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.

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.

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.

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.

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

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.

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.

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.

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.

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: \href{https://github.com/arkel23/FGIR-KD-Teacher}{https://github.com/arkel23/FGIR-KD-Teacher}.

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 ($79.3\%$ vs.\ $75.9\%$ on MATH; $25.2\%$ vs.\ $19.8\%$ 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 $7.8$ MATH points, removing the forward-KL warmup costs $1.7$, and removing on-policy distillation costs $3.3$. 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.

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.

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.

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.

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.

The study examines the adoption of artificial intelligence (AI) tools in education by analyzing the roles of institutional support, teacher confidence, and teacher concerns. It aims to determine whether teacher concerns moderate the relationship between institutional support and two outcomes: teacher confidence and attitudes toward AI adoption. The sample included 260 teachers from the Philippines. Composite scores were calculated for institutional support, confidence, concerns, and attitudes. Moderated multiple regression analysis showed that institutional support significantly predicted both teacher confidence and attitudes toward AI. However, teacher concerns did not significantly moderate these relationships. A follow-up mediation analysis tested whether confidence explains the effect of institutional support on attitudes. Results showed full mediation. The indirect effect was significant based on the Sobel test, and the direct effect became non-significant when confidence was included in the model. This shows that institutional support improves teacher attitudes by increasing their confidence. The study recommends that institutions provide structured and ongoing support to strengthen teacher confidence. Professional development, mentoring, and AI integration in teacher education programs can increase readiness and support effective AI adoption.

Identity teacher forcing (ITF) enables stable training of deterministic recurrent surrogates for chaotic dynamical systems and has been highly effective for dynamical systems reconstruction (DSR) with recurrent neural networks (RNNs), including interpretable almost-linear RNNs (AL-RNNs). However, as an intervention-based prediction loss (and thus a generalized Bayes update), teacher forcing need not match the free-running model's marginal likelihood geometry. We compare the objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs, estimating ambiguity-aware observed information via Louis' identity. In the switching setting studied here, conditioning on a single forced regime path (as ITF does) inflates curvature, while marginal likelihood curvature is reduced by a missing-information correction when multiple switching explanations remain plausible. In Lorenz-63 experiments, windowed evidence fine-tuning improves held-out evidence but can degrade dynamical quantities of interest (QoIs) relative to ITF-pretrained models.

Fine-grained medical image classification is challenged by subtle inter-class variations and visually ambiguous cases, where confidence estimates often exhibit uncertainty rather than being overconfident. In such scenarios, purely discriminative classifiers may achieve high overall accuracy yet still fail to distinguish between highly similar categories, leading to miscalibrated predictions. We propose T-DuMpRa, a teacher-guided dual-path multi-prototype retrieval-augmented framework, where discriminative classification and multi-prototype retrieval jointly drive both training and prediction. During training, we jointly optimize cross-entropy and supervised contrastive objectives to learn a cosine-compatible embedding geometry for reliable prototype matching. We further employ an exponential moving average (EMA) teacher to obtain smoother representations and build a multi-prototype memory bank by clustering teacher embeddings in the teacher embedding space. Our framework is plug-and-play: it can be easily integrated into existing classification models by constructing a compact prototype bank, thereby improving performance on visually ambiguous cases. At inference, we combine the classifier's predicted distribution with a similarity-based distribution computed via cosine matching to prototypes, and apply a conservative confidence-gated fusion that activates retrieval only when the classifier's prediction is uncertain and the retrieval evidence is decisive and conflicting, otherwise keeping confident predictions unchanged. On HAM10000 and ISIC2019, our method yields 0.68%-0.21% and 0.44%-2.69% improvements on 5 different backbones. And visualization analysis proves our model can enhance the model's ability to handle visually ambiguous cases.

Knowledge distillation is widely used to transfer behavior from a large teacher model to a smaller student. It is often assumed to be safe when the teacher is clean, because classic backdoor attacks rely on poisoned labels and triggers in supervised training, whereas distillation trains the student to match a teacher's outputs. We show that this assumption can fail when the distillation dataset itself is poisoned. Our attack injects triggered and manipulated images that a clean teacher already predicts as an attacker chosen target label, which causes the student to learn a backdoor even though the teacher remains unaffected. We evaluate this threat across multiple manipulation strategies, including targeted adversarial perturbations and targeted GAN based class transitions, and study how distillation settings influence both accuracy and attack success. We show that the attack remains effective even at a 10% poisoning rates. The results demonstrate that a clean teacher alone is not a sufficient safeguard: poisoned distillation data can produce a strongly backdoored student while maintaining competitive performance on clean images. These findings show that the integrity and provenance of distillation data are part of the security boundary of data intensive KD pipelines, even when the teacher itself is trusted.

Novice math teachers often encounter students' mistakes that are difficult to diagnose and remediate. Misconceptions are especially challenging because teachers must explain what went wrong and how to solve them. Although many existing large language model (LLM) platforms can assist in generating instructional feedback, these LLMs loosely connect pedagogical knowledge and student mistakes, which might make the guidance less actionable for teachers. To address this gap, we propose MisEdu-RAG, a dual-hypergraph-based retrieval-augmented generation (RAG) framework that organizes pedagogical knowledge as a concept hypergraph and real student mistake cases as an instance hypergraph. Given a query, MisEdu-RAG performs a two-stage retrieval to gather connected evidence from both layers and generates a response grounded in the retrieved cases and pedagogical principles. We evaluate on \textit{MisstepMath}, a dataset of math mistakes paired with teacher solutions, as a benchmark for misconception-aware retrieval and response generation across topics and error types. Evaluation results on \textit{MisstepMath} show that, compared with baseline models, MisEdu-RAG improves token-F1 by 10.95% and yields up to 15.3% higher five-dimension response quality, with the largest gains on \textit{Diversity} and \textit{Empowerment}. To verify its applicability in practical use, we further conduct a pilot study through a questionnaire survey of 221 teachers and interviews with 6 novices. The findings suggest that MisEdu-RAG provides diagnosis results and concrete teaching moves for high-demand misconception scenarios. Overall, MisEdu-RAG demonstrates strong potential for scalable teacher training and AI-assisted instruction for misconception handling. Our code is available on GitHub: https://github.com/GEMLab-HKU/MisEdu-RAG.

Terminology-aware translation asks for more than a correct translation: the output must use the exact terms a glossary prescribes. The standard recipe, fine-tuning on glossary-annotated translation pairs, hides an inefficiency: for most examples the glossary prescribes exactly what the model would have produced anyway, so they teach nothing about following a glossary. We therefore keep only the examples where the model's own translation contradicts the glossary. In a controlled study at fixed data volume, this selection alone raises term accuracy from 78.7% to 89.9%. The filtered data, built by a two-way synthetic pipeline on open models, is part of the instruction-tuning mixture of our public release SalamandraTA-7b-instruct v3.0, which, used exactly as released and wrapped in a document-level inference pipeline, forms the BSC submission to the WMT26 Terminology Shared Task Track 1. At the official WMT26 evaluation, our system achieves 94.2% term success at 74.6 chrF++, with only two of the twenty-two submissions outperforming it on both metrics. On last year's benchmark, it also surpasses our GRPO-based system, despite being trained solely with ordinary supervised fine-tuning.