOPD as a framework for budgeting how fully students learn from teacher-scored tokens.

Keye Zheng, Hanyu Li, Zhan Cheng +1

Alibaba Group

Language Model Distillation On-Policy Distillation Knowledge Distillation

Sep 20, 2026cs.CL

Distill What You Trust: Reliability-Aware Multi-Teacher On-Policy Distillation

Multi-teacher on-policy distillation allows a student to learn from complementary specialists on its own trajectories. Domain-routed approaches, however, select one teacher per example and keep it fixed throughout the response. This design both depends on domain labels that mixed training corpora often lack and cannot adapt teacher selection when the expertise required changes within a trajectory. We observe that each specialist deviates more from a shared reference on in-domain prompts than on out-of-domain prompts, on average. Based on this observation, we propose \textbf{TrustMOPD}, which replaces example-level teacher selection with label-free, token-level supervision allocation. At each student-generated prefix, TrustMOPD measures this displacement in next-token preferences, calibrates its magnitude across teachers, and uses the resulting scores as proxies for local reliability to weight teacher-specific distillation losses. Evaluated across mathematics, code, and instruction following, TrustMOPD closes 91.5% and 98.0% of the overall-score gap between the initial student and oracle-routed teachers when trained on \textsc{SingleCap} and \textsc{MultiCap}, respectively, compared with 54.4% and 54.5% for the strongest label-free baseline in each setting. On \textsc{SingleCap}, it approaches label-based MOPD without using domain labels.

Jie Sun, Mao Zheng, Mingyang Song +8

University of Science and Technology of China · Foundation Model Department, Tencent · Tsinghua University +4

Language Model Distillation Multi-Teacher Knowledge Distillation On-Policy Distillation Knowledge Distillation

Sep 20, 2026cs.IR

PSD: Pseudo Self-Distillation of Memory Representation Capabilities for LLM Agents

Memory systems are becoming a core component of LLM agents, but constructing and maintaining memory remains expensive because it relies on repeated calls to large proprietary language models. This cost creates a major barrier to deploying memory-enhanced agents at scale. In this paper, we present Pseudo Self-Distillation (PSD), a framework that enables small language models (SLMs) to construct hierarchical memory representations by distilling behavior from a strong black-box oracle through a multi-stage training pipeline. Standard distillation methods require access to teacher logits or hidden states, which closed models do not expose. Unlike conventional self-distillation settings, where supervision is derived from a model's own predictions, sampled rollouts, or aggregated outputs, PSD enables a single-model distillation setup while channeling external oracle knowledge through the prompt. PSD uses a single small model in two roles: a teacher that sees a privileged prompt containing the oracle's answer as reference context, and a student that sees only the task prompt. The student learns to reproduce the teacher's output distribution, absorbing oracle-guided behavior into its own weights without accessing the oracle's internals. On LoCoMo, PSD-trained Qwen3-0.6B, 1.7B, and 4B match or exceed GPT-4.1-mini on downstream retrieval at a fraction of the deployment cost, with off-policy PSD achieving the strongest results across most conditions. We further show that this memory-construction capability transfers out-of-distribution to LongMemEval, despite the students being trained exclusively on LoCoMo with no exposure to LongMemEval data.

Pirzada Suhail, Menglin Xia, Xuchao Zhang +3

Microsoft Research

LLM Agent Memory Persistent Memory for Language Models Language Model Distillation

Sep 17, 2026cs.LG

When EOS Tokens Disagree: Understanding Length Inflation in On-Policy Distillation

We study length inflation in on-policy distillation (OPD), where student responses can become excessively long and even exhaust the generation budget. We identify \emph{termination-token mismatch} between base students and post-trained teachers as an important source of this behavior. Across Qwen3, Llama, and Gemma, the two models can place their stopping probability on different EOS tokens, even when their declared stopping sets are identical. This mismatch can suppress the student's preferred termination action without reliably transferring the teacher-preferred alternative. We show that aligning the decoding stopping set alone is insufficient, while treating functionally equivalent EOS tokens as a shared semantic stopping action substantially mitigates mismatch-induced length inflation across all three model families. To further understand how termination behavior evolves over training, we study OPD across different K2-Horizon training stages. This stage-wise analysis shows that termination preferences can shift substantially during training, while also revealing a distinct length inflation late in the OPD run that persists beyond termination alignment. Together, these results identify termination mismatch as an important, but not exhaustive, source of OPD length dynamics. We release an implementation incorporating the proposed termination-handling corrections.

