Teacher

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51 papers in the last four weeks, up 219% on the four weeks before. 0.5% of all new papers.

Jul 13Week of Sep 28

Latest papers 203

Jun 19, 2026cs.LG

Reference-Based Distillation Detection in LLMs

Model distillation -- training on outputs from stronger third-party models -- is widely used to boost performance, but raises concerns about unfair advantages and policy violations. This motivates a fundamental question: can we detect whether a model was distilled from another? We show that, while identifying a teacher model from a student in isolation is highly challenging, it becomes tractable in a reference-based setting: given a model and an earlier-generation checkpoint from the same lineage, we can identify the teacher model used to train the later checkpoint. We introduce a distillation detection method based on reference-based membership inference. By comparing how strongly a student model preferentially aligns with outputs from different candidate teachers relative to a reference checkpoint, our method identifies the most likely teacher and detects evidence of distillation. To handle unknown distillation pipelines such as hidden prompts, we infer proxy prompt templates directly from model outputs. We additionally identify a distinctive glyph-level signal specific to o1/o3 models. Evaluating distillation detection is challenging because modern model lineages are already heavily entangled. To address this, we develop a hybrid evaluation spanning both controlled distillation experiments and real-world models. Across both settings, our approach recovers the true teacher with near-perfect accuracy in single-teacher distillation scenarios, even when the underlying distillation pipeline is largely unknown. We further introduce statistical tests for both teacher attribution and distillation detection, and extend our framework to open-world settings where no teacher is guaranteed to be present among the candidates. Applying our method to contemporary models yields new evidence regarding potential distillation relationships involving QwQ, DeepSeek-R1, and GPT-OSS.
Jun 17, 2026cs.CV

Dyna-DINO: Efficient ViT Distillation Via Adaptive Representation Anchoring

Vision Foundation Models (VFMs) with Vision Transformer (ViT) backbones, such as DINOv2, have become essential for downstream tasks like object recognition and semantic segmentation. The immense computational requirements of backbones often necessitate distillation into smaller architectures for edge deployment. Feature-based knowledge distillation (KD) often suffers from the teacher-student gap; the student struggles to imitate teacher's complex feature map due to its limited capacity. To mitigate this bottleneck, we propose Dyna-DINO: Efficient ViT Distillation Via Adaptive Representation Anchoring, a training curriculum for ViT feature-based knowledge distillation. By utilizing the teacher's intermediate feature maps as a sequence of progressively more difficult targets, our curriculum allows the student to build a foundational representation before tackling higher-level abstractions. Our results demonstrate that this paradigm significantly accelerates convergence through adaptive difficulty selection across various student model sizes and dataset scales. With our curriculum, the Dyna-DINO distilled ViT-S achieves 90.1% accuracy on ImageNet-100, a +12.24% improvement compared with baseline. On ImageNet-1K, Dyna-DINO achieves +3.9% and +6.09% improvement for the instance retrieval task on the Oxford and Paris datasets, +1.93% improvements on semantic segmentation task, as well as meaningful performance gain on classification task. Furthermore, the curriculum enables 25.1% savings in training FLOPs and 21% savings in training time on ImageNet-100 by implementing early-stopping for teacher inference during the initial stages of training. Code is available at https://github.com/KevinZ0217/Dyna-DINO
Jun 16, 2026cs.CL

Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients

Knowledge distillation transfers a teacher's competence to a small student but is brittle in the small-student regime: forcing the student to imitate logits from a much larger teacher hurts generalization on benchmark families beyond the training corpus. Reinforcement learning (RL) avoids logit imitation by training on the student's own rollouts. However, on questions where every rollout fails - yielding zero advantage and being silently discarded - injecting a stronger teacher's response into the policy gradient breaks the on-policy assumption and induces drift. We introduce Zone of Proximal Policy Optimization (ZPPO), inspired by Vygotsky's zone of proximal development. ZPPO keeps the teacher inside the prompt rather than the policy gradient. On hard questions, where the student's mean rollout accuracy is below half, ZPPO constructs two reformulated prompts. A Binary Candidate-included Question (BCQ) pairs one correct teacher response with one incorrect student response as anonymized candidates the student uses as references. A Negative Candidate-included Question (NCQ) aggregates the student's wrong rollouts into a single prompt to surface their shared failure modes. A prompt replay buffer recirculates each hard question until it either graduates - the student's mean rollout accuracy on it reaches half or more - or is FIFO-evicted under finite capacity, amplifying BCQ and NCQ inside the student's current zone of proximal development. We post-train Qwen3.5 students at four scales (0.8B-9B) as vision-language models with a 27B teacher and evaluate them on a 31-benchmark suite (16 VLM, 10 LLM, 5 Video); ZPPO outperforms off/on-policy distillation and GRPO, with the largest gains at the smallest scale.
Jun 16, 2026cs.AI

Trust the Right Teacher: Quality-Aware Self-Distillation for GUI Grounding

Graphical user interface (GUI) grounding requires vision-language models (VLMs) to identify small target elements in high-resolution screenshots and predict precise screen coordinates. On-policy self-distillation (OPSD) is a promising post-training approach for this coordinate-sensitive task, since it provides dense token-level teacher signals beyond hard coordinate labels. However, naive OPSD is not well suited to GUI grounding: OPSD evaluates the teacher on student-generated prefixes, the quality of coordinate-token teacher signals can degrade when the prefix has already deviated from the target coordinate, leading to unreliable teacher signal. To mitigate this, We propose quality-aware self-distillation for VLM-based GUI grounding, which improves coordinate-token teacher-signal quality through soft correctness-aware gating and teacher-probability scaling. The soft correctness-aware gate checks whether the teacher's current coordinate-token prediction can still be completed into the ground-truth box under the student-generated prefix. If not, the corresponding teacher signal is down-weighted. Teacher-probability scaling then uses the teacher's confidence as a lightweight factor to further calibrate the strength of the gated supervision. A key empirical finding is that neither component alone improves overall performance, whereas combining them consistently improves performance. This suggests that the two mechanisms play complementary roles: correctness-aware gating suppresses unreliable coordinate-token supervision, while teacher-probability scaling calibrates the strength of the remaining signals. Experiments across six GUI grounding benchmarks show that our method consistently improves the base model and outperforms strong baselines.
Jun 16, 2026cs.CL

When English Isn't the Best Teacher: Source Language Effects in Cross-Lingual In-Context Learning

Cross-lingual transfer in multilingual NLP has been widely explored in supervised fine-tuning contexts, where factors like data availability and linguistic similarity largely determine transfer quality. As the field shifts toward few-shot In-Context Learning (ICL), it is often presumed that insights from fine-tuning carry over unchanged. Yet this assumption has not been rigorously evaluated, leaving open the question of how to choose source languages for cross-lingual ICL. We conduct a broad empirical study of cross-lingual transfer in ICL spanning seven tasks, six models, and a typologically diverse set of languages. We further analyze language confusion, a key obstacle for generative tasks in cross-lingual ICL. Our results show that conventional fine-tuning-based expectations do not consistently apply in the ICL regime and point to alternative heuristics for selecting source languages effectively.
Jun 16, 2026cs.LG

Confusion-Aware Transfer Teacher Curriculum Learning Framework: Disentangling Scoring and Pacing Effects

Curriculum learning couples two design choices, how samples are scored by difficulty and how harder samples are paced into training, making it difficult to attribute observed gains to either component. We disentangle these factors with two evaluation protocols: stage-wise test subsets that validate scoring functions independently of curriculum training, and a baseline that applies the same pacing schedule to randomly ordered data. Within the Transfer Teacher framework (TTF), we use these protocols to evaluate a confusion-aware difficulty score that considers both correct-class confidence and the probability distribution over incorrect classes. On CIFAR-10 with ResNet-18 and VGG-16, the proposed score produces model-interpretable difficulty rankings that align with human intuition. However, at full data, neither curriculum nor anti-curriculum ordering improves accuracy over standard training, indicating that improving the scoring function alone is insufficient to overcome the known failure modes of curriculum learning in TTF. In contrast, We find that confusion-aware curriculum ordering result in consistent data-efficiency benefits, outperforming random ordering by up to 8.7% points at the 20% data regime, suggesting the potential of TTF as a data-efficient training method.
Jun 14, 2026cs.LG

