A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions
Abstract
Knowledge Distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient ``student'' counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation of KD that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual roadmap and identifies critical open problems for the future of the field.
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BibTeX
@misc{fang2026statistical,
title = {{A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions}},
author = {Luyang Fang and Haoran Lu and Jiazhang Cai and Tao Wang and Huimin Cheng and Wenxuan Zhong and Ping Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33727},
eprint = {2609.33727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33727},
}
RIS
TY - UNPB
TI - A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions
AU - Luyang Fang
AU - Haoran Lu
AU - Jiazhang Cai
AU - Tao Wang
AU - Huimin Cheng
AU - Wenxuan Zhong
AU - Ping Ma
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33727
UR - https://arxiv.org/abs/2609.33727
AB - Knowledge Distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient ``student'' counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation of KD that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual roadmap and identifies critical open problems for the future of the field.
ER -