Language Model Distillation

Skills, reusable procedural guidance added at inference, can substantially improve LLM downstream performance (Li et al., 2026). Prior work retrieves skills from a bank by semantic relevance, then uses them as inference-time patches or for model distillation. The individual utility of each skill, however, is largely neglected. We first show that, in on-policy distillation where skill-conditioned policies serve as teachers, fewer than 25% of retrieved skills provide useful distillation signals. We then propose SGUID, a method for selecting a compact subset of skills for distillation. SGUID retains a skill only if it consistently yields effective learning signals during training. The selected skills are then distilled to produce a better model. Our results show that not all skills are worth distilling. Across four models from the Olmo and Qwen families, distilling 6 selected skills matches or exceeds full-bank distillation in mean avg@12 on three of the four models, and on all four after a second round that distills 3 newly selected skills, while the full banks are up to 11x larger. Importantly, SGUID supports stable model-skill co-evolution: after a distillation round, a new candidate bank is curated from the updated model's rollouts, and SGUID selects which skills to internalize next. In the second round, this loop selects 3 new skills and improves Qwen3-8B from 64.3% to 66.3%. The selection step is essential for stability: on Qwen3-4B, naively updating the model with unfiltered skills degrades performance, including a 0.3 percentage point drop on HMMT25, whereas SGUID improves HMMT25 by 0.5 points after the first round and 1.1 points after the second. These results identify skill selection as the key mechanism for stable model-skill co-evolution.

Unauthorized model distillation, in which a model is trained on the outputs of a proprietary large language model (LLM), is a growing threat to model providers. We study distillation inference: determining whether a suspect model was distilled from another model or trained independently. We formulate this problem as a hypothesis test and estimate the behavior expected under each hypothesis by training shadow models: distilled shadow models learn from the teacher's reasoning traces, whereas independent shadow models learn only from reference answers. The auditor measures how closely each model predicts the teacher's reasoning outputs and then uses the shadow models to convert the suspect's score into a calibrated p-value. In a preliminary study using Qwen2.5-7B as the teacher and Llama-3.2-3B for the suspects, our test achieves a true positive rate of 1.0 at a significance level of 0.02. These results demonstrate the feasibility of using distillation inference to detect distillation attacks.

Knowledge distillation (KD) transfers knowledge from stronger Teacher models to weaker Student models, but most methods require training the Student parameters, thereby binding the distilled knowledge to a specific architecture and checkpoint. This implicit representation is difficult to interpret or reuse across models and limits KD for API-only or costly-to-train models. This paper studies knowledge transfer for large language models (LLMs). We introduce Universal Textual Teaching (UTT), a parameter-update-free framework that distills observed Teacher-Student knowledge gaps into a textual, interpretable, and reusable natural-language artifact called Primer. Specifically, UTT first identifies representative gap cases through paired evaluations, and iteratively updates the Primer via multi-role interactions: the Student attempts each task, the Prompter turns evaluation feedback into a teaching instruction, the Teacher provides a targeted demonstration, and the Synthesizer consolidates validated lessons. Empirically, on the challenging math (Omni-MATH-2) and code generation (KernelBench) tasks, extensive results confirm the effectiveness of the method: UTT remarkably raises the Student's accuracy from 9.4% to 48.6% and Fast1 accuracy from 9% to 35% on KernelBench, while increasing mathematical reasoning accuracy from 27.6% to 51.7%. UTT also performs better than representative prompt engineering and parameter-based KD methods. Of note, UTT is shown to be generalizable across different Teachers and Students: a Primer synthesized for one Teacher-Student pair can generalize to other Students that do not participate in the synthesis.

