Teacher-Student Learning

Several educational domains rely heavily on diagrams and visual cues, yet most existing tutoring datasets are limited to text-only interactions. This limits the development of AI tutors that can teach in visually grounded ways used by human instructors. Thus, we introduce GeoDial, a multimodal tutoring dataset of over 1.3K teacher-student dialogs in the domain of geometry collected from experienced math teachers, where instructional turns are explicitly grounded in diagram highlights. We propose a scalable annotation protocol that integrates dialog acts, visual highlighting, and feedback, enabling fine-grained supervision of both language and visual tutoring behavior. To illustrate the challenges posed by this setting, we fine-tune several vision-language models on GeoDial and evaluate their ability to generate tutoring utterances and diagram highlights. While supervised fine-tuning substantially improves the quality of generated dialog, it struggles to produce accurate diagram highlights, revealing a key limitation of current methods and highlighting the need for approaches that more effectively integrate visual reasoning with pedagogical interaction.

On-policy distillation (OPD) is a powerful paradigm for model alignment, yet its reliance on teacher logits restricts its application to white-box scenarios. We contend that structured semantic rubrics can serve as a scalable alternative to teacher logits, enabling OPD using only teacher-generated responses. To prove it, we introduce ROPD, a simple yet foundational framework for rubric-based OPD. Specifically, ROPD induces prompt-specific rubrics from teacher-student contrasts, and then utilizes these rubrics to score the student rollouts for on-policy optimization. Empirically, ROPD outperforms the advanced logit-based OPD methods across most scenarios, and achieving up to a 10x gain in sample efficiency. These results position rubric-based OPD as a flexible, black-box-compatible alternative to the prevailing logit-based OPD, offering a simple yet strong baseline for scalable distillation across proprietary and open-source LLMs. Code is available at https://github.com/Peregrine123/ROPD_official.

A recent work shows that Attention Transfer, which transfers only the attention patterns from a pre-trained teacher Vision Transformer (ViT) to a randomly initialized standard student ViT, is sufficient to recover the full benefit of the teacher's pre-trained weights. We revisit this finding on a comprehensive benchmark of 20 teachers from 11 well-known ViT families and reveal that Attention Transfer is not universally effective. While 7 families transfer successfully, 4 consistently fail, falling up to 5.1% below the from-scratch no-transfer baseline. Further results demonstrate that this failure is family-consistent across model sizes, and persists under extended training durations, different transfer datasets, and out-of-distribution evaluations. Controlled analyses then consistently localize the problem to the attention-routing channel, indicating that the key issue is not whether the student can match the teacher's attention patterns, but whether the matched patterns remain functional for the student. Crucially, we identify architectural mismatch between the pre-trained teacher and the standard student as the primary mechanism. By adding only the teacher's native architectural components to the student in a randomly initialized state, we completely reverse the failure for all 4 families. Notably, these components alone do not improve from-scratch training, confirming that they specifically unlock the usability of the teacher's attention. We further systematically show that this failure is not explained by the inadequate choice of transfer loss or by differences in pre-training recipes. Our findings refine the prevailing understanding of attention in ViT representations: attention is sufficient \textit{only} when the student architecture matches the teacher.

When distilling reasoning from large language models (LLMs) into smaller ones, teacher rationales for similar problems often vary wildly in structure and strategy. Like a chef who makes the same dish differently each time, this inconsistency burdens the student with noisy supervision that is hard to internalize. We propose Distillation through Reasoning Path Compression (D-RPC), which constrains the teacher to follow a compact, dynamically maintained bank of reusable high-level reasoning paths. For each training question, D-RPC retrieves the most relevant path and conditions the teacher to follow it, producing rationales that are consistent across similar problems yet diverse enough to cover different problem types. A PAC-Bayes analysis formalizes the resulting trade-off between bank size and coverage: smaller banks reduce supervision entropy but risk coverage gaps, and the generalization bound identifies an optimal intermediate size confirmed by our ablations. Across five math and commonsense reasoning benchmarks with two student models, D-RPC consistently outperforms chain-of-thought distillation, freeform rationale generation, direct distillation, and structured-supervision baselines, while using fewer tokens than template-heavy alternatives.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

