A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions

2026-09-27

AI Summary

This work addresses the long-standing absence of a unified statistical perspective on knowledge distillation, which has frequently been perceived as an engineering heuristic. We propose a unifying framework grounded in Bayesian inference that formalizes teacher model predictions as prior information, thereby enabling principled uncertainty quantification. This framework not only bridges classical distillation methods with their extensions to large language models but also integrates seamlessly with modern generative systems. Furthermore, we provide a conceptual roadmap and identify key open problems, establishing a systematic foundation for deepening the theoretical understanding of distillation mechanisms.

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.

Problem

• Knowledge Distillation
• Statistical Perspective
• Bayesian Formulation
• Uncertainty Quantification
• Large Language Models

Innovation

• Knowledge Distillation
• Bayesian Formulation
• Uncertainty Quantification
• Large Language Models
• Statistical Perspective