FAM: Relative Flatness Aware Minimization

TL;DR

This paper introduces FAM, a new regularizer based on relative flatness that improves neural network generalization by efficiently leveraging Hessian information of a single layer, addressing theoretical and practical limitations of previous flatness measures.

Contribution

It proposes a theoretically grounded, computationally efficient flatness regularizer that works with arbitrary loss functions and large neural networks, improving generalization.

Findings

FAM improves generalization across various models and tasks.

The method requires only Hessian computation of a single layer.

FAM outperforms traditional flatness-based approaches in empirical evaluations.

Abstract

Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more recent successful sharpness-aware optimization techniques. Their widespread adoption in practice, though, is dubious because of the lack of theoretically grounded connection between flatness and generalization, in particular in light of the reparameterization curse - certain reparameterizations of a neural network change most flatness measures but do not change generalization. Recent theoretical work suggests that a particular relative flatness measure can be connected to generalization and solves the reparameterization curse. In this paper, we derive a regularizer based on this relative flatness that is easy to compute, fast, efficient, and works with arbitrary loss functions. It requires computing the Hessian only of a single layer of the network, which makes it applicable to large neural networks, and with it avoids an expensive mapping of the loss surface in the vicinity of the model. In an extensive empirical evaluation we show that this relative flatness aware minimization (FAM) improves generalization in a multitude of applications and models, both in finetuning and standard training. We make the code available at github.