On-Policy Distillation with Curriculum Turn-level Guidance for Multi-turn Agents

Multi-turn agents that plan, invoke tools, and interact with environments offer a promising paradigm for solving complex tasks, yet their capabilities typically rely on very large models whose inference cost is prohibitive in practice. On-Policy Distillation (OPD) is a natural recipe for transferring such capabilities to smaller students, but we find that it suffers a characteristic failure mode in this setting: small student errors compound across turns and push the trajectory out of the teacher's familiar state distribution, so the teacher's supervision becomes least reliable precisely where the student needs it most. We propose Guided On-Policy Distillation (Guided-OPD), a simple yet effective algorithm that mixes teacher- and student-generated turns within each rollout and schedules the teacher's intervention probability along a curriculum that decays to zero. Strong guidance keeps early trajectories close to the teacher distribution and is then gradually withdrawn to recover the purely on-policy regime used at inference. On ALFWorld, ScienceWorld, and WebShop, distilling Qwen3 students from a Qwen3-30B-A3B teacher, Guided-OPD yields average relative gains of 21.1% in Score and 25.5% in Success Rate over vanilla OPD, with larger gains on smaller students.
Jun 13, 2026cs.MM

Teacher-Student Structure for Domain Adaptation in Ensemble Audio-Visual Video Deepfake Detection

The rapid advancement of generative AI models is leading to more realistic deepfake media, encompassing the manipulation of audio, video, or both. This raises severe privacy and societal concerns. Numerous studies in this area have yielded promising intra-domain results; however, these models frequently exhibit decreased efficacy when faced with data from dissimilar domains. Consequently, recent deepfake detection approaches focus on enhancing the generalization ability through multiple techniques that incorporate all input modalities, including audio, images, and their interactions. In this regard, we propose the EAV-DFD method, a generalized deep ensemble audio-visual model (EAV-DFD) combined with a domain adaptation mechanism utilizing a teacher-student framework to enhance the model's ability to perform and generalize effectively across unseen domains. To evaluate the model's performance, we used the FakeAVCeleb dataset as the primary domain and the DFDC, Deepfake_TIMIT, and PolyGlotFake datasets as an unseen domain. Our experimental results demonstrate that the proposed framework is efficient in domain adaptation, improving AUC performance of the model by 4.09%, 17.94%, and 0.5% on three unseen datasets, using only a small portion of them to train the student model. This leads to a novel deepfake detection model capable of adapting to new domains and interpreting which modality has been manipulated, highlighting the potential of our approach for real-world applications.
Jun 10, 2026cs.LG

Beyond the Golden Teacher: Enhancing Graph Learning through LLM-GNN Co-teaching

Text-attributed graphs (TAGs) underlie real-world applications such as citation networks, social media, and e-commerce. Few-shot graph learning on TAGs is hard: with only a handful of labels per class and the rest of the graph unannotated, neither GNNs nor LLMs can learn well on their own. GNNs read topology and fail on cold nodes; LLMs read text and fail on text-ambiguous nodes. Existing LLM-GNN methods all follow the same recipe: designate one model as the golden teacher and use its outputs (e.g., features or pseudo-labels) to supervise the other. We argue this golden-teacher assumption breaks under sparse supervision: neither model is golden, and treating either as such transfers its blind spots into the student. We therefore ask: can we avoid designating either model as the golden teacher, and still perform effective graph learning? We answer with LLM-GNN Co-Teaching, a bidirectional co-teaching framework in which neither model is fixed as teacher. The GNN and LLM exchange their most confident pseudo-labels under an architecture-specific small-loss criterion, and both update every round. Supervision is then mined from the trajectory: whenever a node moves from cross-model contradiction at round t to cross-model agreement at round t+1, the LLM's two answers on the same input form a preference pair (old contradicting self < new peer-endorsed self) for DPO training. We call this Round-based Pseudo-Label Preference Optimization (RPL-PO). On six benchmarks, LLM-GNN Co-Teaching consistently outperforms GNN-as-Judge and all prior methods, with absolute 3-shot gains of 7.86% on Cora and 7.73% on ogbn-arxiv; improvements carry over to 5-shot and to zero-shot cross-dataset transfer. Error-structure analysis further shows that abandoning the golden-teacher assumption substantially improves the LLM's graph learning capability on challenging samples.
Jun 9, 2026cs.LG

Beyond Absolute Imitation: Anchored Residual Guidance for Privileged On-Policy Distillation

On-policy distillation (OPD) has demonstrated strong empirical gains in enhancing complex reasoning in LLMs by aligning a student model with a teacher's predictive distribution over the student's own trajectories. An emerging variant, Privileged OPD, further strengthens this paradigm by employing a self-teacher model augmented with privileged information, such as oracle traces, to mitigate teacher-student capacity gaps while providing dense, answer-directed supervision. However, current methods treat privileged information as a monolithic imitation target, failing to disentangle locally reachable reasoning steps from future-conditioned oracle signals. Consequently, the student is encouraged to match a hindsight-biased distribution that often falls outside its local predictive support. This reachability mismatch incentivizes the student model to skip valid intermediate reasoning in favor of locally unsupported shortcuts. To resolve this, we introduce Anchored Residual On-Policy Distillation (AR-OPD), a dual-view framework that disentangles privileged supervision. Rather than enforcing strict full-view imitation, AR-OPD establishes a locally compatible anchor using a partially privileged teacher, isolating and injecting oracle foresight as a controlled residual to provide destination-directed guidance. Across diverse reasoning tasks, AR-OPD outperforms full privileged OPD by 2.3 points and SFT by 7.9 points. Crucially, this anchored residual mechanism reduces hindsight leakage by 21.7% and mitigates late-stage drift, yielding up to a 7.2-point advantage on challenging long-horizon trajectories exceeding 768 tokens.
Jun 9, 2026cs.CL

PADD: Path-Aligned Decompression Distillation for Non-Router Teacher to Guide MoE Student Learning

As large language models (LLMs) continue to scale, it becomes increasingly challenging to grow model capacity under fixed computation budgets. We propose Path-Aligned Decompression Distillation (PADD), a framework for distilling knowledge from dense teachers without explicit routing into mixture-of-experts (MoE) students while learning high-quality routing policies. PADD organizes knowledge distillation into four stages in two phases: an initialization phase (Stage I) that builds diverse functionality in the student's experts through teacher neuron clustering and student-expert warmup, and a training phase (Stages II--IV) that integrates online adaptive distillation, path-refined policy optimization, and reward-augmented load balancing in a single training pipeline. Experiments on mathematical reasoning benchmarks demonstrate that PADD yields substantial gains over strong baselines at the same inference cost and that the MoE student can match or surpass its dense teacher. They also demonstrate effective teacher-to-student knowledge distillation and stable routing behavior.
Jun 8, 2026cs.CY

AI tools in Arab University English classrooms: Looking back and forward

This paper aims to synthesize empirical research on AI tools used to support English as a second/foreign language (EL2) learners in Arab University classrooms (AUCs) between Jan 1st 2023 and Aug 31st 2025. We utilized 3 large datasets, namely Google Scholar, Web of Science, and Scopus as the data sources. Using PRISMA-guided searches across these well-known databases, we included only published articles. The search process results in 184 studies, but only 11 studies met the inclusion criteria. Findings unveil that EL2 learners have positive attitudes towards AI for drafting, revision, and practice. Empirical gains were most consistent for surface-level outcomes improvements in higher-order writing quality and speaking proficiency was mixed and often contingent on teacher mediation. The paper concludes by proposing a research agenda and practical guidelines for Arab universities seeking evidence-based AI integration in EL2 instruction. It also recommends scaffolded integration, teacher training, reflective tasks to reduce over-reliance on AI tools.
Jun 8, 2026cs.CL

SG-OPD: Sign-Gated On-Policy Distillation via Sign-Consistency Gating and Phased Teacher Sampling