On-policy distillation (OPD) supervises student-generated trajectories with token-level teacher signals. Its sampled-token variant avoids the cost of full-vocabulary probabilities. Yet we find that training on fewer tokens can outperform full-token OPD, challenging the intuition that more supervision improves learning. This motivates selecting tokens by learning value. Existing disagreement-based criteria ignore probability scale: tokens assigned negligible probability by both models, termed low-low tokens, can receive large log-ratio rewards and hinder learning. We propose DIAL-OPD, a token-selection method that bridges log-probability and probability spaces by weighting reward magnitude with the logarithmic mean of teacher and student probabilities. A parameter beta controls this weighting, and the highest-scoring tokens are retained. Across 4 teacher-student pairs and 7 mathematical reasoning benchmarks, we compare DIAL-OPD with 9 baselines. Retaining only 40% of tokens, it outperforms Vanilla OPD and its full-token variants, with mean accuracy gains reaching 5.25 percentage points over Vanilla OPD, and doubles AIME25 Pass@16 from 13.33% to 26.67%. It also achieves up to an 18% relative improvement in mean accuracy over the strongest token-selection baseline at matched retention ratios. With a 4B teacher, DIAL-OPD surpasses the strongest full-token baseline using an 8B teacher at both student scales, showing that effective supervision allocation can outweigh teacher scaling. Further analysis shows that moderate beta balances suppressing low-low tokens against preserving useful disagreements. Token-level evidence reveals that DIAL-OPD filters high-reward tokens with limited reasoning value while preserving supervision critical to reasoning correctness.

Self-distillation can improve reasoning without a separately trained, more capable teacher, but its effectiveness depends on how the self-teacher gains an advantage over the student. Conditioning the teacher on reference answers or solutions can provide such an advantage, but this information may be unavailable. Reflection offers a way to derive explicit error diagnoses and revision guidance from self-generated attempts, yet existing reflection-based methods often combine it with reference information, rich task feedback, or persistent memory. We introduce ReTeach, a Reflective self-distillation framework that constructs its self-Teacher through multi-round reflection and retry using only self-generated attempts and outcome-level verification. Starting from an unsuccessful student rollout, the teacher alternates explicit reflection with renewed attempts until success or the retry budget is exhausted, without reference answers or solutions, external diagnostic feedback, or cross-example memory. Each failed retry informs subsequent reflection, while successful correction provides outcome-level evidence for the potential utility of the resulting teacher context. An outcome-aware selection and weighting strategy distinguishes initially correct, reflection-corrected, and unresolved examples, assigning separate weights to their category-normalized distillation losses. Through on-policy distillation, the student matches the teacher's context-conditioned token-level predictive distributions at prefixes of its own rollouts, transferring the benefits of iterative correction while retaining single-pass inference. Across six benchmarks spanning mathematical reasoning, science question answering, and tool use, ReTeach improves average accuracy over GRPO by 1.39 percentage points.

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

On-policy distillation (OPD) enables effective capability transfer between language models, yet the mechanisms underlying its failures are not fully understood. Across code generation and mathematical reasoning, OPD with larger-scale teachers exhibits early loss plateaus, with an average final loss reduction of 25.1% after 200 updates, compared with 96.2% for self-RL teachers, obtained by further reinforcement learning (RL) training of the initial student. To understand this difference, we analyze OPD as an idealized continuous-time dynamical system in the small-learning-rate limit. Our training-log diagnostics associate these plateaus with an early decline in a gradient-based learning-signal proxy while substantial loss remains; these measurements do not establish why the underlying gradient weakens. We further prove a local recovery guarantee for teachers sufficiently close to the initial student in a shared parameterization under regularity conditions, offering a conditional explanation for the success of self-RL teachers in our experiments. Across runs with and without loss plateaus, we observe small relative parameter changes (0.025-0.098%) and high similarity between the student's representations before and after OPD (linear CKA $>0.98$ across layers). These observations suggest that limited representation adaptation may contribute to learning-signal collapse, a hypothesis that remains to be tested. Code is available at https://github.com/leizhao7/opd-learning-signals.

Powerful misaligned AI models might recognize alignment evaluations and strategically behave well on them, rendering direct audits uninformative. However, distilling such a model into a weaker benign student places the teacher in a Distillation Double Bind: if misalignment transfers, the student may conceal it less effectively, revealing evidence about the teacher; if it does not, the student may learn useful capabilities while remaining benign. We introduce two distinct distillation approaches, one targeting each outcome. Distillation for Incrimination (DFI) aims to transfer misalignment but not the ability to conceal it. Distilling AuditBench's secret-keeping models into their underlying instruction-tuned model produces students that are significantly more likely than their teachers to admit their hidden behavior when asked, suggesting that knowledge of the behavior transferred more readily than the propensity to conceal it. Confession gains largely disappear when the student does not share the teacher's pretrained base, so DFI should target the teacher's own pre-RL checkpoint, which is weaker than the teacher but shares its base model. Distillation for Capabilities (DFC) aims to transfer capabilities but not misalignment. Among several techniques we evaluate, two are effective: inoculation prompting and training for more epochs on fewer unique examples. Both preserve the capability gains of standard distillation while substantially reducing the subliminal transfer of an animal preference, our proxy for misalignment. Together, these findings demonstrate two ways distillation can be used for AI safety: incriminating misaligned models, and extracting their capabilities without their misalignment.