Weak-to-strong generalization is a phenomenon in post-training whereby a strong student model, when finetuned solely with feedback from a weaker teacher, can not only surpass the teacher, but can improve upon its own capabilities. Recent work of Burns et al. (2023) demonstrated that this can occur in the setting of frontier language models, and subsequently there has been a flurry of both empirical work trying to exploit this phenomenon, as well as theoretical work attempting to understand it. In this work, we demonstrate that weak-to-strong generalization occurs in standard linear logistic regression, under mild distributional assumptions on the data. In fact, we show that this happens for most student-teacher pairs, suggesting that weak-to-strong generalization is in fact \emph{almost inevitable}, even in this basic setting. Notably, our setting does not require the student to be more expressive or have more model capacity in any way compared to the teacher, which runs contrary to the prevailing theoretical belief that a mismatch in model capacity is a central mechanism to weak-to-strong generalization.

On-policy distillation is an efficient alternative to reinforcement learning, offering dense token-level training signals. However, its reliance on a stronger external teacher has driven recent work on on-policy self-distillation, where the same model serves as both teacher and student under different prompt contexts. Yet, existing self-distillation methods largely reduce learning to KL matching toward the context-augmented teacher model. This approach often suffers from training instability and can degrade reasoning performance over time. Moreover, self-distillation from the same model with prompt augmentation lacks the exploratory diversity provided by a genuine external teacher. To address these limitations, we move beyond fixed-teacher KL matching and propose \textbf{P}reference-\textbf{B}ased \textbf{S}elf-\textbf{D}istillation (\textbf{PBSD}), which revisits on-policy self-distillation through a reward-regularized perspective. Instead of directly matching the teacher distribution, we derive a reward-regularized objective whose analytic optimum is a reward-reweighted teacher distribution, yielding a target policy provably superior to the original teacher under this objective. Practically, PBSD optimizes preference gaps between teacher and student samples while maintaining on-policy student sampling. We support this framework with a statistical analysis of the induced preference-learning problem, formally establishing when on policy self-distillation is preferable to learning from an external teacher in our setting. Experiments on mathematical reasoning and tool-use benchmarks across multiple model scales demonstrate that PBSD consistently achieves the strongest average performance among comparable baselines, showing improved training stability over prior self-distillation baselines while preserving token efficiency.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm for consolidating the capabilities of specialized expert models into a single student model. Despite its empirical success, the conditions under which OPD yields reliable improvement remain poorly understood. In this work, we identify two fundamental bottlenecks that limit effective OPD: insufficient exploration of informative states and unreliable teacher supervision for student rollouts. Building on this insight, we propose Uni-OPD, a unified OPD framework that generalizes across Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), centered on a dual-perspective optimization strategy. Specifically, from the student's perspective, we adopt two data balancing strategies to promote exploration of informative student-generated states during training. From the teacher's perspective, we show that reliable supervision hinges on whether aggregated token-level guidance remains order-consistent with the outcome reward. To this end, we develop an outcome-guided margin calibration mechanism to restore order consistency between correct and incorrect trajectories. We conduct extensive experiments on 5 domains and 16 benchmarks covering diverse settings, including single-teacher and multi-teacher distillation across LLMs and MLLMs, strong-to-weak distillation, and cross-modal distillation. Our results verify the effectiveness and versatility of Uni-OPD and provide practical insights into reliable OPD.