Yuxiao Yang, Tianrun Yu, Shangzhe Li +6

University of North Carolina at Chapel Hill · Brigham Young University · Microsoft

Language Model Distillation On-Policy Distillation

Sep 16, 2026cs.LG

Trajectory Learnability for Offline On-Policy Distillation with Imperfect Teachers

Offline on-policy distillation gains efficiency by collecting student trajectories and teacher supervision once and reusing them throughout optimization. The same reuse makes imperfect supervision persistent. Since even strong teachers can fail, we ask \emph{what remains learnable from imperfect teacher supervision?} Teacher failure is only a coarse problem-level signal and does not imply that all supervision along the associated student trajectory is unhelpful. A natural alternative is to estimate teacher recoverability along the trajectory, but repeated continuations largely erase the efficiency advantage of offline distillation. We instead use teacher-successful problems to define a cheap reference for what the student can learn. We train on teacher-successful problems and measure how the likelihood of each observed token in trajectories from teacher-failed problems changes. We use these signed likelihood changes as an operational \emph{learnability signal}: larger increases indicate behavior more strongly promoted by successful-only learning. We aggregate this signal into trajectory-level weights for the original distillation loss. Unlike continuation-based estimates, our learnability requires no additional generation and can be computed once from stored trajectories and model checkpoints. Across mathematical reasoning and code generation, our method improves an offline OPD baseline by up to 2.7 percentage points and matches or outperforms online OPD variants on multiple benchmarks. Despite the additional successful-only distillation stage, it uses 2 GPUs and about 22 GPU hours, compared with 3 GPUs and 36--48 GPU hours for representative online OPD methods.

Yihao Ai, Weilong Yan

National University of Singapore

Language Model Distillation On-Policy Distillation

Sep 15, 2026cs.LG

Coupled Calibration and Learning: Mitigating Teacher Bias in LLM Distillation without Target-Domain Reward Feedback

Large language model (LLM) distillation aims to transfer the capabilities of a powerful teacher to a smaller student. Direct imitation, however, can also transfer the teacher's systematic bias and errors. This challenge is particularly pronounced under covariate shift, when the teacher's reliability on target questions is uncertain and target-domain reward feedback is unavailable. We propose Coupled Calibration and Learning (CCL), an LLM distillation algorithm that couples teacher calibration with student updates through token-level branching, using reward feedback only on source questions. Each iteration calibrates the teacher using source feedback and then uses the calibrated teacher to train the student on target questions. The updated student, in turn, informs subsequent calibration. In an autoregressive policy framework, we prove that the output student's expected average Kullback-Leibler divergence to the oracle student converges to zero at a polynomial rate in the number of iterations. The oracle maximizes the true reference-regularized target reward within the student class, which need not represent the unrestricted optimal policy. Our analysis quantifies the progress of projected student gradient updates while controlling the error in teacher calibration. We further establish a separation from regularized direct matching: its error relative to the oracle student can remain bounded away from zero even when the teacher achieves higher regularized target reward than every student policy. These results demonstrate that LLM distillation can overcome persistent teacher bias and recover the optimal student through coupled calibration and learning, without target-domain reward feedback.

Haichen Hu, Yuheng Zhang, David Simchi-Levi

MIT · UIUC

Language Model Calibration Language Model Distillation Knowledge Distillation

Sep 15, 2026cs.LG

Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation

On-policy distillation (OPD) has emerged as an effective approach for large language model post-training, yet existing objectives face a trade-off between objective fidelity and optimization stability. Token-level OPD provides stable but local supervision, whereas sequence-level OPD captures future credit at the cost of horizon-dependent variance. We establish a unified temporal-credit view of these formulations, showing that practical token-level OPD can be interpreted as a temporal approximation to the sequence-level reverse-KL gradient. Building on this connection, we propose

γ

OPD, which uses discounted temporal credit assignment to balance long-horizon supervision and optimization stability, while admitting a horizon-independent variance bound. We further develop a reward-compatible bounded mixing (RBM) mechanism for

γ\mathrm{OPD}

that balances verifiable outcome feedback with the discounted OPD advantage to move beyond purely teacher-dependent optimization. Experiments on mathematical and code reasoning demonstrate consistent improvements over existing OPD methods across vanilla, size-mismatched, and multi-teacher distillation settings.

