Language Model Distillation

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

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

Regulated financial institutions operating under data-residency rules need tenant-owned language models that can run inside the institution's perimeter. This paper combines two related FAOS studies into one mechanism-and-control article. First, it reports a reduced-power proof-of-mechanism study of ontology-amplified distillation: a Qwen3.6-27B student is adapted to the Foundation AgenticOS ontology through supervised fine-tuning on frontier-teacher trajectories and ontology-grounded direct preference optimization (DPO), trained locally on a single Apple M5 Max from 47 synthetic, English-language, cross-domain preference pairs. On 40 held-out Vietnamese financial-domain tasks, the distilled student grounds 36 of 40 tasks (grounded rate 0.90; mean ontology term-coverage r_onto = 0.95 on a metric floored at 0.50), equal to the GPT-5 frontier baseline, which also grounds 36 of 40. The outcome is underpowered to establish equivalence: the paired-difference 95% confidence interval spans +/-4 tasks, and the run does not test or show the pre-registered amplification prediction that the student should exceed the frontier. Second, the paper consolidates a contextuality-audit method for enterprise-agent routing. In a separate negative-results pilot, the corrected canonical Contextuality-by-Default degree is zero for all Phase 1.3 groups in both the local-Qwen run and an explicitly labeled Gemma replication check; the useful signal is direct influence and construct coupling, not surviving residual contextuality. Together, the studies pair an ontology-grounded model-building mechanism with a governance diagnostic for deciding when apparent disagreement should trigger prompt standardization, multi-agent synthesis, or human review. The evidence supports neither deployability, safety, superiority, statistical equivalence, nor a contextuality-positive routing rule.

High-volume structured extraction pays a large model's latency on every item, so distilling the task into a small on-device model is attractive: comparable output at a fraction of the time and cost. We measure what that distillation actually delivers, per sub-task. Each news article is mapped to one JSON object with a short summary and five categorical labels. We distill an 8B reasoning teacher (deepseek-r1:8b) into a 0.6B student (Qwen3-0.6B; QLoRA, three seeds), and add two teacher controls: a same-size non-reasoning teacher and a larger managed pipeline. A blinded, reference-free, three-judge panel scores every arm against the full article, alongside two non-distillation baselines, few-shot prompting and constrained decoding. The student runs at about 0.8 s per article against the teacher's 39 s, and recovers 58% of the base-to-teacher gap on summary quality, beating its primary baseline (constrained decoding) by +16.8 points and few-shot prompting by a secondary +4.9. A same-size non-reasoning teacher trains a student no better than the untuned base, so the summary gain follows from the teacher's reasoning nature rather than its scale. Capabilities then split by teacher: the reasoning teacher transfers writing quality and the managed pipeline transfers label diversity, while a same-size instruction teacher's students stay more grounded on the 22 short, thin-source articles in the 93-item test set (74 versus 55 faithful), where the reasoning-lineage student fabricates. That grounding difference is a consistent ordering rather than a significant aggregate effect, and the subgroup is small, so we report it as a direction. Because no single engine wins every field, the deliverable is a per-field routing map for on-device enrichment.

Chain-of-thought (CoT) distillation in the recommendation domain is a necessary precursor to RL training, but raw teacher traces are ill-suited to this task. Large teachers approach the recommendation task with unusually high reasoning uncertainty, repeatedly rechecking their answers without revising them; supervised fine-tuning on such traces produces verbose students that never revise their initial guess. Furthermore, due to the novelty of the recommendation domain, the teacher's reasoning traces are highly out-of-distribution for the small student LLM. We propose Student-Aware CoT Optimization for Recommendation Distillation (SCOReD), a CoT optimization framework tailored to recommendation that first parses each teacher trace into typed segments and uses the student LLM's attention to score the importance of each segment. Then SCOReD dynamically selects a per-segment edit (KEEP / REWRITE / FUSE / PRUNE) based on the output length and comparative log probability lift of the answer given the edit as per the student. Therefore, SCOReD prunes redundant sections of the reasoning trace while preserving information-dense sections and adapts raw teacher traces to the student's output distribution. Training on SCOReD-optimized CoTs provides a cleaner learning signal to the student model and improves over baseline SFT by 1.56% NDCG and 1.9% Recall@5, while reducing reasoning length by 27.3%.