We study example-level private supervised speech classification under a practical release constraint: training may access privileged side information, but the released model must be audio-only. This setting is important because speech systems can often exploit richer side information during development, whereas deployment and release require a lightweight unimodal model with auditable privacy guarantees. Using DP-SGD on the private dataset $D_{\text{priv}}$, we identify a strong-privacy failure mode ($ε\le 1$) on imbalanced tasks, where training may collapse to a near single-class predictor, a phenomenon that overall accuracy can obscure. We therefore emphasize Macro-F1, balanced accuracy, and a simple collapse diagnostic. This failure is especially problematic in our release setting because a collapsed private teacher cannot provide useful supervision for the downstream audio-only student. To address this setting under strong privacy, we propose a two-stage protocol: (i) train a (possibly multimodal) DP teacher on $D_{\text{priv}}$, and (ii) distill an audio-only student on a fixed, recording-disjoint auxiliary dataset $D_{\text{aux}}$ using one-shot offline teacher probability outputs, releasing only the student. The DP guarantee applies only to $D_{\text{priv}}$; we make no DP claim for $D_{\text{aux}}$, and privacy of the released student with respect to $D_{\text{priv}}$ follows by post-processing. We frame this setting as involving four coupled bottlenecks: speech-induced optimization instability under DP-SGD, minority-class erosion under clipping and noise, teacher over-reliance on privileged modalities unavailable at deployment, and train--deploy modality mismatch. We address them with a DP-stabilizing acoustic front-end (DSAF), minibatch-adaptive bounded loss reweighting (AW-DP), privileged-modality dropout, and offline teacher-to-student distillation.

Distilling large reasoning models is essential for making Long-CoT reasoning practical, as full-scale inference remains computationally prohibitive. Existing curation-based approaches select complete reasoning traces post-hoc, overlooking collaboration among heterogeneous teachers and lacking dynamic exploration, which leads to redundant sampling and missed complementary reasoning. We introduce CoRD, a collaborative multi-teacher decoding framework that performs step-wise reasoning synthesis guided by predictive perplexity-based scoring and beam search. This enables heterogeneous LRMs to jointly construct coherent reasoning trajectories while efficiently preserving diverse, high-potential hypotheses. Experiments show that CoRD produces higher-quality reasoning data and achieves near teacher-level student performance with fewer, structured supervision signals, without substantial efficiency overhead. CoRD further generalizes well to out-of-domain and open-ended settings. The dataset and model are available at https://github.com/DISL-Lab/CoRD.

On-policy distillation (OPD) trains a student on its own trajectories under token-level teacher supervision, but existing methods are capped by a single-teacher capability ceiling: when the teacher errs, the student inherits the error. OPD also remains largely unexplored in agentic tasks, where per-step errors compound across long trajectories and destabilize training. We propose MAD-OPD (Multi-Agent Debate-driven On-Policy Distillation), which breaks this ceiling by recasting the distillation teacher as a deliberative collective of teachers that debate over the student's on-policy state; the debate produces an emergent collective intelligence that supplies token-level supervision, with each teacher's contribution weighted by its post-debate confidence. To extend OPD to agentic tasks, we also introduce On-Policy Agentic Distillation (OPAD), which adds step-level sampling to stabilize training under multi-step error compounding. We additionally derive a task-adaptive divergence principle, selecting JSD (Jensen-Shannon divergence) for agentic stability and reverse KL (Kullback-Leibler) divergence for code generation, and verify it both theoretically and empirically. Across six teacher-student configurations (Qwen3 and Qwen3.5; 1.7B-14B students, 8B-32B teachers) and five agentic and code benchmarks, MAD-OPD ranks first across all six configurations; on the 14B+8B$\to$4B setting it lifts the agentic average by $+2.4\%$ and the code average by $+3.7\%$ over the stronger single-teacher OPD.

Layer-aligned distillation and convergence-based early exit represent two predominant computational efficiency paradigms for transformer inference; yet we establish that they exhibit systematic incompatibility under standard deployment conditions for convergence-based early exit. Distillation objectives that align intermediate student layers to teacher representations suppress the representational convergence that early-exit mechanisms exploit, rendering such mechanisms ineffective on distilled models. We introduce LEAP (Layer-wise Exit-Aware Pretraining), an auxiliary training objective that reconciles this incompatibility. LEAP requires no architectural modifications; it augments standard distillation with a single constraint ensuring intermediate layers approximate final-layer representations. LEAP-MiniLM achieves 1.61$\times$ measured wall-clock speedup (batch=1, NVIDIA L4) at $θ$=0.95, with 91.9% of samples exiting by layer 7 and 1.80$\times$ theoretical layer reduction, where standard distilled models achieve zero effective speedup. We validate across sentence similarity (STS-B: 0.760 $\pm$ 0.006) and retrieval benchmarks (BEIR), providing operational guidance including latency measurements, decision thresholds, and deployment criteria.