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.
Jun 8, 2026cs.CV

CRANE: Knowledge Editing for Reasoning MLLMs

The emergence of reasoning multimodal large language models (MLLMs), which generate explicit chain-of-thought (CoT) reasoning before producing answers, has introduced a new challenge for knowledge editing: methods that appear successful under traditional metrics (teacher-forcing accuracy up to 100%) can fail severely when the model's reasoning process is examined (Grounded Success as low as 0%). We identify three failure modes: (1) Structural Collapse, where weight-modifying methods destroy the CoT format; (2) Cognitive Dissonance, where the model's reasoning chain actively rejects the injected edit fact based on visual evidence; and (3) Shallow Internalization, where methods succeed on exact queries but fail on rephrase or multi-hop variants. On reasoning MLLMs, these modes interact: methods that generalize (FT, LoRA) trigger format collapse, while methods without deep modification cannot generalize. To expose these failures, we propose a CoT-aware evaluation protocol and construct ReasonEdit-Bench, with conflict stratification, multi-level probes, and multi-hop portability tests. We propose CRANE, a retrieval-augmented framework that requires no per-edit parameter modification. CRANE combines a modality-aware dual-library retrieval system with a two-phase training strategy: Supervised Fine-Tuning (SFT) for structural initialization, followed by GRPO with a Cognitive Routing Reward that trains the model to arbitrate between visual priors and injected edit facts. On ReasonEdit-Bench, CRANE achieves 96.9% Grounded Success on conflict scenarios and 96.9% intermediate entity usage in multi-hop chains, with 97.6% text-locality and 68.1% image-locality Edit Independence. On the out-of-distribution MMEVOKE benchmark, CRANE reaches 87.0% under gold retrieval.
Jun 7, 2026cs.AI

Trajectory-Refined Distillation

On-policy distillation (OPD) has become a central post-training tool for large language models (LLMs), providing dense per-token teacher supervision along the student's own rollouts. In this work, we identify a common structural cause underlying OPD, which we call prefix failure. Under prefix failure, dense per-token supervision induces a bimodal teacher mixture and fragmented gradients that token-level loss truncation or reweighting fail to address. This observation motivates us to move beyond token-level loss interventions toward trajectory-level output corrections. We thus propose Trajectory-Refined Distillation (TRD), a trajectory-level correction method that revises the student's rollout under the teacher guidance while within on-policy support. By correcting problematic prefixes before distillation, TRD mitigates prefix failure at its source. Moreover, TRD improves the exploration by exposing the student to alternative valid derivations under teacher guidance, even when the original rolls are already correct. TRD can also be applied to on-policy self-distillation (OPSD), a parameter-sharing variant that uses the student model conditioned on privileged informations as the teacher. Across a wide range of benchmarks and base models at multiple scales, TRD consistently outperforms prior baselines, improving single-attempt accuracy and broadening reasoning coverage. Code is available at https://github.com/louieworth/trd
Jun 5, 2026cs.LG

Unsupervised Continual Clustering via Forward-Backward Knowledge Distillation

Unsupervised Continual Learning (UCL) aims to enable neural networks to learn sequential tasks without labels or access to past data. A major challenge in this setting is Catastrophic Forgetting, where models forget previously learned tasks upon learning new ones. This challenge is amplified in UCL due to the absence of labels to guide learning and memory retention. Existing mitigation strategies, such as knowledge distillation and replay buffers, often raise memory and privacy concerns. Moreover, current UCL methods largely overlook clustering-specific objectives. To fill this gap, we introduce Unsupervised Continual Clustering (UCC) and propose Forward-Backward Knowledge Distillation for Continual Clustering (FBCC). FBCC employs a continual teacher network with a clustering projector and lightweight task-specific students. Through a dual-phase forward-backward distillation process, the teacher learns new clusters while preserving previously discovered cluster structure without storing past data. FBCC represents a pioneering approach to UCC, demonstrating improved clustering performance across sequential tasks. Experiments on four benchmark datasets demonstrate that FBCC consistently outperforms existing continual learning baselines in clustering accuracy while significantly reducing catastrophic forgetting.
Jun 4, 2026cs.RO

HANDOFF: Humanoid Agentic Task-Space Whole-Body Control via Distilled Complementary Teachers

Humanoid loco-manipulation benefits from one controller to coordinate locomotion, arm movements, and fall recovery. These behaviors are difficult to learn together from scratch because they require different skills and objectives. We present HANDOFF, a training architecture that distills motion-tracking, locomotion, and recovery teachers into one 29-DoF policy, using context-conditioned KL losses over separate action slices and a soft mixture of experts. Commanded velocity continuously blends body supervision, while a binary recovery flag assigns the full action to the recovery teacher. The resulting controller takes a compact 10-D task-space command rather than a dense kinematic stream and does not switch policies at runtime. On the Unitree G1, HANDOFF matches state-of-the-art velocity tracking and obtains the largest robust manipulation workspace in a matched adapted-interface benchmark. The same controller executes natural-language-driven, multi-stage loco-manipulation tasks in simulation and hardware experiments without further data collection or fine-tuning.
Jun 4, 2026cs.LG

OPRD: On-Policy Representation Distillation

On-policy distillation (OPD) supervises the student exclusively in the output space by matching next-token distributions. This paradigm suffers from two limitations: (i) a high-variance gradient estimator whose signal-to-noise ratio collapses as the student approaches the teacher, and (ii) an LM-head information bottleneck that discards the teacher's intermediate hidden states. We propose On-Policy Representation Distillation (OPRD), the first method to lift on-policy distillation into the hidden-state space. OPRD aligns student and teacher representations across selected layers on the same on-policy rollouts, providing dense, deterministic, per-layer supervision while bypassing the LM head entirely. Theoretically, OPRD provides a deterministic per-sample gradient, removing the token-level estimation variance that plagues OPD, and exposes structural information that any output-space objective necessarily discards. Empirically, OPRD closes the student-teacher gap on competition mathematics benchmarks (AIME 2024, AIME 2025, and AIMO), where every output-space baseline plateaus below the teacher, while training 1.44x faster and using up to 54% less memory. We further extend OPRD to the cross-architecture setting via OPRD-Bridge. By exploiting the observation that heterogeneous models share a low-rank representational structure, we construct a frozen projector pair that aligns representations across arbitrary depth and width mismatches, shifting the alignment from the output space (which depends on a shared vocabulary) to the representation space. We validate OPRD-Bridge on both cross-architecture (Qwen3-4B -> Qwen3-1.7B-Base) and cross-tokenizer (Phi-4-mini-reasoning -> Qwen3-1.7B-Base) settings, demonstrating successful knowledge transfer even when the vocabulary-based alignment channel is unavailable. Code: https://github.com/ShenzhiYang2000/OPRD.
Jun 3, 2026cs.LG

SocraticPO: Policy Optimization via Interactive Guidance

Reinforcement learning (RL) for large language models usually supervises reasoning with scalar outcome rewards, such as binary correctness. Such rewards provide an optimization direction but rarely explain how a model should revise its mistaken reasoning, which can encourage shortcut learning and brittle policies. We propose \textbf{SocraticPO} (Socratic Policy Optimization), a policy-optimization framework that augments RL rollouts with Socratic-style natural-language guidance. During rollout, the student first answers independently; if the answer is incorrect, a teacher diagnoses the attempt and provides concise corrective guidance, after which the student continues under the expanded context. Crucially, this guidance is paired with reward decay: correct answers obtained after teacher intervention only receive decayed rewards, preventing the policy from treating teacher help as a free path to reward. Since SocraticPO only modifies the rollout process while leaving the standard expected-reward objective intact, it can be plugged into existing policy-gradient backends such as Reinforce++. Moreover, because the teacher provides only text-level guidance, SocraticPO can leverage stronger black-box teacher models without requiring access to logits or distribution matching. On undergraduate-level scientific reasoning benchmarks from SciKnowEval, SocraticPO improves over strong RL and self-distillation baselines. Ablations show that both targeted guidance and reward decay are necessary, with reward decay mitigating reliance on assisted correction.
Jun 2, 2026cs.LG

When Should the Teacher Move? Temporal Coupling and Stability in Self On-Policy Distillation

