Black-Box Knowledge Distillation

Reasoning distillation is widely used to transfer the reasoning capabilities of large language models to smaller students through teacher-generated supervision. In the black-box setting, however, teachers may expose only final answers and brief solutions, leaving intermediate calculations and validity conditions unavailable and thus limiting the reasoning supervision available for distillation. We propose Stepwise Querying, which elicits step-specific explanations without requiring access to the teacher's internal chain-of-thought (CoT) traces. Independent queries to the same teacher request intermediate derivations, validity checks, and corrections for individual steps, the assembled solutions are then used for standard supervised fine-tuning. Across two teachers, two students, and four mathematics and code benchmarks, our method achieves the highest score in 14 of 16 comparisons with three baselines. We further introduce Stepwise Explanation Information Gain (SEIG), a diagnostic based on the log-ratio of a frozen student's probabilities of correct step completion under stepwise and global explanations. Analyses on GSM8K show that incorrect-answer trajectories can remain useful when they preserve valid intermediate reasoning, while further decomposition yields limited additional gains.

Frontier language-model agents excel at complex tasks, but high inference costs make transferring their capabilities to smaller models essential. Traditional knowledge distillation achieves this through parameter updates, requiring access to the student's weights and additional training compute while encoding the transferred knowledge implicitly in the parameters. We introduce D-Skill, a framework that treats the teacher as a black box and distills its behavioral advantage into an interpretable natural-language skill by analyzing paired rollouts and identifying behavioral divergences and agreements. The resulting lessons are consolidated offline, with any compatible skill-update backend, into a skill document that is provided to the student at inference time. D-Skill constructs the skill entirely offline from fixed trajectories, without labels, further environment interaction, or weight updates after rollout collection. Across SpreadsheetBench-Verified, ALFWorld, and chess puzzles spanning multiple teacher-student pairs, D-Skill closes 75%-95% of the teacher-student gap without touching model weights. After a single offline pass over the paired traces, D-Skill outperforms one-epoch SFT baselines and remains competitive with multi-epoch SFT. Under the same model family, the resulting student also incurs 5.7x-8.3x lower inference cost per task than the teacher. Our results demonstrate that natural-language skill distillation offers a performant, interpretable, and efficient alternative to weight-based capability transfer.

Frontier web agents using closed models have high inference and computational costs. Smaller open models can be an alternative, but to be performant, they require training supervision from a human or teacher model. Token-level teacher distillation is not an option for closed teachers as it needs access to the model's logits. The standard approach is to imitate teacher demonstrations offline, but it trains the student on states it has never visited, and in a style it does not write in. We introduce WebKD, where the teacher is the editor of the student's failures. Given a failed episode, the teacher finds the first point of mistake, and rewrites the student's reasoning traces, harness states, and actions from that point onward. The editing reveals that the teacher's corrections can be more surprising to the student than the student's own text. WebKD instead aims to edit minimally. In the data space, the teacher writes each correction in the student's style. In the objective space, the reasoning is weighted by its contribution to the action. A role-asymmetric KL anchor allows the corrected action to move freely while keeping the reasoning near the student's prior. On the TimeWarp benchmark, WebKD students gain about 5.5-10.7 pp over behavior cloning, outcome-reward RL, and teacher editing baselines. The performance transfers to unseen versions and to the live web in the OnlineMind2Web benchmark. WebKD opens a new way of distilling black-box models to improve the capabilities of open-weight web agents.

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

Knowledge distillation (KD) is a well-known technique to effectively compress a large network (teacher) to a smaller network (student) with little sacrifice in performance. However, most KD methods require a large training set and internal access to the teacher, which are rarely available due to various restrictions. These challenges have originated a more practical setting known as black-box few-shot KD, where the student is trained with few images and a black-box teacher. Recent approaches typically generate additional synthetic images but lack an active strategy to promote their diversity, a crucial factor for student learning. To address these problems, we propose a novel training scheme for generative adversarial networks, where we adaptively select high-confidence images under the teacher's supervision and introduce them to the adversarial learning on-the-fly. Our approach helps expand and improve the diversity of the distillation set, significantly boosting student accuracy. Through extensive experiments, we achieve state-of-the-art results among other few-shot KD methods on seven image datasets. The code is available at https://github.com/votrinhan88/divbfkd.