Knowledge distillation is an established technique for improving the capabilities of small, efficient student models by training them with the representations of larger, more capable teacher models. Much of the recent work in the distillation of large language models (LLMs) has focused on distilling abilities learned during post-training, such as instruction following, chain-of-thought reasoning, and tool usage. This has left a large research gap in general knowledge distillation for LLMs, which is essential for developing efficient and private systems suitable for deployment on edge devices. We take a first-principles approach, evaluating previous lessons from prior works and conducting new explorations to develop a distillation methodology suitable for modern LLMs. We present KDFP, a novel methodology for white-box general knowledge distillation in LLMs. We demonstrate that KDFP outperforms existing methods by 1.6% $-$ 4.9% across 9 benchmarks while increasing training efficiency by up to 99.1% through ephemeral parameter reduction.

The demand for personalized LLMs is shifting from style imitation toward content quality. We investigate whether self-distillation can bridge this gap in existing fine-tuning paradigm. To address this limitation, we introduce MIRROR(Meta- personalization by Internalizing Reference-Revealed On-policy Reflections), a novel self-distillation framework that shifts LLM personalization from imitation toward preference internalization. First, we replace reference-token imitation with reference-revealed on-policy self-distillation, aligning the model's next-token distributions along its own generation trajectories with those of its reference-conditioned self, thereby internalizing user preferences rather than reproducing reference wording.Second, we introduce MIRROR-F, a focal plug-in that augments on-policy distributional alignment with selective supervision over informative reference tokens, thereby strengthening content generation while preserving user-specific expression. Across three personalized generation benchmarks, two model scales, and complementary reference-based and LLM-based evaluations, MIRROR and MIRROR-F achieve leading overall personalization performance and superior text quality, while exhibiting less catastrophic forgetting than SFT-based baselines on three unseen personalized generation tasks. The gains are consistent across model scales and application scenarios, translating to improved performance in LLM personalization tasks.

On-policy post-training can improve large language models by learning from their own trajectories, but requires costly rollout generation. We ask whether fixed demonstrations can support competitive off-policy learning through better supervision. Our premise is that their usefulness depends not only on the training trajectories, but also on whether supervision provides informative preferences among continuations and connects this guidance to the reasoning decision being learned. We introduce Step-Aligned Privileged Distillation (SAPD), a rollout-free self-distillation method that turns demonstrations into step-aligned distributional supervision. Its key insight is to use the known progression of a reference solution to associate each reasoning transition with targeted privileged guidance, rather than treating the solution as undifferentiated context. On mathematical reasoning benchmarks, SAPD outperforms supervised fine-tuning and label smoothing on average while remaining competitive with on-policy reinforcement learning and self-distillation. Analyses support both the value of context-dependent distributional guidance and the benefit of aligning privileged information with the current step. SAPD also largely preserves out-of-domain coding performance and achieves approximately 2x training-loop speedups over the on-policy baselines. These findings suggest that carefully constructed supervision can make fully off-policy post-training a competitive and computationally efficient alternative. Our code is available at https://github.com/Miaow-Lab/SAPD.

Probability-only models, which TypeSafe calls System One models, return calibrated probabilities for fixed choices in milliseconds and generate no text. We study one such model, Jev, through two tasks that require decisions under tight constraints. In bullet chess, a bot that places Jev's judgment inside Stockfish search alongside an opening book and endgame tablebases climbs above a 2200 Lichess bullet rating against other bots. Live model calls are too slow for search, so we distill pairwise judgments into a compact evaluator that runs at every position. We then ask how best to spend a fixed labeling budget when an LLM, Qwen3-32B, is available as a second teacher. In chess, averaging both judges' labels beats spending the whole budget on Qwen alone by 9.6 Elo (95% interval 4.3 to 14.9), and the gain replicates on fresh openings; a second answer from the same judge is no substitute, and Jev is the strongest partner for Qwen among the models tested. In passage reranking, Jev's labels alone train a reranker that scores as high as Qwen's, from 21 minutes of API calls instead of 5.1 GPU-hours, and adding Qwen gains at most a few thousandths in ranking quality. Search supplies the lookahead, distillation makes the judgment cheap enough to use at every position, and an LLM partner pays off in chess.

