Abstract

Classical distillation methods transfer representations from a “teacher” neural network to a “student” network by matching their output activations. Recent methods also match their Jacobians, or the gradient of output activations with the inpu However, this involves making some ad hoc decisions, in particular, the choice of the loss functi 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 distilla tion. We then show experimentally on standard image datasets that Jacobian-based penalties improve distillation, robustness to noisy inputs, and transfer learning.