Knowledge Transfer with Jacobian Matching

TL;DR

This paper introduces a principled approach to Jacobian matching for neural network distillation, linking it to input noise methods, and demonstrates its benefits for transfer learning and robustness.

Contribution

It establishes an equivalence between Jacobian matching and input noise-based distillation, deriving suitable loss functions and applying this to improve transfer learning.

Findings

Jacobian matching improves distillation performance

Enhances robustness to noisy inputs

Benefits transfer learning tasks

Abstract

Classical distillation methods transfer representations from a "teacher" neural network to a "student" network by matching their output activations. Recent methods also match the Jacobians, or the gradient of output activations with the input. However, this involves making some ad hoc decisions, in particular, the choice of the loss function. In this paper, we first establish an equivalence between Jacobian matching and distillation with input noise, from which we derive appropriate loss functions for Jacobian matching. We then rely on this analysis to apply Jacobian matching to transfer learning by establishing equivalence of a recent transfer learning procedure to distillation. We then show experimentally on standard image datasets that Jacobian-based penalties improve distillation, robustness to noisy inputs, and transfer learning.