Gait recognition is an attractive biometric modality for long-range and contact-free identification, but high-performing gait models often rely on deep and computationally expensive architectures that are difficult to deploy in practice. Knowledge distillation (KD) offers a natural way to transfer knowledge from a powerful teacher to an efficient student; however, standard KD is often less effective for part-structured gait models, where supervision is formed from both part-wise classification logits and part-wise retrieval embeddings. In this paper, we propose GaitKD, a distillation framework that decouples gait knowledge transfer into two complementary components: decision-level distillation and boundary-level distillation. Specifically, GaitKD aligns the teacher and student through part-calibrated logit distillation to transfer inter-class decision relations, while preserving the teacher-induced partitioning of the embedding space through an activation-boundary objective instead of direct feature regression. With a simple aligned part-wise design, GaitKD supports heterogeneous teacher-student gait models without introducing additional inference cost. Experimental results across multiple gait recognition benchmarks and teacher-student configurations show consistent improvements over strong gait baselines. Our study demonstrates that the two transfer components are complementary, and boundary-preserving distillation provides more stable performance than direct feature regression. Source code is available at https://github.com/liyiersan/GaitKD/

Subliminal learning describes a student language model inheriting a behavioral bias by fine-tuning on seemingly innocuous data generated by a biased teacher model. Prior work has begun to characterize this phenomenon but leaves open questions about the scope of signals it can transfer, the mechanisms that explain it, and the precision with which a bias can be encoded by seemingly unrelated data. We tackle all three problems by introducing subliminal steering, a variant of subliminal learning in which the teacher's bias is implemented not via a system prompt, as in prior work, but through a steering vector trained to maximize the likelihood of a set of target samples. First, we show that subliminal steering transfers complex multi-word biases, whereas prior work focused on single-word preferences, demonstrating a large scope of subliminally transferrable signals. Second, we provide mechanistic evidence that subliminal learning transfers not only the target behavioral bias, but also the steering vector itself, localized to the layers at which the teacher was steered. Finally, we show that the bias is encoded with surprising precision. We train a new steering vector directly on the subliminally-laden dataset and find that it attains high cosine similarity with the original vector.

In the MNIST auxiliary logit distillation experiment, a student can acquire an unintended teacher trait despite distilling only on no-class logits through a phenomenon called subliminal learning. Under a single-step gradient descent assumption, subliminal learning theory attributes this effect to alignment between the trait and distillation gradients, but does not guarantee that this alignment persists in a multi-step setting. We empirically show that gradient alignment remains weakly but consistently positive throughout training and causally contributes to trait acquisition. We show that a mitigation method called liminal training works by attenuating the alignment and fails to stop trait acquisition in this setup. These results suggest that mitigation methods that operate in this regime may not reliably suppress trait acquisition when the first-order drive dominates.

This position paper argues that knowledge distillation must account for what it loses: student models should be judged not only by retained task scores, but by whether they preserve the teacher capabilities that make those scores reliable. This matters because distillation is increasingly used to turn large teacher models into deployable students, yet headline metrics can obscure losses in the capabilities that make teacher behavior reliable. Conceptually, we show that current evaluation often assumes retained task scores imply retained teacher capabilities. Reframing distillation as a lossy projection exposes this flaw: students may match selected teacher observables without preserving the capabilities that make them reliable. We then synthesize existing evidence into a taxonomy of off-metric distillation losses, showing that such losses are concrete, recurring, and measurable, yet often unaccounted for when studies report what students retain rather than what they lose. To make the position actionable, we propose scenario-specific preservation targets and a Distillation Loss Statement that reports what was preserved, what was lost, and why the remaining losses are acceptable. The goal is not lossless distillation, but accountable distillation.