Self on-policy distillation trains a student policy against a teacher derived from its own parameter history, yet the teacher's update schedule -- which governs the \emph{temporal coupling} between teacher and student -- has not been systematically studied as a stability variable. Through a controlled schedule sweep on Qwen3-8B, we establish that \emph{isolation periods}, defined as complete teacher freezing between updates, are the key structural property enabling stable learning, not teacher age. To characterize these underlying training dynamics, we introduce a diagnostic framework of temporal KL structure, refresh shock, and length-tail risk. This framework further uncovers \emph{state-oblivious collapse}: optimal short-horizon fixed schedules catastrophically fail under long-horizon training because a clock-driven refresh can copy a transiently drifting student into the teacher in a single, irreversible step. This failure mode is invisible under short-horizon evaluation and mechanistically distinct from EMA's chronic contamination. To address this, we propose \emph{Consolidation-Gated Teacher Refresh} (CGTR), which preserves isolation periods while gating each refresh on joint evidence of reward improvement and length-tail safety, ensuring every teacher movement responds to genuine student consolidation rather than a clock signal. With a single shared parameter set and no per-dataset retuning, CGTR achieves \textbf{zero collapse} and the best final score on all four tasks (Chemistry, Biology, Physics, ToolUse), self-regulating its refresh frequency to each task's learning dynamics.
Jun 1, 2026cs.CV

VLMs are Good Teachers for Video Reasoning via Adaptive Test-Time Optimization

The recent "Reasoning with Video" paradigm utilizes Video Generation Models (VGMs) to generate temporally coherent visual trajectories to complete reasoning tasks. Although state-of-the-art VGMs excel at visual quality, they often struggle to understand and follow task-specific rules, leading to logical failures across diverse reasoning scenarios. Existing efforts try to utilize Vision-Language Models (VLMs) as problem pre-solvers to produce or refine textual guidance for the VGM. However, textual descriptions fail to capture intricate spatiotemporal details, and VGMs often struggle to faithfully execute fine-grained or long-tail instructions even with a valid plan. While VLMs struggle as solvers, they possess strong perception capabilities to evaluate process-constraint satisfaction and final-goal achievement. Leveraging this strength, we introduce a paradigm shift that transitions the role of VLMs to "teachers". Specifically, a VLM teacher extracts task-specific rules to formulate differentiable rewards, guiding a VGM Reasoner via test-time online optimization of a lightweight LoRA module. This strategy enables adaptive test-time optimization and extends the reasoning capabilities beyond the VGM's intrinsic boundaries. Evaluations on symbolic (VBVR-Bench) and general-purpose (RULER-Bench) video reasoning benchmarks show that the proposed method yields a 16.7-point average performance gain, outperforming the VLM-as-Solver paradigm (+0.4 points) and Best-of-N scaling (+2.2 points) by a large margin at comparable test-time cost. These findings reveal that integrating VLMs as test-time teachers offers a promising paradigm for achieving generalizable video reasoning. Project Page: https://VLM-as-Teacher.github.io/
Jun 1, 2026cs.CL

When Rating Scales Fall Short: LLM-Assisted Discovery of ADHD Signals in Turkish Teacher Narratives

Attention Deficit Hyperactivity Disorder (ADHD) is one of the most common neurodevelopmental disorders in childhood, and its diagnosis relies on assessments combining clinician judgment with standardized rating scales and reports from parents and teachers. While structured instruments such as the Conners' Teacher Rating Scale-Revised Short Form (CTRS-R:S) quantify ADHD-related behaviors, teachers also provide open-ended narratives that may contain complementary signals not captured by structured assessments. However, it remains unclear to what extent teacher narratives encode signals overlooked by rating scales. In this study, we analyze de-identified Turkish teacher evaluation forms collected during clinical ADHD assessments, including both CTRS-R:S scores and open-ended teacher narratives. We compare predictive signals from structured scores and narrative text and identify cases where structured assessments fail to clearly distinguish ADHD from non-ADHD students while narrative-based models capture distinct behavioral patterns. Notably, these cases show minimal overlap with those missed by the narrative model, suggesting that structured and narrative information encode complementary signals. To interpret these differences, we apply a large language model (LLM)-assisted theme discovery pipeline that reveals distinct attention, behavioral, and family-related patterns, highlighting the potential of natural language processing (NLP) to uncover clinically relevant signals from teacher narratives and to complement traditional ADHD screening tools.
May 31, 2026cs.LG

OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.
May 31, 2026cs.LG

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression

Teacher-Student Knowledge Transfer (KT) is ubiquitous in modern machine learning, ranging from classical model compression via Knowledge Distillation (KD) to the emergent phenomenon of Weak-to-Strong (W2S) generalization. While existing studies offer isolated insights, a unified theoretical framework explaining the efficacy of KT across these disparate regimes remains lacking. In this work, we establish a unified spectral analysis of SGD dynamics in high-dimensional linear regression, elucidating the efficiency of KT across seemingly disparate regimes. We characterize KT efficiency through two distinct mechanisms: \emph{Spectral Horizon Expansion} in KD, which enables the capture of statistically inaccessible high-frequency signals, and \emph{Spectral Denoising} in W2S, where the student acts as a filter for optimization noise. Our framework unifies these phenomena, revealing that the efficacy of transfer is governed by the interplay between implicit regularization and heterogeneous spectral learning speeds over the spectrum.
May 31, 2026cs.LG

Trust Functions: Near-Lossless Weak-to-Strong Generalization by Learning When to Trust the Weak Teacher

Weak-to-strong generalization studies how to improve a strong student using supervision from a weaker teacher when reliable labels are scarce. We view this primarily as a data selection problem, where the key challenge is to identify which weak labels are reliable enough to serve as a training signal. To address this, we introduce trust functions that assign each weak label a scalar trust score and use these scores to filter weak supervision. Across several domains, including world knowledge, quantitative reasoning, and strategy games, trust filtering yields students that match and sometimes surpass ground-truth supervision, achieving near-lossless weak-to-strong generalization. Moreover, trust functions enable an iterative weak-to-strong chain that compounds gains by training a student and reusing it as the next teacher, amplifying the gains. There are several mechanisms to which advantage of trust functions can be attributed.
May 31, 2026cs.AI

Subliminal Learning Is Steering Vector Distillation

Subliminal learning refers to a student language model acquiring a teacher's traits (e.g. a system-prompted preference for owls) when fine-tuned on the teacher's outputs, despite the outputs being semantically unrelated to those traits. It remains poorly understood how data without semantic meaning can transfer specific semantic traits. In this work, we show that subliminal learning is mediated by a single steering vector, i.e. a vector added to the model's activations. Across two open-source models, we find that the teacher's system prompt is well approximated by a steering vector, and that the student's behavior is driven by learning an aligned vector over fine-tuning. System prompts that are not well approximated by steering vectors are not subliminally learned. This is a special case of steering vector distillation, in which a student trained on the outputs of a steered teacher learns to imitate that steering. We demonstrate steering vector distillation on a range of semantic and random vectors. Adding a semantic vector to a model's activations can have both model-independent and model-specific (i.e. non-semantic) effects on its behavior, so generated data that is non-semantic can transmit a vector with semantic effects, enabling subliminal learning. This also explains why subliminal learning does not transfer between models. We find that adaptive optimizers are necessary for subliminal learning in language models: activation gradients on steered data carry a small but consistent component along the steering direction, and non-adaptive optimizers impede this by allowing outlier gradients to dominate.
May 30, 2026cs.LG

Logit Distillation on Manifolds: Mapping by Learning

A simple way to improve the performance of almost any machine learning model is not to train a single but several models with diverse algorithms which will make slightly distinct kinds of predictions and errors on the same data, and thus improve the average predictions and robustness. However, making predictions using a whole ensemble of models is cumbersome and computationally too expensive to allow deployment to a large number of users, especially if the models are large neural nets. In response to this, we introduce a layer and point wise projection mapping, which maps student and teacher representations into an aligned high-dimensional embedding space during training process. The proposed approach combined with LoRA injection reduces the student model trainable parameters to less than 1% of the teacher model, while significantly improving word error rate (WER) compared to other distillation methods, as demonstrated in ablation studies. Unlike a mixture of experts, our method can be trained rapidly and in parallel.
May 30, 2026cs.AI

Hidden Thoughts Are Not Secret: Reasoning Trace Exposure in LLMs

Reasoning traces have become a valuable form of learning signals for improving and transferring the capabilities of large language models. In particular, detailed traces can help distill reasoning behavior from stronger teacher models into weaker student models. The value of capability transfer has motivated many deployed systems with reasoning models to hide raw internal traces and expose at most summaries and answers to users. As a result, we ask whether such interface-level trace hiding prevents users from obtaining useful reasoning supervision through prompting. We study this question with Reasoning Exposure Prompting (REP), a lightweight in-context elicitation method that uses shadow-model-generated demonstrations wrapped in auxiliary code-like formats to raise user-visible reasoning traces from a victim model. Across the common reasoning dataset, different victim models, and different student model distillation, REP substantially increases similarity between exposed and REP-conditioned internal traces while preserving useful reasoning signals.
May 29, 2026cs.LG

