Learning deep neural networks by iterative linearisation

Adrian Goldwaser, Hong Ge

Keywords: neural tangent kernel, ntk, optimization, feature learning, infinite width network, deep learning optimization

TL;DR: We propose an interpolation between standard gradient descent and linearised training that lets us control and interpret the amount of feature learning throughout training.

Abstract: The excellent real-world performance of deep neural networks has received increasing attention. Despite the capacity to overfit significantly, such large models work better than smaller ones. This phenomenon is often referred to as the scaling law by practitioners. It is of fundamental interest to study why the scaling law exists and how it avoids/controls overfitting. One approach has been looking at infinite width limits of neural networks (e.g., Neural Tangent Kernels, Gaussian Processes); however, in practise, these do not fully explain finite networks as their infinite counterparts do not learn features. Furthermore, the empirical kernel for finite networks (i.e., the inner product of feature vectors), changes significantly during training in contrast to infinite width networks. In this work we derive an iterative linearised training method. We justify iterative lineralisation as an interpolation between finite analogs of the infinite width regime, which do not learn features, and standard gradient descent training which does. We show some preliminary results where iterative linearised training works well, noting in particular how much feature learning is required to achieve comparable performance. We also provide novel insights into the training behaviour of neural networks.