Even your Teacher Needs Guidance: Ground-Truth Targets Dampen Regularization Imposed by Self-Distillation

TL;DR

This paper provides a theoretical analysis of self-distillation in kernel regression, demonstrating how incorporating ground-truth targets influences regularization and offering practical methods to optimize distillation parameters.

Contribution

It introduces the first theoretical framework for weighted ground-truth targets in self-distillation and derives closed-form solutions for optimal weighting, reducing computational costs.

Findings

Infinite distillation amplifies regularization effects.

Optimal weighting parameters can be efficiently estimated.

Ground-truth targets significantly impact regularization in self-distillation.

Abstract

Knowledge distillation is classically a procedure where a neural network is trained on the output of another network along with the original targets in order to transfer knowledge between the architectures. The special case of self-distillation, where the network architectures are identical, has been observed to improve generalization accuracy. In this paper, we consider an iterative variant of self-distillation in a kernel regression setting, in which successive steps incorporate both model outputs and the ground-truth targets. This allows us to provide the first theoretical results on the importance of using the weighted ground-truth targets in self-distillation. Our focus is on fitting nonlinear functions to training data with a weighted mean square error objective function suitable for distillation, subject to $\ell_2$ regularization of the model parameters. We show that any such function obtained with self-distillation can be calculated directly as a function of the initial fit, and that infinite distillation steps yields the same optimization problem as the original with amplified regularization. Furthermore, we provide a closed form solution for the optimal choice of weighting parameter at each step, and show how to efficiently estimate this weighting parameter for deep learning and significantly reduce the computational requirements compared to a grid search.