Student Capacity Moderates Knowledge Distillation Effectiveness: A Systematic Study Across ResNet Teacher-Student Pairs on CIFAR-10

We investigate how teacher-student capacity relationships modulate knowledge distillation (KD) effectiveness in ResNet-based image classification on CIFAR-10. Across four teacher-student pairs (R50->R18, R34->R18, R50->R34, and R101->R34) we compare Logit-KD and Feature-KD under a strict evaluation protocol: hyperparameters and checkpoints are selected on a held-out validation split, selected configurations are re-run with five seeds, and the test set is used exclusively for final reporting. Beyond accuracy, we measure distillation fidelity directly via teacher-student agreement and KL divergence. We report four findings. First, the student-capacity pattern survives the corrected protocol at reduced magnitude: the only statistically significant gains occur for R34 students under Feature-KD (+0.19 and +0.21 pp, p<0.05), in two pairs whose teachers differ two-fold in parameters but not in accuracy, localizing the moderating variable on the student side, while no KD gain for R18 students is distinguishable from zero. Second, Feature-KD matches or outperforms Logit-KD in all four pairs, and its students land closer to the teacher's output distribution (KL at T=1) than Logit-KD students despite never observing teacher logits. Third, top-1 teacher-student agreement is flat across all pairs, decoupling fidelity from accuracy gains. Fourth, architecture dominates KD: correcting the ResNet stem for 32x32 inputs is worth +5.5 to +7.2 pp, more than 25x the largest KD gain. We also retract an attribution made in v1: a controlled re-run shows the reported gradient-clipping bug had no measurable effect, and v1's larger gains are explained by test-set selection. Code and results: github.com/umutonuryasar/kd-capacity-gap (tag v2.0).
May 29, 2026cs.CL

Your Teacher Can't Help You Here: Combating Supervision Fidelity Decay in On-Policy Distillation

On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, \textbf{Supervision Fidelity Decay (SFD)}: as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce \textbf{Lookahead Group Reward (\ours{})}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, \ours{} evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, \ours{} improves mean@8 by \textbf{2.57} points over OPD for a 7B student, with gains increasing in longer-generation and reaching +\textbf{4.92} points on AIME-26 at 39k tokens.
May 28, 2026cs.AI

Surfacing Isolated Learners with Outcome-Independent Mediation of Feedback between Teachers and Students Using AI

AI-augmented classrooms generate rich teacher and student feedback before graded outcomes become available, yet these signals can be difficult to translate into timely instructional decisions. We propose an interpretable decision layer: a transparent mechanism that ranks course topics requiring attention without using grades or post-hoc outcome labels. The approach combines three signals: student learning difficulty prevalence, disagreement between learner self-reports and observed difficulties, and unresolved teacher concerns. The output is a ranked set of topic priorities with per-topic decision records explaining each ranking. In one graduate CS course offering (n=5n=5 instructor interviews; n=279n=279 survey responses), prioritized topics aligned with instructor concerns (top-5 overlap 3/5; Spearman ρ=0.80ρ=0.80) and student-reported topic difficulty (ρ=0.46ρ=0.46, p=.048p=.048). Multi-signal integration also surfaced learners not identified through individual signal sources alone (AUC =0.96=0.96 vs. 0.910.91 for gap prevalence alone). Reflective thinking, help-seeking, and self-efficacy provided additional evidence that student behavioral signals align with learning-related constructs. While preliminary, these findings suggest that transparent coordination mechanisms may help support human-AI co-agency when feedback is incomplete.
May 27, 2026cs.CL

Skill-Conditioned Gated Self-Distillation for LLM Reasoning

On-policy self-distillation (SD) improves LLM reasoning by using teacher-side privileged information (PI) to turn sparse verifier outcomes into dense token-level supervision. Existing methods usually assume trusted PI, such as reference answers or successful traces. We ask whether PI can instead come from an experience-derived skill bank, where retrieved skills are compact and reusable but may also be irrelevant or misleading. We propose Skill-Conditioned Gated Self-Distillation (SGSD), which formulates skill-based SD as teacher hypothesis validation rather than unconditional imitation. SGSD retrieves skill-mistake pairs, constructs a multi-teacher pool, and lets all skill-conditioned teachers score the same plain-prompt student rollout. The verifier validates each teacher's polarity: supporting a success or suppressing a failure gives positive supervision, while the opposite stance is reversed. A robust gated objective then distills informative teacher-student disagreements while suppressing uncertain or extreme signals. Experiments on multiple mathematical reasoning benchmarks show that SGSD consistently improves over GRPO and remains competitive with answer-conditioned OPSD under a weaker PI assumption. For example, on Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and OPSD by 1.7% on average on AIME24, AIME25, and HMMT25.
May 27, 2026cs.LG

Teacher-Student Representational Alignment for Reinforcement Learning-Driven Imitation Learning

Imitation learning (IL) from a state-based reinforcement learning (RL) policy is a common approach to overcome the curse of dimensionality in complex and high-dimensional observation spaces prevalent in robotics. This paper addresses the irreducible imitation gap that emerges when teacher and student are learned in isolation, and the teacher policy has the liberty to rely on privileged state information that the student cannot infer from its observations. Instead of improving poor student performance with RL finetuning after IL, which often requires a whole new training setup, we propose a novel algorithm which learns a shared embedding space that hides agent-specific observations and thus trains imitable teacher policies by construction. We train the shared embedding space with self-supervised contrastive learning in parallel to the teacher policy and prevent it from extracting private information by limiting its gradients from updating the encoder networks. We perform evaluations on several example domains and compare to state-of-the-art baselines showing that our algorithm enables higher student performance with substantially reduced imitation gap.
May 27, 2026cs.CV

Reflective Dialogue between Teacher and Solver Agents for Video Question Answering

Various approaches have been proposed to adapt Vision-Language Models (VLMs) to specialized domains for Video Question Answering, including fine-tuning and in-context learning. However, acquiring task-specific knowledge at the inference phase from only a small labeled support set without fine-tuning remains a challenge. In this paper, we propose a method that achieves adaptation solely through inference-time context injection. Our method first constructs a Reflective Dialogue (RD) -- a multi-turn conversation between two agents, in which Teacher poses each support question and delivers correctness feedback, and Solver answers and provides visual grounding explanations (or reflections) for both correct and incorrect answers. This dialogue history is then used as context at the inference phase. Experiments on the EgoCross benchmark demonstrate that our method outperforms both a baseline zero-shot setting and a standard in-context learning approach that passes support set examples directly, achieving 3rd place in the Open-source Track of the 1st Cross-Domain EgoCross Challenge at the CVPR 2026 EgoVis Workshop, for which this paper also serves as a technical report.
May 26, 2026cs.LG

Adversarial Dual On-Policy Distillation from Expressive Teacher

Learning from demonstrations in embodied control is often cast as behavioral cloning, and recent diffusion or flow-matching policies improve this paradigm by modeling multi-modal expert actions. Yet these methods remain offline supervised learners: the policy is trained only on expert states and receives no corrective signal on the states it actually visits. On-policy distillation (OPD) offers a natural remedy, but standard OPD assumes a strong fixed teacher, which is unavailable in demonstration-only control. We propose \textbf{FA-OPD}, an \emph{adversarial dual on-policy distillation} method in which a Flow Matching (FM) teacher is learned from demonstrations and co-trained with a lightweight MLP student. The teacher provides two complementary signals on student rollouts. The reward channel learns an expert-likeness objective over state-action pairs and drives online exploration through long-horizon policy optimization. The action channel supplies dense local targets at student-visited states, stabilizing exploitation. FA-OPD couples them so that reward distillation enables generalization beyond point-wise demonstrations, while action distillation keeps exploration anchored near expert-like behavior. Across six robot navigation, manipulation, and locomotion benchmarks, FA-OPD beats strong baselines and shows much stronger robustness under noisy or limited demonstrations. Source code: https://github.com/vanzll/FA-OPD.
May 26, 2026cs.LG