Multi-label topic assignment for user-generated content (UGC) -- including product reviews and buyer-seller conversations -- poses unique scalability challenges in large-scale e-commerce due to informal language, extreme label sparsity, and rapidly evolving taxonomies. While utilizing Large Language Models (LLMs) as labeling oracles to distill ground-truth data has emerged as an industry standard to bypass prohibitive manual annotation costs, determining the optimal, low-latency architecture for the resulting student models remains an open challenge. To address this, we conduct a comprehensive evaluation across Small Language Model (SLM) parameter scales (1B, 4B, and 8B) and architectural paradigms (causal generative versus bidirectional discriminative). Comparing generative text-to-label classifiers against discriminative baselines (DeBERTa-V3 and ModernBERT), our analysis reveals a crucial data-dependent trade-off: while discriminative models outperform ultra-lightweight generative models on structured product reviews, even the smallest 1B generative model surpasses discriminative baselines on complex, multi-turn conversational data. Furthermore, generative models maintain robust performance under massive label-set expansion (up to 112 topics) and severe long-tail distributions, whereas discriminative baselines suffer a 35% drop in Macro-F1 at scale. Finally, we detail the successful production deployment of these optimized models across both product review and conversational domains, demonstrating strict latency compliance and tangible business impact at a global marketplace scale.

Simulating individual behavior requires large language models (LLMs) to preserve persona traits while adapting to dynamic social contexts. However, general-purpose LLMs often flatten distinct personas, while task-specific tuning suffers from fragmentation and generalization. To overcome these challenges, we organize individual simulation into the \textbf{FONTS Taxonomy}, comprising five complementary capability dimensions: \emph{persona fidelity} (\textbf{F}), \emph{outcome realization} (\textbf{O}), \emph{behavioral naturalness} (\textbf{N}), \emph{trajectory coherence} (\textbf{T}), and \emph{social grounding} (\textbf{S}). Grounded in this taxonomy, we curate a standardized training corpus library of approximately 10 million instances across 14 representative datasets and present \textbf{Socio-Foundation}. Socio-Foundation decouples specialization from integration via a three-stage pipeline: learning task experts via DAPO, consolidating them into capability experts via off-policy distillation, and unifying them via multi-teacher on-policy distillation (MOPD). We also establish \textbf{IndiEval}, consolidating 29 metrics across the FONTS dimensions. Experiments show that Socio-Foundation outperforms its \textit{Qwen3-8B} base by 11.0 points and approaches frontier models such as \textit{GLM-5.2}, with ablations and out-of-distribution evaluations further demonstrating the effectiveness and generalization of our model.

On-Policy Distillation (OPD) trains a student on its own generations using teacher feedback. With different tokenizers, comparing teacher and student predictions requires alignment at both sequence and vocabulary levels. In this paper, we examine whether expanding this alignment coverage improves learning. Across three heterogeneous teacher--student pairs on mathematical reasoning and code generation, strict 1:1 groups already cover most student-generated tokens despite substantial vocabulary mismatch. On responses sampled from the students before distillation, the shared vocabulary retains nearly all teacher and student probability mass at strictly aligned positions on average. Restricting reverse KL to a student-selected top-16 subset of the shared vocabulary at each strict position achieves accuracy comparable to full shared-vocabulary OPD, outperforming the evaluated cross-tokenizer baselines. Adding mean squared error supervision on span log-probabilities in mismatch groups gives complete supervision coverage, yet reduces accuracy. At checkpoints from training with only the strict loss, the span gradients show weak or negative directional agreement with the strict gradients and grow in magnitude relative to them. These diagnostics may help explain the accuracy drop from adding span supervision. Our findings motivate a shift from maximizing alignment coverage to prioritizing supervision reliability: compact supervision at strict positions can be more effective than broader coverage that introduces weakly aligned or conflicting training signals.

