Exact, Tractable Gauss-Newton Optimization in Deep Reversible Architectures Reveal Poor Generalization

TL;DR

This paper demonstrates that exact Gauss-Newton optimization in deep reversible architectures leads to poor generalization, with models overfitting mini-batches and not developing transferable features, especially in the lazy training regime.

Contribution

It introduces a tractable form of exact Gauss-Newton updates for deep reversible architectures and investigates their training and generalization behaviors.

Findings

Exact GN updates are tractable in deep reversible architectures.

GN optimizer exhibits poor generalization, overfitting mini-batches.

Training occurs in the lazy regime with minimal NTK change.

Abstract

Second-order optimization has been shown to accelerate the training of deep neural networks in many applications, often yielding faster progress per iteration on the training loss compared to first-order optimizers. However, the generalization properties of second-order methods are still being debated. Theoretical investigations have proved difficult to carry out outside the tractable settings of heavily simplified model classes -- thus, the relevance of existing theories to practical deep learning applications remains unclear. Similarly, empirical studies in large-scale models and real datasets are significantly confounded by the necessity to approximate second-order updates in practice. It is often unclear whether the observed generalization behaviour arises specifically from the second-order nature of the parameter updates, or instead reflects the specific structured (e.g.\ Kronecker) approximations used or any damping-based interpolation towards first-order updates. Here, we show for the first time that exact Gauss-Newton (GN) updates take on a tractable form in a class of deep reversible architectures that are sufficiently expressive to be meaningfully applied to common benchmark datasets. We exploit this novel setting to study the training and generalization properties of the GN optimizer. We find that exact GN generalizes poorly. In the mini-batch training setting, this manifests as rapidly saturating progress even on the \emph{training} loss, with parameter updates found to overfit each mini-batchatch without producing the features that would support generalization to other mini-batches. We show that our experiments run in the ``lazy'' regime, in which the neural tangent kernel (NTK) changes very little during the course of training. This behaviour is associated with having no significant changes in neural representations, explaining the lack of generalization.