When the Strongest Teacher Is Not the Best Teacher: Student-Centric Answer Selection

LLM training increasingly relies on teacher-generated supervision, from synthetic responses to reasoning traces and tool-use demonstrations. Current practice often chooses the highest-performing teacher to generate student training data, implicitly treating teacher test performance as a proxy for teaching quality. We show that this assumption can fail: even when multiple teachers provide correct answers to the same question, the answer from the strongest teacher is not necessarily the best supervision for a given student. To address this gap, we propose Student-Centric Answer Sampling (SCAS), a framework that selects from verified teacher-generated answers according to their estimated student-centric learning cost. Motivated by a token-wise gradient decomposition, we derive an efficient forward-only proxy for this cost and use it to guide answer selection during training. Experiments across 30 teacher models, 6 student base models, and 6 tasks show that SCAS consistently improves student performance, suggesting that effective distillation should prioritize supervision matched to the current student rather than teacher strength alone.
May 25, 2026cs.CV

On-Policy Adversarial Flow Distillation for Autoregressive Video Generation

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.
May 22, 2026cs.LG

Strong Teacher Not Needed? On Distillation in LLM Pretraining

Knowledge distillation generally assumes a strong-to-weak relationship where stronger teachers yield better students. In this work, we examine this assumption about distillation in large language model pretraining. By varying architecture sizes and training token budgets, we create strong-to-weak, same-level, and weak-to-strong teacher-student relationships, and study distillation's effectiveness under each. We find that the teacher need not be strong: with proper mixing of the language modeling and knowledge distillation losses, even small and undertrained teachers improve larger students. At the same time, a stronger teacher is not always better: pushing the teacher further, through more parameters or more training tokens, can saturate or even reverse the distillation gains. We further observe that distillation improves generalization (out-of-distribution and downstream performance) more readily than in-domain fitting. Together, these results challenge the common belief that distillation pretraining always requires a strong teacher.
May 21, 2026cs.LG

The Distillation Game: Adaptive Attacks & Efficient Defenses

Distillation attacks create a deployment trade-off for model providers: the same outputs that make a model more useful can also make it easier to imitate. We study this trade-off through a minimax game between a utility-constrained teacher and an adaptive student. Our framework yields tractable one-sided response rules: an adaptive evaluation rule in which the student reweights high-value examples, and a teacher-side defense template that suppresses outputs most useful for distillation. From a cheap proxy for example value, we derive Product-of-Experts (PoE), a simple forward-pass-only defense that combines the teacher with a proxy student during generation. Empirically, adaptive evaluation reveals a large passive--adaptive gap: on state-of-the-art defenses, adaptive students recover substantially more capability than passive evaluation suggests on GSM8K and MATH. Under this stronger evaluation, the apparent robustness gap between expensive defenses and PoE narrows considerably, while PoE remains substantially cheaper and preserves higher-quality reasoning traces. Overall, our results suggest that strong distillation remains difficult to stop, and that progress on antidistillation should be judged against adaptive students rather than passive ones. Our code is available at: https://github.com/ysfalh/distillation-game.
May 21, 2026cs.LG

A Boundary-Layer Mechanism for One-Third Scaling in Online Softmax Classification

Hard-label classification is usually trained with smooth surrogate losses, most prominently softmax cross-entropy. We isolate an asymptotic mechanism by which this mismatch between smooth surrogate and discrete labels produces power-law learning curves in an online teacher-student model. After subtracting the mean logit, the thermodynamic-limit dynamics close in centered variables: a growing centered student-teacher alignment DD and the residual student variance ΔΔ. At late times, examples away from teacher decision boundaries are already classified confidently and contribute exponentially little. Only boundary layers of width O(D−1)O(D^{-1}) remain active, while the noise of fixed-learning-rate online gradient descent maintains a nonzero ΔΔ. As a function of the training time αα the late-time solution yields a α−1/3α^{-1/3} power law not only for the test loss but also for the generalization error εgε_g, i.e., one minus test accuracy. This is much slower than the α−1α^{-1} Bayes-optimal reference for the same model. We further show that learning-rate schedules can improve the generalization error towards a εg∼α−1/2ε_g \sim α^{-1/2} power law. Simulations support the predicted order parameter dynamics and learning curves. Controlled experiments with correlated Gaussian inputs and whitened pretrained features show that data structure can dominate transients. Therefore, our result is an asymptotic, complementary mechanism rather than an alternative to spectral explanations of neural scaling laws.
May 21, 2026cs.CV

TextTeacher: What Can Language Teach About Images?

The platonic representation hypothesis suggests that sufficiently large models converge to a shared representation geometry, even across modalities. Motivated by this, we ask: Can the semantic knowledge of a language model efficiently improve a vision model? As an answer, we introduce TextTeacher, a simple auxiliary objective that injects text embeddings as additional information into image classification training. TextTeacher uses readily available image captions, a pre-trained and frozen text encoder, and a lightweight projection to produce semantic anchors that efficiently guide representations during training while leaving the inference-time model unchanged. On ImageNet with standard ViT backbones, TextTeacher improves accuracy by up to +2.7 percentage points (p.p.) and yields consistent transfer gains (on average +1.0 p.p.) under the same recipe and compute. It outperforms vision knowledge distillation, yielding more accuracy at a constant compute budget or similar accuracy, but 33% faster. Our analysis indicates that TextTeacher acts as a feature-space preconditioner, shaping deeper layers in the first stages of training, and aiding generalization by supplying complementary semantic cues. TextTeacher adds negligible overhead, requires no costly multimodal training of the target model and preserves the simplicity and latency of pure vision models. Project page with code and captions: https://nauen-it.de/publications/text-teacher
May 21, 2026cs.LG

Toward Understanding Adversarial Distillation: Why Robust Teachers Fail

Adversarial Distillation aims to enhance student robustness by guiding the student with a robust teacher's soft labels within the min-max adversarial training framework, yet its success is notoriously inconsistent: a more robust teacher often fails to improve, or even harms, the student's robust generalization. In this paper, we identify a key mechanism of this teacher dependency: the misalignment between the teacher's supervisory confidence and the student's representational limitations on a consistent subset of training data -- the Robustly Unlearnable Set. We present a theoretical framework analyzing the feature learning dynamics of a two-layer neural network, demonstrating that this mismatch creates a dichotomy in distillation outcomes. We prove that when a teacher provides confident supervision on unlearnable samples, it compels the student to memorize spurious noise patterns that eventually overpower the learned robust signal, thereby driving robust overfitting. Conversely, a teacher that exhibits high uncertainty on these samples effectively suppresses noise memorization, allowing the student to rely solely on the learnable signal for robust generalization. We empirically validate our theory across both synthetic simulations and real-image classification datasets, confirming that robust overfitting is driven by the teacher's interaction with unlearnable samples. Finally, we demonstrate that a teacher's predictive entropy on unlearnable samples serves as a strong indicator of student robustness, validating our theoretical framework and offering a principled guideline for robust teacher selection.
May 20, 2026cs.LG

X-Token: Projection-Guided Cross-Tokenizer Knowledge Distillation

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.
May 20, 2026cs.LG

When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.
May 20, 2026cs.LG

AVSD: Adaptive-View Self-Distillation by Balancing Consensus and Teacher-Specific Privileged Signals

Self-distillation enables language models to learn on-policy from their own trajectories by using the same model as both student and teacher, with the teacher being conditioned on privileged information unavailable to the student. Such information can come in different types or views, such as solutions, demonstrations, feedback, or final answers. This setup provides dense token-level feedback without relying on a separate external model, but creates a fundamental asymmetry: the teacher may rely on view-specific information that the student cannot access at inference time. Moreover, the best type of privileged information is often task-dependent, making it difficult to choose a single teacher view. In this work, we address both these challenges jointly by introducing AVSD (Adaptive-View Self-Distillation), a novel method of self-distillation with multiple privileged-information views, which reconstructs token-level supervision by separating stable cross-view consensus from view-specific residual signals. AVSD identifies the consensus signal shared across views, which provides a reliable update direction, and then selectively adds the view-specific residual signal to adjust the update magnitude when it both aligns with the consensus direction and remains proportionate to the consensus signal. Experiments on math competition benchmarks (AIME24, AIME25, and HMMT25) show that AVSD consistently outperforms both single-view self-distillation baselines and GRPO, achieving average Avg@8 gains of 3.1% and 2.2% over the strongest baselines on Qwen3-8B and Qwen3-4B, respectively. Moreover, on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, AVSD outperforms the single-view self-distillation baseline by 2.4% on average.
May 18, 2026cs.LG