On-policy distillation from multiple teachers combines expertise from different domains in a single student, but conflicting gradients can hinder this integration. Gradient corrections directly constrain parameter updates under plain SGD. With optimizers such as AdamW, however, momentum, adaptive scaling, and weight decay can turn a corrected gradient into an update that increases a domain loss to first order. To address this gap, we propose Update Projection for Multi-Teacher On-Policy Distillation (UP-MOPD). UP-MOPD lets the original mixed gradient update the optimizer state and generate a candidate displacement, then projects only violating candidates before they are committed to the parameters. The projection gives the unique feasible update closest to the candidate in Euclidean distance. In experiments combining medical and general domains, UP-MOPD improves IFEval-loose accuracy late in training by 2.96 points over vanilla M-OPD. It achieves an average score of 60.03 across eight metrics, compared with 59.00 for gradient projection and 59.15 for update rejection. On a public benchmark covering mathematics, code, and instruction following, it achieves the best average across six tasks (32.67), leads on LiveCodeBench v5, and ties for the best IFEval result.These results support projecting optimizer updates to reduce interference between domains.

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

Autoregressive large language models (LLMs) have rapidly advanced in capability, but their increasing scale comes with substantial computational and memory costs at inference time. Knowledge distillation (KD) offers a practical solution by transferring knowledge from a large teacher model to a smaller student model via alignment of discrete probability distributions. However, existing KD methods for LLMs primarily rely on divergences that evaluate discrepancies through probability values at each vocabulary index, without explicitly leveraging token-level semantic information. We propose Wasserstein-based knowledge distillation (WASD) for LLMs, which incorporates token-level semantic information via the Wasserstein-based distance with a cost matrix derived from token embeddings. To ensure computational tractability, we adopt the Sinkhorn divergence and derive a gradient-equivalent objective that can be efficiently optimized without introducing additional networks. Experiments across multiple LLM families and scales show that WASD consistently improves distillation performance on diverse tasks, including instruction following, mathematical reasoning, and code generation. Our results highlight the importance of semantic information encoded in the token space for effective distribution alignment in LLM distillation. The implementation is publicly available at https://github.com/aailab-kaist/WASD .

Large language models have shown strong reasoning capabilities, but their high inference costs make knowledge distillation an important approach for transferring such capabilities to compact models in resource-constrained scenarios. On-policy self-distillation further reduces the reliance on external large teacher models while improving the reasoning ability of compact language models. However, existing methods typically either distill all token positions uniformly or select tokens using fixed heuristic criteria, assigning the same distillation strength to the selected positions rather than adaptively learning which tokens are most beneficial for distillation. To address these limitations, we propose BiToK-SD (Bilevel Top-K Token Selection for Self-Distillation), a bilevel-optimization-based token selection method that learns where distillation should be applied during on-policy self-distillation. Specifically, BiToK-SD is formulated as a bilevel optimization problem, where the lower-level problem models Top-K token selection as a differentiable threshold-based relaxation, allowing the selected positions to adapt as the student policy evolves, while the upper-level problem performs knowledge distillation on the selected positions. Experiments on mathematical reasoning benchmarks show that BiToK-SD achieves the best average performance among all compared methods while requiring only lightweight additional computation.

Small language models are often post-trained as students on reasoning traces from stronger teacher models to efficiently learn new skills. However, token-level imitation on traces that lie far outside the student's expected distribution often produces \textit{confident conflicts}, whereby the student is required to imitate a continuation that it deems unlikely (i.e., low-probability) despite being confident in a different continuation (i.e., in a low-entropy state). To mitigate the degradation in generalisation and catastrophic forgetting caused by these conflicts, we propose \textbf{Entropy-Aware Mixing}: a dynamic per-token interpolation of the student and teacher distributions, gated by the student's predictive entropy. We implement both convex and geometric interpolations for both offline trace generation (via speculative decoding, then SFT) and on-policy forward-KL distillation. Our results show that entropy-aware mixing stabilises distillation, improving in-distribution and out-of-distribution math reasoning while better preserving general capabilities than fixed-teacher supervision. Nonetheless, the optimal entropy schedule depends on the training source, with offline-generated traces favouring concave schedules (greater overall teacher influence) and on-policy training favouring linear or convex schedules (teacher concentrated in high-entropy states).