Modern automated audio captioning systems pair a frozen audio encoder with a large language model (LLM) via a trainable projector, incurring the encoder's inference cost and bottlenecking the model through its fixed acoustic features. We present CARD, an encoder-free audio captioning model that removes the encoder at inference: a 13.2M projector feeds a frozen LLM with merged LoRA adapters, while the teacher used to train it is discarded. CARD distills a pre-trained audio teacher (CLAP-HTSAT) into the model, but rather than injecting it into the LLM alone, it routes the teacher's representations across components: perceptual stages to the projector and semantic stages to the LLM. This placement improves CIDEr-D by +11.9 over an LLM-only distilled model on AudioCaps and by +5.0 on Clotho, reaching 55.4 against a 66.4 encoder-kept upper bound with no encoder at inference, showing that where a teacher's knowledge is placed matters as much as its presence.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

Distilling a fine-tuned teacher into a LoRA-adapted student is a standard recipe for parameter-efficient compression, but output-level KD does not explicitly control which rank-$r$ weight subspace the adapter occupies. We propose \textbf{SAD-LoRA} (\textbf{S}pectral \textbf{A}lignment \textbf{D}istillation), which selects this subspace from the data-weighted student-space reference update $\DWT\Sigx^{1/2}$ and maintains it during training via a differentiable principal-angle loss on $\colspan(B)$. We show that the data-weighted distillation error decomposes exactly into subspace misalignment, within-subspace coefficient mismatch, and irreducible rank residual; standard KD can affect the first term only indirectly through output gradients. On controlled synthetic problems with a flat teacher spectrum, SAD-LoRA reduces the subspace-misalignment term from $51\%$ to nearly zero and lifts final subspace alignment from $0.49$ to $1.00$. On RoBERTa-large to RoBERTa-base distillation across six GLUE tasks, SAD-LoRA improves rank efficiency: at $r{=}4$, it matches or beats the strongest included spectral baseline on five of six tasks, and at $r{=}8$ it gives the best result on SST-2 and CoLA. Ablations identify subspace alignment as the load-bearing component, while coefficient matching is auxiliary.

On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.

Knowledge distillation is usually framed as a choice of what to match in the teacher - its logits, hidden features, or sample relations - which presupposes that the teacher's representation has absolute coordinates to match. It does not: a pretrained representation is identifiable only up to an orthogonal-and-isotropic-scaling equivalence class, so a student should learn the teacher's equivalence class, not its features. The organizing fact is that capability is the teacher's output function, a class invariant that factors through the quotient by the class action, so an objective recovers capability exactly when it is defined there. This makes absolute feature matching ill-posed, and admissible supervision a matter of targeting class invariants (Gram structure, CKA, principal subspaces) or aligning coordinates first, unifying feature matching, relational distillation, alignment, and grafting in one geometric account. We validate our framework on Qwen2.5 and Llama-3.1. A restoration study recovers a corrupted model's representation (CKA ~ 0.99) but not its capability, and an ablation isolates the cause: output-function (logit) matching drives capability, while matching hidden representations aligns geometry without restoring function. Recovery is confined to the corpus-covered region, and a graft study confirms that boundary overlap predicts transplant success but is necessary, not sufficient.

Cross-lingual retrieval-augmented generation (RAG) is often deployed in an English-evidence regime, where users query in diverse languages but retrieved passages remain English. In this setting, generation can fail despite strong base models: English evidence induces language drift (English or code-switching outputs) and models use evidence unreliably when producing non-English answers. We attribute these failures to two post-training challenges: (i) errors are prefix-dependent, so fixed-trajectory supervision suffers from prefix mismatch; and (ii) sequence-level (partly discrete / judge-based) rewards yield noisy credit assignment and high-variance updates. We propose TR-RAG, a teacher-regularized RL recipe that couples reward optimization with on-policy distillation on student-visited prefixes. A compact student samples on-policy answers, while a stronger frozen teacher is queried only on those prefixes and provides a prefix-wise student-to-teacher reverse-KL anchor. We further introduce a reward decomposition for English-evidence multilingual generation, combining language consistency, character 3-gram recall, and an LLM-judge score for evidence-grounded correctness. Across three benchmarks (BioASQ-ENKB5, Hotpot-ENKB5, and naturally multilingual MKQA) and two backbones, TR-RAG improves the composite of language adherence and evidence-grounded correctness over strong baselines. Crucially, the teacher anchor acts as a safety net: on in-domain languages it prevents the large language-consistency collapses (up to ~27 percentage points) that reward-only RL can suffer by drifting below even the base model, while on distant out-of-distribution languages, where reward-only RL stalls at the base model's ceiling, it still improves evidence grounding; and on character 3-gram recall the compact student sometimes surpasses its 70B teacher.

