Understanding Sparse Feature Updates in Deep Networks using Iterative Linearisation

TL;DR

This paper introduces an iterative linearisation method to empirically study feature updates in deep networks, revealing that less frequent feature learning can suffice for good performance and challenging the NTK theory.

Contribution

It proposes a novel iterative linearisation approach to control and analyze feature updates, bridging finite and infinite network regimes, and providing evidence against NTK kernel constancy during training.

Findings

Iterative linearisation performs comparably to standard training.

Less frequent feature learning can achieve similar performance.

Empirical evidence shows NTK kernel changes during training.

Abstract

Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and their corresponding kernels. However, these theoretical tools cannot fully explain finite networks as the empirical kernel changes significantly during gradient-descent-based training in contrast to infinite networks. In this work, we derive an iterative linearised training method as a novel empirical tool to further investigate this distinction, allowing us to control for sparse (i.e. infrequent) feature updates and quantify the frequency of feature learning needed to achieve comparable performance. We justify iterative linearisation as an interpolation between a finite analog of the infinite width regime, which does not learn features, and standard gradient descent training, which does. Informally, we also show that it is analogous to a damped version of the Gauss-Newton algorithm -- a second-order method. We show that in a variety of cases, iterative linearised training surprisingly performs on par with standard training, noting in particular how much less frequent feature learning is required to achieve comparable performance. We also show that feature learning is essential for good performance. Since such feature learning inevitably causes changes in the NTK kernel, we provide direct negative evidence for the NTK theory, which states the NTK kernel remains constant during training.