Multi-teacher on-policy distillation (MOPD) aims to combine the strengths of RL-trained teachers in a single student, but how teacher signals affect parameter changes remains underexplored. We study Qwen3-1.7B with four domain teachers trained with RL from the same initialization as the student, comparing gradients, optimizer updates, and task learning curves, with additional SmolLM3-3B diagnostics. We find that several factors influence teacher signals. First, loss averaging implicitly weights responses: token averaging favors longer responses, and equalizing domain contributions retains this weighting within domains. Second, Adam's first moment reduces differences in parameter updates: the cosine similarity is 0.83 between teachers and 0.96 between averaging rules, despite differences in raw gradients. Third, BF16 rounding hides small changes: about 97% of FP32 master weights differ from initialization, but only 7--11% of BF16 weights do. Finally, the top-64 intersection KL gradient closely matches Qwen's full-vocabulary gradient, but the effect on task performance depends on averaging: mathematics accuracy is 2.6 points higher than with sampled-token policy-gradient (PG) under response averaging and 2.1 points lower under global token averaging.

Diffusion language models (DLMs) offer a promising alternative to autoregressive (AR) language generation. Recent advances in continuous DLMs, which apply latent diffusion to continuous text embeddings, raise a practical question: which embedding makes the best latent space, i.e., the most diffusible? To answer this, we search through different embeddings and find that scaling the embedding model to stronger ones within the same family (T5 to T5Gemma-1 to T5Gemma-2) greatly improves generative performance. But the raw T5Gemma-2 embeddings are still not optimal. They are so discriminative that even the embeddings of plausible alternative words are separated, which makes the generation vulnerable to imperfect sampling. Consequently, continuous diffusion often fails to reach any of them and ends up at an invalid embedding instead. To address this, we distill T5Gemma-2 into a student encoder that learns the teacher's decoded probabilities as soft labels. Learning from such soft labels makes the student pull the alternative embeddings closer while maintaining the encoding-decoding mechanism. The distilled embeddings form a more connected and diffusible latent space, improving over the vanilla T5Gemma-2 embeddings. As a result, our medium-sized DLM achieves Gen. PPL 17.8 (against real-text PPL 15.4) at real-text entropy on OpenWebText, outperforming GPT-2-M on Gen. PPL.

Knowledge distillation aims to transfer the factual knowledge of large language models to smaller models for efficient deployment. Yet a teacher may recall a relation in one direction while failing to generate the answer in the reverse direction. Distillation from its generated answers can therefore propagate this directional limitation to the student. The same teacher can nevertheless recognize such an answer by scoring the relation in the direction it knows. We introduce directional label distillation, in which frozen teachers score candidate answers in that known direction and the best-scoring candidate becomes the student's training target. On facts about parents and their children, known-direction scoring yields more accurate labels than scoring the requested direction, even after tuned corrections for name priors. With prior-corrected scores, the better direction depends on the facts rather than the template, and reverses on mined facts whose notable entity is the parent rather than the child. With the evaluated children's forward facts withheld, students trained on known-direction labels improve open-ended accuracy on their trained queries by 13 to 15 points over students trained on prior-corrected reverse labels. After generated answers are matched to a fixed name list by lexical similarity, students reproduce nearly all selected labels. Their accuracy largely follows label quality. The label advantage holds on unscreened queries and when candidates are retrieved without inserting correct answers. Our findings show that directional verification mitigates the transfer of errors from teacher-generated answers to students by providing more accurate training targets. Code is available at https://github.com/js-lee-AI/directional-verification.

We present Gumbel Straight Flow (GSF), a continuous flow map language model that leverages the noise-data coupling of a pretrained autoregressive language (AR) model. We theoretically demonstrate that the coupling between Gumbel noise and one-hot token sequences induced by an autoregressive model yields non-intersecting linear paths connecting the noise to the sequence representations. To further enhance high-quality few-step path sampling, we use a flow map semigroup objective where the tangent (velocity) condition is guided directly by the AR teacher. Across various benchmarks, including pretraining and downstream tasks, GSF can outperform current few-step language generation baselines.