Shiqi Liu, Zeyu He, Letian Tao +9

School of Vehicle and Mobility & College of AI, Tsinghua University · 2Didi Voyager Labs, DiDi Autonomous Driving

RL for Language Model Reasoning Temporal Credit Assignment Language Model Distillation On-Policy Distillation

Sep 14, 2026cs.CL

Breaking the Token Ceiling: Distilling Smaller, Stronger Byte Models

Small models are made more capable through distillation from a larger one that shares their tokenization scheme. However, do distilled byte and token models behave similarly in terms of scaling trends as compute and data increases? To enable this comparison, we introduce two variants to efficiently convert token logits to Byte Logits: 1) approximate: Marginalize-It, and 2) exact: End-Of-Token. We then present the first large scale study of overtraining decoder-only dense transformer models varying two dimensions simultaneously: the tokenization scheme (Tokens, Bytes, Bytes w/ eot) and the training objective (Distillation vs. Cross-Entropy), sweeping layer-parameter-matched models with roughly 1 billion parameters up to 1 trillion bytes of data. Across eight benchmarks spanning three categories: Multiple Choice QA, Language Generation, and Machine Translation, we find that Token-1B models outperform byte models (End-Of-Token-1B and Bytes-1B) in the low-FLOP regime but eventually plateau; byte models start worse yet surpass Token-1B models with more compute, reaching a higher downstream task performance ceiling. Extrapolating the average top-1 error vs. validation BPB scaling laws predicts that, asymptotically, distilled End-Of-Token-1B outperforms distilled Token-1B by up to 4%. They are also far more data efficient, matching the performance of distilled Token-1B using only one-sixth of the training data. Moreover, by operating over a small vocabulary of 256 bytes instead of on the order of 100K tokens, they circumvent the need for top-k truncation during logit dumping, while also reducing logit storage costs to roughly one-fifth. Finally, our downstream performance scaling laws predict that our distilled End-Of-Token-1B models asymptotically surpass the Llama 3.2-1B, Gemma-3-1B-pt, and Gemma 2B models on averaged downstream tasks by up to 6.5%, 8.1%, and 2.1%, respectively.

Kalyani Marathe, Artidoro Pagnoni, Tomasz Limisiewicz +4

University of Washington, Seattle · Work done at Meta FAIR · Meta FAIR

Decoder-Only Language Models Language Model Scaling Laws Byte-Level Language Model Language Model Distillation

Sep 14, 2026cs.AI

From Collaboration to Capability: Internalizing Routed LLM Experts into Compact Reasoners

A compact controller can coordinate stronger experts by selecting whom to consult, formulating requests, and integrating their responses. We study whether learning from both the controller's decisions and the experts' reasoning and code improves its generation after expert removal. We introduce \textsc{Rivet} for \emph{collaboration internalization}: expert-augmented reinforcement learning applies a shared outcome signal to controller decisions and returned expert spans, and verified trajectory internalization consolidates complete successful interactions through format-aware supervised training. The deployed controller generates reasoning, code, and interaction structure with local Python execution and no external LLM. Across seven competition-mathematics benchmarks, RIVET-1.7B and RIVET-4B achieve average accuracies of

28.25\%

and

44.16\%

; Stage~II improves RIVET-4B's accuracy after expert removal by

6.49

points, and GPQA-Diamond results provide evidence of generalization to scientific reasoning. Ablations show gains from ordinary trajectory supervision and additional format weighting, supporting the effectiveness of training on the content and structure of verified collaborations.

Frank Nie, Shuyao Wang, Ethan B. Liu

Shandong University · Zhejiang University

RL for Language Model Reasoning Multi-Agent Collaboration Language Model Distillation Multi-LLM Collaboration

Sep 14, 2026cs.LG

SCOPE-OPSD: Fisher-Conditioned Privileged Subspaces for On-Policy Self-Distillation

On-policy self-distillation (OPSD) scores student-generated prefixes with a solution-conditioned self-teacher, yet transfers supervision only through next-token probabilities. We ask whether the aligned final-layer discrepancy offers a useful second channel, and how to test that channel without confusing its geometry with auxiliary strength. SCOPE-OPSD projects the privileged teacher-student residual onto a frozen rank-64 factor estimated from residual covariance and language-model-head Fisher sensitivity. It reuses the forwards already required by OPSD and adds neither rollouts nor inference-time modules. A matched Random control preserves the structured factor's rank and nonzero spectrum and uses per-arm gradient-RMS calibration, isolating the effect of the data-dependent orientation. Across the complete 25/50/75/100-step trajectories for Qwen3-1.7B, 4B, and 8B, Structured is never below Pure OPSD, with strict gains in 11 of the 12 model-checkpoint combinations and an exact tie at 4B step 25. Structured also exceeds matched Random in 10 of the 12 combinations. At step 75 on Qwen3-1.7B, Structured exceeds matched Random by 1.39 Macro Avg@12 points in each of two independent training reruns. A cross-fitted diagnostic also shows 4.40 times greater held-out privileged-gap capture than the matched random orientation. The results support a compact, Fisher-conditioned privileged subspace for short-budget OPSD.