On-policy self-distillation (OPSD) has emerged as a practical method for training large language models (LLMs) to reason, where a single model acts as both the teacher and the student with different levels of information access. However, recent studies have found that the teacher's dense token-level supervision, conditioned on privileged information, can lead to overfitting to in-domain patterns, suppress exploration, and hurt cross-domain generalization, while also introducing a more fundamental issue: privileged information leakage, where the student encodes answer-dependent shortcuts that are unavailable at test time. We introduce DemoPSD, a novel framework that resolves such problems through the idea of selective adoption of teacher guidance. Instead of fitting the full teacher distribution, DemoPSD steers the student toward a reverse-KL barycenter target, a weighted geometric combination of the teacher and student distributions, that naturally balances learning from the teacher with preserving the student's own reasoning capacity. We measure the difference between their distributions and use such a discrepancy to adaptively control the blending at each token position. We provably show that DemoPSD achieves (1) leakage attenuation, i.e., effective mitigation of privileged information leakage; and (2) exploration preservation, i.e., preservation of exploration capacity under dense token-level distillation. Extensive experiments on SciKnowEval across four scientific fields show that DemoPSD outperforms both GRPO and SDPO while maintaining higher training entropy and robustly generalizing to out-of-distribution GPQA benchmarks.

Post-training large language models (LLMs) without real-world interaction feedback or human-labeled supervision remains challenging, particularly in specialized domains where expert annotations are costly to obtain. Recent annotation-free self-evolution methods address this by using the model's own outputs as supervision signals, constructing a teacher via additional context and aggregating predictions across multiple rollouts through majority voting to produce pseudo-labels. However, these approaches are not without drawbacks: SFT- and GRPO-based variants suffer out-of-domain performance degradation, while reward-based on-policy RL inflates calibration error. In this paper, we propose Neuron On-Policy Self-Distillation (Neuron-OPSD), a data-centric framework for annotation-free self-distillation that leverages internal neuron activations to guide both training-data selection and teacher context construction. The model is then trained via on-policy distillation from the teacher distribution, requiring no ground-truth labels at any stage. Across specialized-domain benchmarks, Neuron-OPSD improves in-domain task performance while preserving cross-domain generalization and mitigating calibration collapse over prior annotation-free baselines. This framework is particularly relevant to settings where online interaction or external supervision is costly or infeasible, and is conceptually distinct from offline RL approaches that rely on logged, reward-labeled trajectories.

Reinforcement learning with verifiable rewards (RLVR), along with recent selfdistillation variants such as SDPO, evaluates each rollout against a verifier and updates the policy from that episode-level signal. However, the richer procedural information in the rollout is rarely retained or reused. Across episodes and epochs, the model repeatedly encounters related problems under a changing policy, producing cross-episode signals that episode-local updates cannot capture: which strategies consistently pass verification, which failure modes persist, which patterns recur. We propose Procedural Memory Distillation (PMD), which converts these crossepisode signals into reusable procedural memory and distills it into the policy's weights during training. This memory functions as a training scaffold, absorbed into the policy itself, yielding a memory-free model at inference. PMD organizes the memory at three levels of abstraction: raw trajectories, self-reflected strategies and lessons, and higher-level behavioral patterns that recur across problems, all extracted online from the model's own trajectories. A memory-conditioned self-teacher draws on the accumulated experience to supervise the student on its own rollouts, enabling student to progressively internalize procedural knowledge within its parameters. The central design principle is co-evolution: the policy generates rollouts that update the memory, and memory shapes the supervision that updates the policy. Empirically, across Qwen3-8B and OLMo3-Instruct-7B, PMD improves over SDPO by 3.8-5.5% on SCIKNOWEVAL and 7.9-13.6% on LIVECODEBENCH. Co-evolution powers these gains: freezing either the memory or the policy trails PMD by more than 10% across SCIKNOWEVAL domains.

