The Distributional View of Knowledge Distillation

[2608.15215] The Distributional View of Knowledge Distillation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2608.15215 (stat) [Submitted on 15 Aug 2026] Title: The Distributional View of Knowledge Distillation Authors: Gordei Verbii , Juho Lee View a PDF of the paper titled The Distributional View of Knowledge Distillation, by Gordei Verbii and 1 other authors View PDF HTML (experimental) Abstract: Token-level knowledge distillation (KD) matches two conditional distributions per position, yet the standard objectives compare them pointwise: a Kullback-Leibler gradient is blind to which wrong token receives probability mass. We develop a distributional view in which the teacher is represented not by a single softened output but by a family of multi-temperature views - marginals of the annealing path of its logits - and the student is trained against a geometry-aware aggregate of these views under an embedding-based ground cost. We formalize the resulting design space (mixtures, log-linear pooling, entropic Wasserstein barycenters, and a debiased Sinkhorn-divergence flagship in hub and path forms), prove an exact collapse result showing log-linear pooling of tempered views is equivalent to a single temperature, and give a multi-marginal Schrodinger-bridge reading that yields falsifiable predictions. On instruction-tuned Pythia pairs, experiments yield three empirical laws: (i) dispersion law - the benefit of multi-temperature aggregation grows monotonically with the effective temperature dispersion of the views, not with their number; (ii) dispersed views unlock the aggregation operator - the barycenter separates from the arithmetic mixture exactly when transport-based aggregation starts to beat averaging; and (iii) two-regime picture governed by the ceiling gap $\Gamma=\mathrm{PPL}_{\mathrm{SFT}}-\mathrm{PPL}_{T}$: when the fine-tuned teacher barely beats a supervised student the gentle transport objective is the best KD loss but no KD beats supervised fine-tuning, whereas at a real ceiling the ranking inverts - and the sign of the fidelity-generalization correlation flips. We argue that "which distillation loss is the best" is not a fixed property of the loss but a function of $\Gamma$. Comments: 11 pages, 4 figures Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:2608.15215 [stat.ML] (or arXiv:2608.15215v1 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2608.15215 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gordei Verbii [ view email ] [v1] Sat, 15 Aug 2026 13:03:31 UTC (1,002 KB) Full-text links: Access Paper: View a PDF of the paper titled The Distributional View of Knowledge Distillation, by Gordei Verbii and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2026-08 Change to browse by: cs cs.LG stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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