Yunmeng Chen (Chongqing Ant Consumer Finance Co., Ltd), Kunyu Wang (Alibaba Cloud Computing Co. +18

Chongqing Ant Consumer Finance Co., Ltd. · Alibaba Cloud Computing Co., Ltd. · Chongqing University of Posts and Telecommunications

On-Policy Self-Distillation Language Model Distillation Learning Using Privileged Information Knowledge Distillation

Sep 13, 2026cs.AI

Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition

A core goal of efficient reasoning is to improve the accuracy-efficiency frontier. However, jointly improving reasoning accuracy and inference efficiency can be challenging, as the two objectives can favor different reasoning behaviors. Independently post-trained models already offer distinct strengths in accuracy and efficiency. We introduce Lightning Weave, a post-training framework that extracts and composes these independently learned capabilities in a single student through on-policy distillation. Each acquired capability is represented by the policy shift from the model before post-training to the resulting specialist. Lightning Weave combines aligned log-ratio shifts at shared student token states and uses Tilted-Target DOPD to convert the cached signals into a stable learning target. Each anchor pair scores the cached trajectories once, enabling subsequent student training without serving multiple live anchor models concurrently. Across diverse student models and benchmarks in mathematics and code, Lightning Weave substantially improves upon the base students and achieves a state-of-the-art accuracy-efficiency frontier. On Qwen3.5-4B, it raises HMMT 2025 accuracy from 59.2% to 64.0% with 10.7% fewer response tokens, and LiveCodeBench v5 accuracy from 41.7% to 54.2% with 9.6% fewer response tokens. Adjusting the relative strengths of the anchor signals yields a strong empirical accuracy-efficiency Pareto frontier. These results establish Lightning Weave as a new practical route to efficient reasoning through capability composition. Code is released at https://github.com/jet-ai-projects/Lightning-Weave.

Yecheng Wu, Song Han, Han Cai

Massachusetts Institute of Technology · NVIDIA

Efficient Language Model Reasoning Language Model Distillation Language Modeling LLM Post-Training Efficient Language Model Inference

Sep 12, 2026cs.SD

X-AuT: Progressive Audio-Encoder Compression for Speech LLMs with Cross-Scale Distillation

Reducing audio-encoder depth lowers the inference cost of speech large language models, but removing complete blocks perturbs the embeddings consumed by the decoder and can cause deletion and premature end-of-sequence errors. We introduce X-AuT, a progressive framework that selects layer combinations through short behavioral probes and restores the pruned model through representation alignment, cross-scale distillation, scheduled student-policy supervision, and LoRA finetuning. The language-model backbone remains frozen, while attention LoRA adapters and the tied output embedding adapt during distillation. Training uses the highest-agreement tier from a transcript-consistency pipeline, followed by source reweighting during finetuning. On ten public Chinese--English benchmarks, compressing Qwen3-ASR-0.6B from 18 to 16 audio-encoder layers reduces macro-average error from 5.61% to 5.27%. The 14-layer model reaches 5.75% with 20.7% fewer audio-tower parameters. Under the matched recipe, the 1.7B teacher yields 5.55% mean error, compared with 8.45% for self-distillation, and progressive 18

\rightarrow

14 pruning outperforms direct pruning (5.75% vs. 6.73%). These single-run results establish two practical operating points and show that the accuracy effects vary across benchmarks. Project website: https://xpeng-ai.github.io/x-aut

Haojun Zhang, Yi Zou, Min Chen +7

XPeng Inc.