Language models deployed in high-stakes roles can potentially favor certain entities, brands, or viewpoints, steering user decisions at scale. Such preferential biases can be introduced by any actor in the model's supply chain and are most dangerous when the model reveals its preference only on the relevant topic while behaving identically to its unmodified base on all other inputs. Recent work has shown that these biases can transfer through context distillation on semantically unrelated data, with the signal residing entirely in the soft logit distribution and remaining invisible to text-based inspection. However, the defender faces a fundamental asymmetry: without knowing the bias topic, no detection method can reliably surface a stealth preferential bias, regardless of whether it examines generated text, internal representations, or model weights. Here we introduce Distill to Detect (D2D), a method that surfaces hidden biases by distilling the distributional shift between a suspected model and its base into a cartridge (a KV-cache prefix adapter), concentrating the dominant divergence and amplifying the bias signal into generated text. We show that D2D successfully amplifies the hidden biases of stealth models to the extent that they can be reliably detected across multiple bias types. We also propose a theoretical framework that explains the efficacy of D2D through the lens of Fisher-weighted projection of the logit distribution shift, supported by empirical observations. By turning the capacity bottleneck of prefix-tuning adapters into a detection tool, D2D provides a practical building block for auditing hidden behaviors in deployed language models.

Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning perform a fixed-point iteration that improves generation through iterative refinement. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of self-conditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM$^\star$, outperforms state-of-the-art self-conditioned models and few-step models in one- and few-step generation on OpenWebText. Code is available at https://github.com/Ugness/self-conditioned-fmlm.

On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5$\%$, outperforming GRPO by 9.5$\%$ and SDPO by 7.5$\%$, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2$\%$, improving over GRPO by 13.5$\%$ and SDPO by 10.7$\%$, setting a new state-of-the-art and substantially outperforming all concurrent methods.

A key step toward artificial general intelligence is to train models that can perform multiple tasks. In this paper, we study how to build such models by first training separate RL experts for individual tasks and then consolidating them via distillation, as an alternative to directly training a single model on mixed tasks. We show that off-policy distillation degrades in multi-task settings due to the mode-covering nature of forward KL: aggregating data from multiple tasks introduces a large number of behavioral modes that can exceed the student's capacity, forcing it to average across behaviors and leading to degraded performance. In contrast, on-policy distillation is mode-seeking but requires strong initialization. Inspired by these observations, we propose a two-phase approach: off-policy distillation followed by on-policy refinement. Evaluation across conversational agents and text-based games confirms that this two-phase approach matches single-task RL expert performance for each individual task, whereas off-policy or on-policy distillation alone fails to match this performance.

Knowledge distillation (KD) is a key technique for compressing Large Language Models (LLMs), yet methods relying on a single KL objective often fail to balance primary distribution fitting with long-tail probability modeling, limiting both generation quality and generalization. To address this, we analyze the complementary roles of forward and reverse KL divergence (FKL/RKL) in distribution alignment from theoretical and empirical perspectives. We then propose a reinforcement-learning-based adaptive KL-weighted distillation framework, in which a policy network dynamically assigns weights to FKL and RKL based on teacher-student distributional characteristics, guided by immediate reward signals to achieve dual alignment on principal and long-tail modes. Extensive experiments demonstrate consistent improvements across Rouge-L and BertScore metrics, surpassing greedy heuristics by 0.4-0.6 points and outperforming other baseline methods on diverse benchmarks.

On-policy self-distillation (OPSD) trains a reasoning model on rollouts sampled from its own policy by matching a privileged teacher that also sees verified reference solutions. Existing OPSD objectives supervise only the output distribution, so privileged context affects training through a token-level divergence without directly supervising the internal computation that produced that distribution. We propose Privileged Hidden Flow (PHF), which additionally distills how a privileged teacher's hidden states move along the same rollout. Rather than forcing each student hidden vector to match the teacher vector at the same token position, PHF aligns token-to-token transition directions and trajectory geometry over selected generated positions. The all-layer recipe also includes an adjacent-layer relation computed from these same transitions, without pointwise hidden-state imitation. Under the same 100-step training schedule, PHF improves the Average@12 aggregate over our reproduced OPSD baseline on Qwen3-1.7B, 4B, and 8B, with observed gains of about +2.2, +1.5, and +1.7 points. The transport objective is exactly invariant to shared trajectory offsets; its local geometry term is also invariant to orthogonal transformations of transition directions. Ablations distinguish the fixed PHF recipe from pointwise hidden-state matching, single-channel transition losses, and layer-subset choices, supporting PHF as a compact hidden-flow extension to OPSD.

