Understanding the Gains from Repeated Self-Distillation

TL;DR

This paper investigates how repeated self-distillation improves model performance, demonstrating significant risk reduction in linear regression and empirical benefits on UCI datasets.

Contribution

It provides a theoretical analysis of multi-step self-distillation, showing potential for large risk reduction, and validates findings with empirical experiments.

Findings

Multi-step self-distillation reduces excess risk by up to a factor of input dimension d.

Empirical results show up to 47% reduction in MSE on UCI regression tasks.

Theoretical analysis confirms significant gains from repeated self-distillation.

Abstract

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose studying the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor as large as $d$, where $d$ is the input dimension. Empirical results on regression tasks from the UCI repository show a reduction in the learnt model's risk (MSE) by up to 47%.