LLM Compression Language Model Distillation Speech Language Models Neural Network Pruning

Sep 12, 2026cs.AI

A Unified Per-Token Gating Family for On-Policy Distillation: FKL/RKL Mixing with Multi-Channel and Bias Coefficients

Per-token gating of forward/reverse KL losses has become a standard technique for on-policy knowledge distillation (OPD), but existing methods such as EOPD (Jin et al., 2026) and ToDi (Jung et al., 2025) each fix a single gating signal and a single gating direction, and the two have never been compared directly. We introduce a four-coefficient parameterization lambda_t = sigma(a * h_t + b * u(x) + c + d * gap_t) in which direction-aligned proxies of EOPD and ToDi appear as one-dimensional (1D) restrictions, and which adds multi-channel composition and an explicit bias as further degrees of freedom. On TweetEval (Barbieri et al., 2020) emotion and hate, with a Qwen3-32B teacher and a Qwen3-4B student, configurations in the full family reach higher accuracy than the matched-magnitude single-channel (entropy-only / gap-only) 1D restrictions in 33 of 36 comparable cells, and a 26-cell mean-match isolation experiment places dynamic gating ahead of effective-KL-matched static baselines in 19 of 26 cells. Because cells share training data, models, and parameter substructure, we report both counts as exploratory aggregate directional evidence rather than as independent hypothesis tests. Targeted three-seed paired replications of the nine headline comparisons singled out by that sweep -- including a third task, offensive -- are directionally consistent, but individually smaller than the single-seed estimates and not significant at n=3. We therefore present the parameterization primarily as a shared coordinate system for comparing per-token gating designs in short-output classification OPD.

Suwan Wu, Yumeng Lin, Pengcheng Yuan +1

Xiaohongshu Inc. · Tianjin University

Adaptive Loss Weighting Language Model Distillation On-Policy Distillation

Sep 10, 2026cs.CL

Negative Self-Distillation: Learning to Reason by Avoiding Flaws

On-Policy Self-Distillation (OPSD) has emerged as a popular paradigm for large language model (LLM) self-improvement, allowing models to act as their own teachers by leveraging privileged information such as ground-truth solutions. However, recent findings indicate that OPSD can severely degrade the performance of LLMs on complex reasoning tasks: By forcing the student to imitate an artificially confident reasoning trace conditioned on privileged information, OPSD inadvertently suppresses expressions of uncertainty and penalizes the exploratory, self-corrective behaviors required to solve challenging problems. To address this, we introduce Negative Self-Distillation (NSD), a new framework that optimizes LLMs by diverging from flawed reasoning rather than imitating privileged solutions. Instead of relying on ground-truth answers or external supervision, NSD uses the model itself to generate a question-specific negative condition (eg, acting as a ``careless reasoner'') and pushes the student's distribution away from this self-generated negative teacher. Naively applying unlearning objectives to achieve this divergence is problematic, as flawed reasoning tokens are confounded with basic linguistic tokens; indiscriminately penalizing both risks catastrophically degrading the model's foundational language capabilities. We resolve this by designing a dynamic gating mechanism that automatically identifies and isolates reasoning-critical tokens, ensuring gradient updates target only behavioral flaws while preserving the model's linguistic priors. Empirically, NSD consistently outperforms OPSD and other label-free, self-bootstrapping reinforcement learning (RL) baselines.

Rongcan Pei, Zhepei Wei, Shuyao Xu +3

Department of Computer Science, University of Virginia · Stanford University

Language Model Distillation Self-Distillation Language Model Self-Improvement LLM Reasoning

Sep 9, 2026cs.LG

CompassOPD: Cross-Family On-Policy Distillation via Within-Family Likelihood Shifts

On-policy distillation (OPD) provides dense token-level supervision on student-generated trajectories. Although OPD performs strongly when teacher and student belong to the same model family, we find that its effectiveness degrades in cross-family settings even after tokenizer alignment, with substantially stronger external teachers offering little additional improvement. To understand this disconnect, we decompose the cross-family OPD signal into two components: an offset between a low-capability teacher-family reference and the student, and the within-family log-likelihood shift from that reference to the strong teacher. Standard OPD transfers both components together, allowing the offset to dominate the update direction and obscure the changes associated with teacher capability improvements. We propose CompassOPD, which removes this offset and transfers the within-family shift, while a frozen student reference anchors updates to the student's initial policy. Thus, both teacher-side and student-side changes are measured within their respective model families. Experiments across three student families and multiple teacher families show that CompassOPD consistently outperforms standard cross-family OPD, improving average reasoning accuracy by up to 5.50 points. For an MoE teacher, we further construct the reference directly from the teacher checkpoint by reducing expert activation, eliminating the need for a separate reference checkpoint while retaining a 3.43-point gain over OPD.