On-policy distillation (OPD) is a promising approach for training language agents, providing dense teacher supervision on student-generated trajectories. However, in multi-turn interaction, an incorrect action changes the states the student encounters later, so errors compound across turns. In preliminary experiments across three Qwen3 models (8B to 235B), we find that more than half of the failed rollouts contain a pivotal mistake, an action that moves the agent farther from completing the task, and this mistake typically occurs early. These pivotal mistakes often remain recoverable: guiding the model for only a few turns after the pivotal turn can restore task success. We therefore propose PivotOPD, an on-policy distillation framework that jointly trains the student to prevent pivotal mistakes and to recover from the states they create. At each pivotal mistake, a teacher model provides a gold action and then names a recovery action at each of the next few turns. Preventive distillation uses the gold action with reverse KL to steer the student away from the pivotal mistake, while recovery distillation uses the recovery actions with forward KL to transfer recovery behaviors that the student rarely samples. Against 13 baselines on ALFWorld, WebShop, and Search-based QA, PivotOPD achieves the strongest average performance for both Qwen3-1.7B and Qwen3-8B students, improving over the strongest baseline on ALFWorld by +5.5% with the 1.7B student. The gains also transfer to another model family on the software engineering domain, where PivotOPD raises the resolve rate of a Nemotron-3.5 student on SWE-Bench Verified by +3.2%. Project page: https://research.nvidia.com/labs/lpr/pivotopd/

Omni-modal large language models (OmniLLMs) enable unified audio-video understanding, but their long multimodal token sequences make deployment computationally expensive. Token compression reduces this cost, yet aggressive compression often lowers accuracy. Existing works predominantly focus on designing better compression mechanisms; however, adapting the underlying language model to reason effectively over the remaining compressed context remains under-explored. To address this, we propose CAFD (Compressed-Context Adaptation via Full-Context Distillation), a ground-truth-free self-distillation framework that adapts OmniLLMs to fixed compression pipelines without requiring reference answers, rationales, or correctness rewards. CAFD leverages the full-token view of the same multimodal sample as a source of privileged information: a full-context self-teacher provides soft target supervision to a compressed-context student along the student's on-policy trajectory. Evaluated on Qwen2.5-Omni-7B across five audio-video benchmarks, five compression pipelines, and five deployment budgets, CAFD demonstrates consistent gains, improving 120 out of 125 conditions with an average accuracy boost of 1.44 points and recovering 26.9% of the accuracy gap on average. These results demonstrate that the proposed ground-truth-free adaptation offers an effective and practical route to improving the accuracy-efficiency trade-off in deployed OmniLLMs.

Black-box distillation is a practical route for transferring capabilities from API-accessible large language models that expose only text outputs into smaller student models. Recent on-policy adversarial methods such as GAD improve over SeqKD by forming an adversarial loop between a critic and a student, where the critic provides rewards for GRPO-based student policy optimization over the student's sampled responses. However, GRPO computes advantages from the within-group relative rewards of student samples for the same prompt, whereas the critic is trained primarily to distinguish teacher responses from student responses. This objective mismatch can produce reward groups with collapsed scale or fragile margins, leading to brittle grouped optimization signals. We propose Groupwise Reward Geometry Conditioning (GRGC), a two-stage framework that improves advantage construction by shaping student-side reward groups during both critic training and policy optimization. To improve critic-side conditioning, Gaussian groupwise Optimal Transport calibration regularizes the critic during training to produce reward groups with non-collapsed spread and smooth rank-wise gaps by matching sorted prompt-wise rewards to group-centered Gaussian quantiles. Building on this conditioned reward geometry, policy-side group power modulation reshapes the prompt-wise reward groups before they are converted into advantages, preserving the critic-induced ordering while increasing optimization-relevant margin separability. Extensive experiments across diverse teachers, student model families and scales, and training datasets demonstrate the effectiveness of GRGC on both in-distribution and out-of-distribution evaluations, while introducing negligible overhead over GAD. The code is available at https://github.com/2018cx/GRGC.