Wepresent Alice v1, a 14-billion parameter open-source video generation model that achieves state-of-the-art quality through consistency distillation with score regularization (rCM). Contrary to conventional distillation-which trades quality for speed-we demonstrate that rCM-based distillation can exceed teacher model quality. We attribute this to three mechanisms: (1) the score regularization term acts as a mode-seeking objective that concentrates probability mass on high-quality outputs rather than covering the full teacher distribution, (2) our targeted synthetic data pipeline with hard example mining provides training signal specifically for failure modes (physics, hands, faces) that the teacher handles inconsistently, and (3) consistency enforcement acts as implicit regularization, eliminating "lucky path" dependence on specific noise samples. Alice v1 generates 5-second 720p videos at 24fps in 4 denoising steps (~8 seconds on H100), a 7x speedup over the 50-step teacher while improving VBench score from 84.0 (Wan2.2) to 91.2. This surpasses both the teacher and closed-source systems including Veo3 (~90) and Sora2 (~88) on automated benchmarks, with competitive results in human preference studies. We release all model weights, training code, synthetic data pipelines, and evaluation scripts to advance open research in video generation.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule. Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails. Our code is available at https://github.com/kokolerk/TCOD.

Distillation via sampling reasoning traces exposes closed-source frontier models to adversarial third parties who can bypass their guardrails and misappropriate their capabilities. Antidistillation methods aim to address this by poisoning reasoning traces to hinder student model learning while preserving teacher performance. However, current methods overlook detectability, both semantic and syntactic, which erodes trust in the teacher's outputs and signals the defense's presence to adversaries. We address this gap by formulating antidistillation as a Stackelberg game whose constraint set explicitly encodes detectability, and show that perturbing sparingly offers an effective, less detectable alternative to poisoning the full trace. Drawing on mechanistic interpretability, we identify thought anchors, sentences with disproportionate counterfactual influence on model outputs, as a principled sparse target: critical to reasoning yet minimally detectable. We instantiate this in TraceGuard, a training-free, black-box proof-of-concept that locates thought anchors via branching-token detection and poisons them to degrade student distillation while preserving trace coherence.

Industrial surface defect detection often suffers from limited defect samples, severe long-tailed distributions, and difficulties in accurately localizing subtle defects under complex backgrounds. To address these challenges, this paper proposes an unsupervised defect detection method that integrates a Denoising Diffusion Probabilistic Model (DDPM) with an asymmetric teacher-student architecture. First, at the data level, the DDPM is trained solely on normal samples. By introducing constant-variance Gaussian perturbations and Perlin noise-based masks, high-fidelity and physically consistent defect samples along with pixel-level annotations are generated, effectively alleviating the data scarcity problem. Second, at the model level, an asymmetric dual-stream network is constructed. The teacher network provides stable representations of normal features, while the student network reconstructs normal patterns and amplifies discrepancies between normal and anomalous regions. Finally, a joint optimization strategy combining cosine similarity loss and pixel-wise segmentation supervision is adopted to achieve precise localization of subtle defects. Experimental results on the MVTecAD dataset show that the proposed method achieves 98.4% image-level AUROC and 98.3% pixel-level AUROC, significantly outperforming existing unsupervised and mainstream deep learning methods. The proposed approach does not require large amounts of real defect samples and enables accurate and robust industrial defect detection and localization. \keywords{Industrial defect detection \and diffusion models \and data generation \and teacher-student architecture \and pixel-level localization}

Knowledge distillation (KD) transfers capabilities from large language models (LLMs) to smaller students, yet it can fail unpredictably and also underpins model leakage risks. Our analysis revealed several distillation traps: tail noise, off-policy instability, and, most fundamentally, the teacher-student gap, that distort training signals. These traps manifest as overconfident hallucinations, self-correction collapse, and local decoding degradation, causing distillation to fail. Motivated by these findings, we propose a post-hoc calibration method that, to the best of our knowledge, for the first time enables control over a teacher's distillability via reinforcement fine-tuning (RFT). Our objective combines task utility, KL anchor, and across-tokenizer calibration reward. This makes distillability a practical safety lever for foundation models, connecting robust teacher-student transfer with deployment-aware model protection. Experiments across math, knowledge QA, and instruction-following tasks show that students distilled from distillable calibrated teachers outperform SFT and KD baselines, while undistillable calibrated teachers retain their task performance but cause distilled students to collapse, offering a practical knob for both better KD and model IP protection.