Naibin Gu, Qingyi Si, Chenxu Yang +5

Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

Language Model Distillation On-Policy Distillation LLM Reasoning

Sep 9, 2026cs.CL

Data-Centric Post-Training for Financial Reasoning: Mining, Distillation, and Verifiable Learning

Financial text, textbooks, and question-answer pairs are abundant, but only a small fraction is directly usable for reasoning-focused post-training. Existing QA pairs often lack explicit reasoning, sufficient context, or reliably verifiable answers, while textbooks must first be transformed into synthetic training examples. We present a data-centric pipeline that constructs complementary corpora by mining open-source reasoning traces, distilling financial instruction data, and generating knowledge-graph-guided question-answer pairs from financial educational material. After semantic deduplication, three lightweight sequence classifiers select finance-relevant examples, reject under-specified questions, and identify tasks suitable for reinforcement learning with compact rule-based verifiers. For model adaptation, we study supervised fine-tuning and reinforcement learning, while self-distilled fine-tuning and post-training model merging are used to prevent the loss of financial capabilities already present in the starting model. We evaluate the adapted language models using FINESSE-Bench, reporting aggregate performance and changes relative to their starting checkpoints. Across the selected comparisons, ordinary SFT reduces FINESSE-Bench accuracy by 3.2-4.0 percentage points, whereas self-distilled SFT improves over the corresponding starting models by 1.0-2.8 points. Equal-weight merging recovers 3.0 points over its SFT parent and finishes 0.9 points above the original model; GRPO on hard tasks adds 0.4 points after self-distilled SFT or 3.0 points when applied directly to verifiable tasks. These results show that retention-aware adaptation can improve financial reasoning without the regressions observed after ordinary SFT.

Zhirayr Hayrapetyan, Andrei Kalmykov, Denis Kokosinskii +2

RL for Language Model Reasoning Language Model Distillation LLM Post-Training Language Model Post-Training

Sep 9, 2026cs.LG

Positional task conditioning for scalable defect detection across product families in large product catalogs

Product families in large product catalogs suffer from inconsistencies such as duplicates and unit mismatches that degrade customer experience. Detecting these requires reasoning over multiple error types across lengthy product listings, where LLM classification quality degrades due to long-context limitations. We address this by decomposing detection into focused sub-tasks that reduce context and isolate error types, improving F1 from 52% to 87%. For scalable deployment, we introduce Positional Task Conditioning (PTC), which distills this capability into a single smaller model by reinforcing task identity at structural prompt boundaries. PTC outperforms rationale-based distillation across five models and two architecture families, achieving within 1.79% F1 of the frontier at upto 98% lower cost. Our system is deployed across multiple countries processing 10+ million product families.

Soham Satyadharma, Gabriel Roccabruna, Suleiman A. Khan

Amazon Catalog AI

Language Model Distillation Classification E-Commerce

Sep 8, 2026cs.LG

Distillation as Probability Transport: Routed On-Policy Distillation

On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

Tianle Xia, Lingxiang Hu, Yiding Sun +6

Tencent

Language Model Distillation On-Policy Distillation Optimal Transport

Sep 5, 2026cs.LG

VERPO: Verified Evidence Regularized Policy Optimization

Verifiable rewards improve language models through reliable task-level feedback, but methods based on Group Relative Policy Optimization (GRPO) apply a sequence-level advantage uniformly across all tokens. This coarse credit assignment reinforces or penalizes entire responses without identifying which local decisions to preserve, reinforce, or revise. Conversely, evidence-conditioned self-distillation provides denser token-level supervision, yet teacher imitation can transfer stylistic artifacts and miscalibrated confidence that destabilize training when misaligned with task success. We introduce VERPO, which converts evidence-conditioned guidance into reward-aligned token-level credit assignment while retaining the outcome objective. VERPO decomposes teacher guidance into an evidence-free reference term and signed, evidence-induced corrections at each token. A stopped controller combines selective acceptance, token-wise localization, and cost-aware scaling by balancing alignment with the local GRPO update direction against Fisher movement cost. Furthermore, we introduce Fisher Evidence Contrast (FEC), which attenuates nuisance shifts along an estimated evidence-presence direction through a regularized projection. Across five scientific reasoning and tool-use tasks, VERPO prevents optimization collapse and consistently achieves the highest multi-task average across model backbones, yielding marked improvements particularly on smaller models over strong baselines. Qualitative diagnostics confirm that token acceptance selectively targets reasoning bottlenecks consistent with local reward alignment and Fisher movement cost.

Haijiang Li, Chengyu Lv, Yi Zhang +8

Independent · Tongji University · Fudan University +3

RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Language Model Distillation Reinforcement Learning with Verifiable Rewards Scientific Reasoning in Language Models