Distilling Tabular Foundation Models for Structured Health Data

Tabular foundation models (TFMs) achieve strong performance on health datasets, but their inference cost and infrastructure requirements limit practical use. We study whether their predictive behavior can be transferred to lightweight tabular models through knowledge distillation. Since in-context TFMs condition on the training set at inference time, naive distillation can introduce context leakage; we address this with stratified out-of-fold teacher labeling. Across 1919 healthcare datasets, 66 TFM teachers, 44 student families, and several multi-teacher ensembles, we find that distilled students retain at least 90%90\% of teacher AUC, outperforming teachers in some cases, while running at least 26×26\times faster on CPU and preserving calibration and fairness critical for health applications. Moreover, multi-teacher averaging does not consistently improve over the best single teacher. Leakage-aware distillation is thus a viable route for bringing TFM-quality predictions into inference-constrained health settings.
May 18, 2026cs.LG

Pocket Foundation Models: Distilling TFMs into CPU-Ready Gradient-Boosted Trees

A fraud scorer needs to answer in under 2 ms. The best tabular foundation models (TFMs) take 151-1,275 ms on GPU. We close this gap by distilling the TFM offline into an XGBoost or CatBoost student that runs natively on CPU. The central obstacle is specific to in-context learning (ICL) teachers: they leak labels when scoring their own training set, so the soft targets collapse to near-one-hot vectors with no inter-class structure left to distill. Stratified out-of-fold (OOF) teacher labeling prevents this. Across 153 classification datasets drawn from TALENT, OpenML-CC18, TabZilla, and TabArena, distilling TabICLv2 into XGBoost gives 0.882 macro-mean AUC (96.5% of teacher AUC) at 1.9 ms on CPU, a 38x to 860x speedup across teacher-student pairs with a statistically significant edge over a tuned CatBoost baseline (Wilcoxon p = 0.0008; 51% win rate). Four further findings: teacher rank transfers exactly to student rank; gains concentrate on low-dimensional data (< 21 features: +0.011 over CatBoost vs. >21 features: +0.001); multi-teacher averaging helps MLP students (+0.006, p = 0.003) but adds less than 0.001 for tree students; and on high-dimensional tasks where the teacher itself trails CatBoost, distillation makes things worse rather than better. The full pipeline is open-sourced as part of the TabTune library.
May 16, 2026cs.CL

Roll Out and Roll Back: Diffusion LLMs are Their Own Efficiency Teachers

Diffusion Large Language Models (DLLMs) promise fast parallel generation, yet open-source DLLMs still face a severe quality-speed trade-off: accelerating decoding by revealing multiple tokens often causes substantial quality degradation. We attribute this dilemma to a train-inference mismatch amplified by irreversible decoding. While training reconstructs tokens from randomly corrupted states, efficient inference requires an adaptive denoising order, where easier tokens are revealed earlier and context-dependent ones are deferred. This view motivates two complementary methods: an inference-time method that makes parallel decoding revokable, and a training-time extension that distills the reliable order exposed by this revokable process. Accordingly, we first propose Wide-In, Narrow-Out (WINO), a training-free decoding algorithm that enables revokable parallel generation. WINO aggressively drafts multiple tokens, verifies generated tokens with enriched global context, and re-masks unreliable ones for later refinement. Building on this discovered order, we further introduce WINO+, which injects the verified denoising trajectories produced by WINO into model parameters, aligning training with efficient inference. Experiments on LLaDA and MMaDA show that WINO improves both quality and efficiency, while WINO+ further strengthens this progression. On GSM8K, WINO improves accuracy from 73.24% to 75.82% with a 6.10x step reduction, and WINO+ further achieves 76.58% with a 6.83x reduction. On Flickr30K, WINO+ reaches a 16.22x step reduction with improved CIDEr. These results demonstrate that DLLMs can serve as their own efficiency teachers by first discovering reliable denoising orders through revokable decoding and then learning to follow them for faster generation. Code is available at https://github.com/Feng-Hong/WINO-DLLM/tree/WINO-plus.
May 15, 2026cs.CV

How to Choose Your Teacher for Fine Grained Image Recognition

Fine-grained image recognition classifies subcategories such as bird species or car models. While state-of-the-art (SOTA) models are accurate, they are often too resource-intensive for deployment on constrained devices. Knowledge distillation addresses this by transferring knowledge from a large teacher model to a smaller student model. A key challenge is selecting the right teacher, as it heavily impacts student performance. This paper introduces a teacher selection metric, \textbf{Ratio 1-2}, based on teacher prediction ratios. Extensive analysis of over one thousand experiments across 3 students, 8 teachers, and 8 datasets under 4 training strategies demonstrates that our metric improves teacher selection by 18% over previous methods, enabling small student models to achieve up to 17% accuracy gains. Experiment codebase is available at: https://github.com/arkel23/FGIR-KD-Teacher.
May 14, 2026cs.LG

Cognitive-Uncertainty Guided Knowledge Distillation for Accurate Classification of Student Misconceptions

Accurately identifying student misconceptions is crucial for personalized education but faces three challenges: (1) data scarcity with long-tail distribution, where authentic student reasoning is difficult to synthesize; (2) fuzzy boundaries between error categories with high annotation noise; (3) deployment parado-large models overlook unconventional approaches due to pretraining bias and cannot be deployed on edge, while small models overfit to noise. Unlike traditional methods that increase diversity through large-scale data synthesis, we propose a two-stage knowledge distillation framework that mines high-value samples from existing data. The first stage performs standard distillation to transfer task capabilities. The second stage introduces a dual-layer marginal selection mechanism based on cognitive uncertainty, identifying four types of critical samples based on teacher model uncertainty and confidence differences. For different data subsets, we design difficulty-adaptive mechanism to balance hard/soft label contributions, enabling student models to inherit inter-class relationships from teacher soft labels while distinguishing ambiguous error types. Experiments show that with augmented training on only 10.30% of filtered samples, we achieve MAP@3 of 0.9585 (+17.8%) on the MAP-Charting dataset, and using only a 4B parameter model, we attain 84.38% accuracy on cross-topic tests of middle school algebra misconception benchmarks, significantly outperforming sota LLM (67.73%) and standard fine-tuned 72B models (81.25%). Our code is available at https://github.com/RoschildRui/acl2026_map.
May 13, 2026cs.LG

Teacher-Guided Policy Optimization for On-Policy Reasoning Distillation under Large Policy Divergence

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.
May 13, 2026cs.IT

On the Generalization of Knowledge Distillation: An Information-Theoretic View

Knowledge distillation is widely used to improve generalization in practice, yet its theoretical understanding remains elusive. In the standard distillation setting, a teacher model provides soft predictions to guide the training of a student model. We model teacher and student training as coupled stochastic processes and introduce a distillation divergence, defined as the Kullback-Leibler divergence between these two stochastic kernels. Within this framework, we derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaussian assumption via algorithmic stability, and a lower bound under a central condition with sharper dependence on the distillation divergence. We further develop a loss-sharpness-aware bound with an explicit tightness regime, showing that the teacher's local flatness can strictly tighten the bound. Additionally, in a linear Gaussian case study, the distillation divergence admits an interpretable decomposition into bias, variance, and rank-bottleneck costs, yielding practical guidance for distillation design.
May 12, 2026cs.LG

Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated to the model and reward density where it is most informative. We identify a reward-density principle that governs this allocation: sparse sequence-level reward is most useful on models that can explore and discover better behavior, while dense token-level teacher supervision is better suited for compressing that behavior into a smaller deployment model. The principle yields a simple allocation rule: use scarce labeled data upstream on the strongest available teacher, then transfer the reward-shaped behavior downstream as dense supervision. We evaluate this rule through a four-stage workflow -- teacher RL, forward-KL warmup, on-policy distillation, optional post-bridge student RL -- on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student (79.3%79.3\% vs.\ 75.9%75.9\% on MATH; 25.2%25.2\% vs.\ 19.8%19.8\% on AIME~2024, avg@16), while transfer from the same teacher \emph{before} RL underperforms. A component ablation confirms that each stage is load-bearing: replacing the RL-improved teacher with a raw teacher costs 7.87.8 MATH points, removing the forward-KL warmup costs 1.71.7, and removing on-policy distillation costs 3.33.3. The teacher-quality ordering -- raw-teacher transfer << direct GRPO << RL-teacher transfer -- replicates on Llama-3.1-8B-Instruct with a Llama-3.3-70B-Instruct teacher. The operational lesson is to avoid spending scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.
May 12, 2026cs.AI

Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning

On-policy self-distillation has become a strong recipe for LLM reasoning, where a privileged teacher supervises the student's own rollouts while conditioning on the reference solution. A design choice shared by nearly all such methods, however, has gone unquestioned: the teacher always sees the full reference reasoning. We argue that this default itself is part of the problem and identify a teacher-side exposure mismatch: when the teacher conditions on reasoning far beyond the student's current competence, the resulting token targets become too strong to absorb. A controlled fixed-exposure sweep makes this concrete on two fronts: 1) full exposure is not reliably the best choice, and 2) student-teacher mismatch grows monotonically as the teacher sees more privileged reasoning. This motivates treating teacher exposure not as a fixed hyperparameter but as a learnable training-time control variable. We therefore propose Adaptive Teacher Exposure for Self-Distillation (ATESD). ATESD models the reveal ratio with a lightweight Beta-policy controller conditioned on compact training-state statistics, and uses one sampled exposure for a short hold window of student updates. To make this exposure controller learnable, we optimize it with a discounted learning-progress reward that scores each held decision by its effect on the student's future improvement rather than its immediate loss change, addressing the delayed credit assignment induced by on-policy distillation. Experiments on AIME 24, AIME 25, and HMMT 25 across Qwen3-{1.7B, 4B, 8B} show that ATESD consistently outperforms competitive self-distillation and RL baselines, improving over OPSD by +0.95, +2.05, and +2.33 Average@12 points respectively, and establishing adaptive teacher exposure as an effective new axis for reasoning self-distillation.
May 11, 2026cs.LG

Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR

Self-distillation has emerged as a powerful framework for post-training LLMs, where a teacher conditioned on extra information guides a student without it, both from the same model. While this guidance is useful when the student has failed, on successful rollouts, the same mechanism instead overwrites the student's choices and suppresses it's own reasoning. Therefore, we propose reading the original self-distillation signal in reverse: when the student succeeds along a path the teacher would not have predicted, these tokens reflect its self-driven reasoning. Building on this, we propose RLRT (RLVR with Reversed Teacher), which augments GRPO by reinforcing these tokens on correct rollouts. We interpret this as a new form of exploration in RLVR: not uniform diversity, but valuable exploration grounded in the student's own success. Across base, instruction-tuned, and thinking-tuned Qwen3 checkpoints, RLRT substantially outperforms self-distillation and exploration-based baselines, establishing information asymmetry as a new, principled design axis for RLVR.
May 11, 2026cs.CV

LLaVA-CKD: Bottom-Up Cascaded Knowledge Distillation for Vision-Language Models

Large Vision-Language Models (VLMs) are successful in addressing a multitude of vision-language understanding tasks, such as Visual Question Answering (VQA), but their memory and compute requirements remain a concern for practical deployment. A promising class of techniques for mitigating this concern is Knowledge Distillation, where knowledge from a high-capacity Teacher network is transferred to a considerably smaller Student network. However, the capacity gap between the two networks is both a blessing and a curse: the smaller the Student network, the better its efficiency, and the larger the Teacher, the more knowledge it carries; yet, beyond a point, the larger capacity gap between the two leads to worse knowledge transfer. To counter this effect, we propose a bottom-up cascaded knowledge distillation (CKD) framework. Instead of treating knowledge transfer as an activity involving one high-capacity Teacher (or an ensemble of such), inspired by human formal education systems, we introduce one (potentially, more) additional Teacher(s) of intermediate capacity that gradually bring the Student network to the next level, where the next (higher-capacity) Teacher can take over. We provide a theoretical analysis in order to study the effect of cascaded distillation in the generalization performance of the Student. We apply the proposed framework on models build upon the LLaVA methodology and evaluate the derived models on seven standard, publicly available VQA benchmarks, demonstrating their SotA performance.
May 10, 2026cs.CL

Cornerstones or Stumbling Blocks? Deciphering the Rock Tokens in On-Policy Distillation

While recent work in Reinforcement Learning with Verifiable Rewards (RLVR) has shown that a small subset of critical tokens disproportionately drives reasoning gains, an analogous token-level understanding of On-Policy Distillation (OPD) remains largely unexplored. In this work, we investigate high-loss tokens, a token type that--as the most direct signal of student-teacher mismatch under OPD's per-token KL objective--should progressively diminish as training converges according to existing studies; however, our empirical analysis shows otherwise. Even after OPD training reaches apparent saturation, a substantial subset of tokens continues to exhibit persistently high loss; these tokens, which we term Rock Tokens, can account for up to 18% of the tokens in generated outputs. Our investigation reveals two startling paradoxes. First, despite their high occurrence frequency providing a disproportionately large share of total gradient norms, Rock Tokens themselves remain stagnant throughout training, resisting teacher-driven corrections. Second, through causal intervention, we find that these tokens provide negligible functional contribution to the model's actual reasoning performance. These findings suggest that a vast amount of optimization bandwidth is spent on structural and discourse residuals that the student model cannot or need not internalize. By deconstructing these dynamics, we demonstrate that strategically bypassing these ``stumbling blocks'' can significantly streamline the alignment process, challenging the necessity of uniform token weighting and offering a more efficient paradigm for large-scale model distillation.
May 9, 2026cs.LG

The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs

On-policy distillation (OPD) is widely used for LLM post-training. When pushed with a reward-extrapolation coefficient lambda > 1, the student can lift past the teacher in domain, but past a threshold lambda* the same step violates the output contract on structured-output tasks. In a single-position Bernoulli reduction, we derive a closed-form base-relative clip-safety threshold lambda*(p,b,c) determined by three measurable quantities: the teacher modal probability, the warm-start mass, and the importance-sampling clip strength. Above lambda*, the extrapolated fixed point exits the clip-safe region, changing training from format-preserving to format-collapsing. We extend the rule to calibrated K-ary listwise JSON tasks where a single binding equivalence class dominates the output contract and SFT retains parse headroom. On Amazon Fashion, three pre-registered tests--a fine-grid cliff interval, a budget-extension test, and a small-clip cross-prediction--fall within their locked prediction windows, with the small-clip value matching the closed-form prediction below grid resolution. Operating just below lambda*, ListOPD brings a 1.7B Qwen3 student to in-domain parity with an 8B-SFT baseline at one-fifth the parameters. The gain is driven primarily by format adherence: NDCG@1 on parsed outputs remains flat across lambda, while parse validity sharply changes at the predicted boundary. The cliff diagnostic is rubric-independent, whereas the parity claim uses a Gemini-graded rubric and inherits that evaluator's exposure.
May 8, 2026cs.CL

SOD: Step-wise On-policy Distillation for Small Language Model Agents

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.
May 8, 2026cs.CL

SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation

On-policy distillation (OPD) is a standard tool for transferring teacher behavior to a smaller student, but it implicitly assumes that teacher and student predictions are comparable token by token, an assumption that fails whenever the two models tokenize the same text differently. Under heterogeneous tokenizers, exact shared-token matching silently discards a large fraction of the teacher signal at precisely the positions where vocabularies disagree. We propose \textbf{\underline{Sim}ple \underline{C}ross-\underline{T}okenizer OPD (SimCT)}, which restores this signal by enlarging the supervision space: alongside shared tokens, SimCT compares teacher and student over short multi-token continuations that both tokenizers can realize, leaving the OPD loss form itself unchanged. We show that these units are the finest jointly tokenizable supervision interface, and that coarser alternatives remove teacher-student distinctions that are useful for on-policy learning. Across three heterogeneous teacher-student pairs on mathematical reasoning and code-generation benchmarks, SimCT shows consistent gains over shared-vocabulary OPD and representative cross-tokenizer baselines, with ablations confirming that the improvements come from recovering supervision discarded by exact shared-token matching. Code is available at https://github.com/sunjie279/SimCT-.