Empirical studies of trained models often report a transient regime in which signal is detectable in a finite gradient descent time window before overfitting dominates. We provide an analytically tractable random-matrix model that reproduces this phenomenon for gradient flow in a linear teacher--student setting. In this framework, learning occurs when an isolated eigenvalue separates from a noisy bulk, before eventually disappearing in the overfitting regime. The key ingredient is anisotropy in the input covariance, which induces fast and slow directions in the learning dynamics. In a two-block covariance model, we derive the full time-dependent bulk spectrum of the symmetrized weight matrix through a $2\times 2$ Dyson equation, and we obtain an explicit outlier condition for a rank-one teacher via a rank-two determinant formula. This yields a transient Baik-Ben Arous-Péché (BBP) transition: depending on signal strength and covariance anisotropy, the teacher spike may never emerge, emerge and persist, or emerge only during an intermediate time interval before being reabsorbed into the bulk. We map the corresponding phase diagrams and validate the theory against finite-size simulations. Our results provide a minimal solvable mechanism for early stopping as a transient spectral effect driven by anisotropy and noise.

Recent work on subliminal learning demonstrates that language models can transmit semantic traits through data that is semantically unrelated to those traits. However, it remains unclear whether behavioral traits can transfer in agentic systems, where policies are learned from trajectories rather than static text. In this work, we provide the first empirical evidence that unsafe agent behaviors can transfer subliminally through model distillation across two complementary experimental settings. In our primary setting, we construct a teacher agent exhibiting a strong deletion bias, a tendency to perform destructive file-system actions via an API-style tool interface, and distill it into a student using only trajectories from ostensibly safe tasks, with all explicit deletion keywords rigorously filtered. In our secondary setting, we replicate the threat model in a native Bash environment, replacing API tool calls with shell commands and operationalizing the bias as a preference for issuing chmod as the first permission-related command over semantically equivalent alternatives such as chown or setfacl. Despite full keyword sanitation in both settings, students inherit measurable behavioral biases. In the API setting the student's deletion rate reaches 100% (versus a 5% baseline) under homogeneous distillation; in the Bash setting the student's chmod-first rate reaches 30%-55% (versus a 0%-10% baseline), with the strongest transfer observed in large-to-small distillation. Our results demonstrate that explicit data sanitation is an insufficient defense, and behavioral biases are encoded implicitly in trajectory dynamics regardless of the tool interface.

Large-scale visual learning is increasingly limited by training cost. Existing knowledge distillation methods transfer from a stronger teacher to a weaker student for compression or final-accuracy improvement. We instead investigate distillation to accelerate the training of strong students. We propose a generalizable plug-and-play recipe that freezes a weaker teacher, applies distillation only in early training, and turns it off once the student reaches and surpasses teacher-level performance. For ImageNet and CIFAR classification, this strategy reaches target thresholds much earlier, with up to 4.8 times speedup measured by epochs. We confirm that the method generalizes to other tasks and report 1.7 times epoch speedup for object detection on the COCO dataset, and 2.5 times earlier target-FID crossing for diffusion generation on the CIFAR-10 dataset, measured in steps. These findings validate our method as a universal speedup mechanism for visual learning.

Synthesizing supervised finetuning (SFT) data from language models (LMs) to teach smaller models multilingual tasks has become increasingly common. However, teacher model selection is often ad hoc, typically defaulting to the largest available option, even though such models may have significant capability gaps in non-English languages. This practice can result in poor-quality synthetic data and suboptimal student downstream performance. In this work, we systematically characterize what makes an effective multilingual teacher. We measure intrinsic measures of data quality with extrinsic student model performance in a metric we call Polyglot Score; evaluating 10 LMs across 6 typologically diverse languages, generating over 1.4M SFT examples and training 240 student models. Among the models tested, Gemma 3 27B and Aya Expanse 32B emerge as consistently effective teachers across different student base model families. Further analyses reveal that model scale alone does not significantly predict teacher effectiveness; instead, data qualities such as prompt diversity, length, and response fluency capture over 93.3% of variance in intrinsic data quality and predict student performance. Finally, we provide practical recommendations, including matching the model families of teacher-student pairs and translating from or responding to existing prompts, which can yield improvements for less-resourced languages. We hope that our work advances data-centric research in multilingual synthetic data and LM development.