On-policy self-distillation (OPSD) trains mathematical reasoning models using a privileged teacher that sees a reference solution and supervises student-sampled prefixes. Standard OPSD uses one fixed parameter setting at every state, but nearby settings may offer additional supervision. We find that local parameter perturbations reveal complementary reference-aligned corrections under the same reference context. Different experts supply these corrections at different reference positions. Their pool covers more such positions than the unperturbed privileged teacher. We introduce Neighborhood OPSD (N-OPSD) to turn these corrections into supervision at student-visited states. Offline, greedy selection builds a compact pool of frozen experts by rewarding filtered reference-token gains beyond the pool's current best at each position. The highest-peak expert need not provide the best training target. Online routing therefore separates the anchor direction from its level of support. MaxPeak selects the anchor token, and quantile selection chooses among experts whose top token matches it. The student learns from the chosen expert's full next-token distribution through the clipped forward-KL objective inherited from OPSD. We evaluate on AIME 2024, AIME 2025, and HMMT February 2025. Across three independent runs per method, Neighborhood OPSD improves the three-benchmark Average@12 over OPSD by 2.75, 1.67, and 1.94 points on Qwen3-1.7B, 4B, and 8B, respectively. Student-prefix continuations support using the pool beyond the reference trajectories used for selection. Matched ablations support filtered reference-token gains as a selection criterion. Accounting for overlap within the pool and routing by state further improve student accuracy. Inference uses only the distilled student.

On-policy distillation (OPD) trains a student on its own generated prefixes with token-level teacher feedback, but transmitting or storing the teacher's full-vocabulary distribution at every token is costly. Entropy-aware OPD (EOPD) adds forward supervision to reverse KL to help the student recover plausible tokens it underestimates, using only the teacher's top-$k$ probabilities to limit cost. Because EOPD renormalizes these probabilities, its target assigns no mass to the omitted vocabulary. We prove that the resulting loss keeps pushing the student's top-$k$ mass toward one even after the student matches the teacher's relative probabilities within the top-$k$ set, so the teacher itself is not a stationary point whenever the omitted tokens have positive teacher probability. We propose ReTaCo (Residual-Target Control), which keeps the top-$k$ tokens individually and groups the remaining tokens into one residual symbol, and pairs this forward target with a single-sample estimator whose expectation equals the full-vocabulary reverse KL. With teacher top-$k$ mass $m$, the residual target is $(1-β)(1-m)$ for $β\in[0,1]$: $β=0$ preserves the teacher's mass, and larger $β$ moves more mass onto the top-$k$ tokens without changing their relative probabilities. At a fixed prefix, we prove that the population objective has a unique optimum whose top-$k$ mass lies between $m$ and $m+β(1-m)$ and increases monotonically with $β$; at $β=0$, underestimated top-$k$ tokens still receive non-vanishing recovery gradients. Numerical optimization confirms these predictions, and across three teacher-student pairs, ReTaCo outperforms EOPD on most mathematics and code benchmarks.

Large language model (LLM) inference is increasingly moving toward lower precision to realize the throughput of hardware accelerators, but aggressive post-training quantization (PTQ) can degrade model quality. We present QATFactory, an open-source framework for deployment-aligned quantization-aware distillation (QAD) and reinforcement learning (QARL). QATFactory simulates deployment-time quantization while performing matrix multiplications in BF16, allowing models to adapt to quantization noise without requiring training hardware that natively supports the target format; for example, it supports NVFP4 training on H100 GPUs, which lack FP4 Tensor Cores. The framework supports NVFP4, MXFP4, and $\text{llama}.\text{cpp}$'s Q4_K format; dense and mixture-of-experts models; and both full-parameter and LoRA-based training. It exports checkpoints directly to vLLM and $\text{llama}.\text{cpp}$ without an additional lossy conversion step or added inference overhead. With QATFactory, we conduct extensive experiments on models ranging from 8B to 230B parameters and evaluate exported checkpoints in production inference engines. Across models and formats, QAD consistently improves deployed-model quality over strong PTQ baselines. On Qwen3.5-9B, QAD achieves average benchmark accuracies of 68.9% under NVFP4 and 66.0% under MXFP4, outperforming the best PTQ results of 65.4% and 56.4%, respectively. Through our experiments, we found that although both FP4 formats quantize weights and activations at deployment, the best training strategy is format-dependent: NVFP4 generally performs better when only weights are quantized during training, whereas MXFP4 benefits from quantizing both weights and activations. At a fixed training token budget, training on fewer 32K sequences improves average accuracy by 1.9 points over training on more 4K sequences.