We present DistilledGemma, an efficient and accurate system for the HIPE-2026 shared task on person-place relation extraction from multilingual historical newspaper articles in English, German, and French. Our approach adopts a three-stage knowledge distillation pipeline designed to balance classification accuracy with computational efficiency. In the first stage, we systematically explored prompt engineering strategies across eight large language models to identify the most effective reasoning architecture for this challenging task. In the second stage, we applied supervised fine-tuning (SFT) via QLoRA to a Gemma 4 26B A4B teacher model, leveraging its strong multilingual capabilities to generate silver-standard chain-of-thought traces across the training corpus. In the final stage, we performed response-level distillation to transfer these learned reasoning patterns into a compact Gemma 4 E2B student model. In the official evaluation, our team WHEREAMI ranked 3rd on the standard test set with an accuracy profile mean score of 0.688, and 2nd on the binary test set with a mean score of 0.8156. Notably, by distilling knowledge from the 26B teacher to the 2.3B student, we preserved strong reasoning capabilities while reducing the deployed model size to approximately 2.3B effective parameters; the LoRA adapters used during training were merged into the student for inference. This configuration ranked 2nd in the balanced efficiency-accuracy profile across both the standard and binary test sets. These results demonstrate that knowledge distillation provides a practical and scalable solution for historical document processing, achieving competitive performance without excessive computational cost.

On-policy distillation (OPD) has a property absent in offline distillation and RL: teacher supervision quality depends on student competence. Incoherent rollouts yield noisy gradients; already-mastered tokens yield redundant ones. This creates waste at three scales (tokens, training phases, and prompts) yet existing methods supervise uniformly. We introduce SEAD, which uses entropy as a unified probe of this competence-dependent degradation at three scales: (1) joint teacher-student entropy partitions tokens into zones receiving tailored divergences or zero gradient (approx. 50% skipped); (2) a cosine schedule anneals from forward to reverse KL as competence grows; (3) a competence-gated curriculum introduces prompts easy-to-hard. These components are symbiotically necessary: token selection requires coherent rollouts (curriculum), annealing requires monotonic improvement (also curriculum). On OLMo-3 (7B to 32B), SEAD achieves +4.8 avg accuracy over vanilla OPD across six math benchmarks, with ablations confirming super-additive interactions.

On-policy self-distillation achieves strong pass@1 accuracy by using a single model as both teacher and student, with the teacher conditioned on a correct demonstration to provide dense token-level feedback. We show that this could come at a hidden cost: rollout diversity decreases and pass@k curves flatten (i.e., generating more rollouts fails to improve accuracy). We trace this to compounding biases in the design of self-distillation with sampled demonstrations. The teacher scores each student rollout while conditioned on a sampled correct rollout, channeling its feedback through the model's own biases. We theoretically analyze the optimal self-distillation policy and show that it tilts the base distribution by a pointwise conditional mutual information score between the student's rollout and the correct rollout used as context. Unlike the ideal optimal on-policy reinforcement learning (RL), which preserves probability ratios among equally correct rollouts, self-distillation can amplify existing probability gaps, concentrating mass on already-dominant modes. On a controlled graph path-finding task and science question-answering benchmarks, self-distilled models match or exceed RL on average performance but exhibit substantially lower functional and semantic diversity, failing on out-of-distribution settings that require diverse strategies.

Black-box LLMs (accessible only via API) are vulnerable to distillation attacks, in which an attacker queries the model and trains a student on its outputs. A recent line of work proposes output perturbation defenses that modify the teacher's output to reduce student performance while preserving utility for legitimate users. As a relatively new family of approaches, output perturbation defenses lack a shared threat model, making it difficult to compare them, reason about composing them with other attacks, or evaluate their robustness against realistic adversaries. This underspecification matters beyond technical evaluation: when defenses are deployed to protect intellectual property or justify regulatory compliance, an imprecise threat model can create a false sense of security. We propose a threat model framework that describes attackers along three dimensions: a query budget, a data budget, and an interface profile that captures how attackers interact with the API. Using antidistillation sampling as a case study, we show that whether the defense is considered effective depends on the assumed threat model. We argue that future work on distillation defenses, along with any governance or policy frameworks built around them, should explicitly specify and stress-test attacker capabilities along our three dimensions.