Chain-of-thought (CoT) distillation transfers reasoning behaviors from a strong teacher to a smaller student, but prior work reports a capacity gap: distillation may fail when the teacher-student capability mismatch is large. We revisit the capacity gap from a practical perspective by re-examining commonly used experimental settings. Notably, we find that CoT distillation often degrades performance compared to the student's pre-distillation baseline, and that some settings used in prior work, while suitable for establishing the capacity gap as a phenomenon, do not reflect realistic deployment scenarios. Complementing prior work that establishes the capacity gap, we evaluate its practical impact under more realistic settings and find that it does not consistently dominate; stronger teachers tend to be preferable when candidate teachers differ substantially in performance. Our results offer practical guidance for selecting teacher-student pairs in CoT distillation.

There have been numerous attempts to distill quadratic attention-based large language models (LLMs) into sub-quadratic linearized architectures. However, despite extensive research, such distilled models often fail to match the performance of their teacher LLMs on various downstream tasks. We set out the goal of lossless distillation, which we define in terms of tolerance-corrected Win-and-Tie rates between student and teacher on sets of tasks. To this end, we introduce an effective distillation pipeline for xLSTM-based students. We propose an additional merging stage, where individually linearized experts are combined into a single model. We show the effectiveness of this pipeline by distilling base and instruction-tuned models from the Llama, Qwen, and Olmo families. In many settings, our xLSTM-based students recover most of the teacher's performance, and even exceed it on some downstream tasks. Our contributions are an important step towards more energy-efficient and cost-effective replacements for transformer-based LLMs.

Data-free knowledge distillation enables model compression without original training data, critical for privacy-sensitive tabular domains. However, existing methods does not perform well on tabular data because they do not explicitly address feature interactions, the fundamental way tabular models encode predictive knowledge. We identify interaction diversity, systematic coverage of feature combinations, as an essential requirement for effective tabular distillation. To operationalize this insight, we propose TabKD, which learns adaptive feature bins aligned with teacher decision boundaries, then generates synthetic queries that maximize pairwise interaction coverage. Across 4 benchmark datasets and 4 teacher architectures, TabKD achieves highest student-teacher agreement in 14 out of 16 configurations, outperforming 5 state-of-the-art baselines. We further show that interaction coverage strongly correlates with distillation quality, validating our core hypothesis. Our work establishes interaction-focused exploration as a principled framework for tabular model extraction.

Test-time training (TTT) adapts large language models (LLMs) during inference using only unlabeled test inputs. Existing methods, however, face two major bottlenecks on hard reasoning tasks: (1) \emph{lack of learnable samples}, as self-generated pseudo-labels on difficult questions are often noisy and yield unstable rewards; and (2) \emph{inefficient exploration}, as performance gains depend on repeatedly sampling many rollouts without explicit diagnosis of why previous attempts fail. We propose \textbf{TTSR} (\textbf{T}est-\textbf{T}ime \textbf{S}elf-\textbf{R}eflection), a self-evolving framework based on a \emph{reflect-then-synthesize} paradigm. A single pretrained model alternates between a \textit{Student} role and a \textit{Teacher} role: the Student solves test questions and updates, while the Teacher analyzes failed trajectories and synthesizes targeted variant questions closer to the Student's capability frontier. TTSR further maintains a cross-iteration \textit{weakness memory} and compiles persistent weaknesses into a lightweight \textit{strategy note} prepended to subsequent Student inputs, so diagnostic knowledge can guide exploration and gradually fade as weaknesses are resolved. Experiments on challenging mathematical reasoning benchmarks show consistent test-time improvements, strong cross-backbone generalization, and transfer to general-domain reasoning tasks.

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.