Knowledge distillation (KD) represents a vital mechanism to transfer expertise from complex teacher networks to efficient student models. However, in decentralized or secure AI ecosystems, privacy regulations and proprietary interests often restrict access to the teacher's interface and original datasets. These constraints define a challenging black-box data-free KD scenario where only top-1 predictions and no training data are available. While recent approaches utilize synthetic data, they still face limitations in data diversity and distillation signals. We propose Diverse Image Priors Knowledge Distillation (DIP-KD), a framework that addresses these challenges through a three-phase collaborative pipeline: (1) Synthesis of image priors to capture diverse visual patterns and semantics; (2) Contrast to enhance the collective distinction between synthetic samples via contrastive learning; and (3) Distillation via a novel primer student that enables soft-probability KD. Our evaluation across 12 benchmarks shows that DIP-KD achieves state-of-the-art performance, with ablations confirming data diversity as critical for knowledge acquisition in restricted AI environments.

Every call to an LLM classification endpoint produces a labeled input-output pair already retained in production logs. These pairs constitute a free, growing training set: a lightweight surrogate trained on them can absorb a significant portion of future traffic at near-zero marginal inference cost. The open questions are when the surrogate is reliable enough to deploy, what it handles versus defers, and how that boundary evolves as data accumulates. We introduce TRACER (Trace-based Adaptive Cost-Efficient Routing), an open-source system that trains ML surrogates on an LLM's own production traces and governs deployment through a parity gate: the surrogate is activated only when its agreement with the LLM exceeds a user-specified threshold α. To make the routing boundary transparent, TRACER generates interpretability artifacts describing which input regions the surrogate handles, where it plateaus, and why it defers. On a 77-class intent benchmark with a Sonnet 4.6 teacher, TRACER achieves 83-100% surrogate coverage depending on the quality target α; on a 150-class benchmark, the surrogate fully replaces the teacher. On a natural language inference task, the parity gate correctly refuses deployment because the embedding representation cannot support reliable separation. The system is available as open-source software.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.

Knowledge distillation (KD) methods are pivotal in compressing large pre-trained language models into smaller models, ensuring computational efficiency without significantly dropping performance. Traditional KD techniques assume homogeneity in modalities between the teacher (source) and the student (target) models. On the other hand, existing multimodal knowledge distillation methods require modality-specific pre-training of the teacher model, which is computationally infeasible in most cases. In this paper, we introduce ARMADA, an efficient cross-modal knowledge distillation framework designed to transfer knowledge from large vision-language models, including black-box models, to language-only models. Unlike existing KD techniques that rely on the internal structures of multimodal teachers or require computationally expensive pre-training, ARMADA leverages novel alignment techniques to distil knowledge without altering the teacher model, ensuring efficiency and scalability. We empirically validate ARMADA on twelve natural language understanding, eight complex generative reasoning and five instruction-tuning tasks, demonstrating consistent performance improvements in large models such as DeBERTa-v2-1.4B, OPT-1.3B, LLaMA-{3B, 7B, 8B}. ARMADA achieves up to 3.4% improvement on language understanding tasks and 2.6% boost in generative reasoning, all without requiring expensive multimodal pre-training or fine-tuning of the teacher model. Our findings challenge conventional knowledge distillation paradigms by demonstrating that even vision-language models, despite lacking direct textual understanding, can significantly enhance language models when distilled appropriately.

Knowledge distillation transfers reasoning capabilities from large teachers to efficient students. However, token-level on-policy distillation (OPD) constrains student exploration and requires teacher token probabilities, precluding distillation from black-box teachers that provide only text outputs. We introduce On-policy Verbal Distillation (OVD), a framework that uses verbal scores from black-box teachers to rank student-generated sub-trajectories, retaining high-scoring ones and replacing low-scoring ones with teacher-generated continuations. We analyze when ranking induced by verbal scores can guide distribution approximation: under a density-ratio calibration condition on acceptance probabilities and bounded teacher-replacement error, we bound the approximation error between the resulting mixed trajectory distribution and a teacher-preferred target. On Web Q&A, OVD achieves 41.09% average EM with teacher feedback at inference, exceeding the strongest evaluated baseline by 5.89 percentage points. On AMC23, OVD-FR improves accuracy over RLVR by 10.0 percentage points (52.5% to 62.5%) after 600 training steps on 128 problems. Further experiments suggest that retaining student-generated prefixes helps preserve exploration and mitigate trajectory-level entropy collapse. OVD also improves training efficiency: resampling selected suffixes rather than entire responses reduces mean per-step training time by 10.2% in the 128-problem setting. Project page: https://menik1126.github.io/ovd-project-page/.