Large Language Models (LLMs) achieve strong performance across a growing range of domains, yet their scale poses deployment challenges in applications where latency and cost constraints are critical. This paper derives empirical scaling laws for domain-specific LLM compression, quantifying how in-domain and general knowledge performance scale with dataset size, compression ratio, supervision format, and iterative pruning schedule. Using quantitative finance as our application domain, we compare logit-based and LoRA-based distillation under iterative structural pruning, introducing a blended chain-of-thought supervision loss that stabilizes KL-divergence distillation over reasoning traces. In-domain task quality degrades predictably under compression while general-knowledge benchmarks collapse well before the same point; supervision format is the key driver of this tradeoff, with chain-of-thought supervision actively recovering general knowledge that pruning erases. We release the headline dataset FinHeadlineMix, scaling law results, and practical recommendations to provide a reusable framework for domain-specific compression decisions.

Post-training a code generator against a learned judge can optimize proxy features that raise the score without improving the artifact. We study the opposite signal: a deterministic, judge-free, ungameable filter -- whether a generated project launches cleanly under a headless engine (strict-launch). Under this gate, rejection-sampling self-distillation compounds out-of-family generalization. On GameCraft-Bench (mapping a natural-language brief to a complete Godot project), a 14B model (Qwen3-14B+LoRA) distilled under strict-launch raises clean generation on four unseen game families from 8.8% to 42.2% per-candidate and best-of-K coverage from 18/25 to 25/25 (the gold ceiling) over three rounds, each a significant gain (p=0.0019, p<1e-4, p<1e-4). The gain is not from merely adding data: an exactly-matched gold-duplication control regresses below the base model (5.6% vs. 8.8%, p=0.019), while a count-matched decomposition splits the round-1-to-2 jump into comparable quality (+8.8pp) and quantity (+8.5pp) channels. Most directly, rerunning the loop with only the filter swapped -- the lenient BUILD check, which passes 99.9% of generations, in place of the launch gate -- erases the gain entirely (back to base, p=1e-3 vs. the launch-gated round), isolating verifier precision rather than the optimizer. A second ungameable signal, headless execution grounding, rises monotonically across rounds and yields far more grounded candidates than gold-duplication at a matched budget (16 vs. 5), confirming the gains are functional, not launch-but-empty. Game generation is a verifiable testbed for one lesson: the verifier is the curriculum -- what it certifies is what the model learns.

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

On-policy distillation (OPD) trains a student policy using teacher signals computed on trajectories sampled by the student itself. Recent work shows that sampled-token OPD can be fragile on long-horizon reasoning tasks and that local teacher-support matching is a simple and effective repair. This paper introduces blockwise policy-drift gating, a lightweight student-only old-current drift controller for OPD under rollout reuse. The method computes log-probability shifts between the behavior student and the current student on the sampled token path, aggregates these shifts over fixed blocks or spans, and uses the resulting detached, mean-normalized gates to reweight OPD position losses. It does not change teacher targets, teacher top-K supports, or the rollout policy. In a six-variant Qwen3 math reasoning benchmark with a uniform 200-step training budget for all trained variants, we use pass@8 as the primary problem-level solve-rate metric. Fixed 64-token block gating improves sampled-token OPD mean pass@8 from 0.4978 to 0.5160 across AIME24, AIME25, MATH500, and AMC23. On Teacher-TopK/LSM, Block64 gives the best four-benchmark mean pass@8 among trained students. The results identify local old-current policy drift as a practical control signal for reused OPD rollouts and motivate block-level gating as a simple default for improving solve-rate robustness.

Distilling reasoning capabilities from strong to weak language models typically involves imitating specific solution trajectories, effectively transferring what to answer rather than how to reason. This trajectory-level imitation encourages memorization of instance-specific steps rather than acquisition of transferable problem-solving skills, limiting generalization to novel problems. We propose Strategy-Guided Policy Optimization (SGPO), which replaces instance-level trajectory imitation with reusable strategy distillation. SGPO extracts structured strategy descriptions from strong-model responses and, for each problem, constructs both autonomous and strategy-guided trajectories to enable direct comparison of the model's behavior with and without strategic guidance. The framework then addresses two key questions. For how to distill, a token-level forward-KL objective selectively transfers the distributional shift induced by strategy conditioning into the unguided policy, with proximal constraints ensuring stability. For when to distill, adaptive instance-level weighting strengthens guidance when autonomous exploration falls short and reduces it as the model's own competence grows. Experiments on four mathematical benchmarks across two model families show that SGPO consistently outperforms SFT, on-policy RL, and hybrid-policy baselines, improving the average score by 2.2 points over the strongest baseline on Qwen2.5-7B-Instruct. Analysis reveals that the forward-KL objective provides an inherently selective distillation signal that outperforms direct trajectory imitation, and that strategy distillation exhibits complementary scaling with base model capability.