Avoiding spurious sharpness minimization broadens applicability of SAM

TL;DR

This paper introduces Functional-SAM, a curvature regularization method that avoids spurious minimization by focusing on function statistics, improving generalization in both vision and NLP tasks, especially for large language models.

Contribution

We propose Functional-SAM, an alternative to SAM that targets curvature regularization through function statistics, enhancing applicability across domains including NLP and large language models.

Findings

Functional-SAM outperforms SAM and AdamW baselines in various training settings.

Preconditioning SAM perturbation further improves performance.

Our methods are effective at billion-parameter scale models.

Abstract

Curvature regularization techniques like Sharpness Aware Minimization (SAM) have shown great promise in improving generalization on vision tasks. However, we find that SAM performs poorly in domains like natural language processing (NLP), often degrading performance -- even with twice the compute budget. We investigate the discrepancy across domains and find that in the NLP setting, SAM is dominated by regularization of the logit statistics -- instead of improving the geometry of the function itself. We use this observation to develop an alternative algorithm we call Functional-SAM, which regularizes curvature only through modification of the statistics of the overall function implemented by the neural network, and avoids spurious minimization through logit manipulation. Furthermore, we argue that preconditioning the SAM perturbation also prevents spurious minimization, and when combined with Functional-SAM, it gives further improvements. Our proposed algorithms show improved performance over AdamW and SAM baselines when trained for an equal number of steps, in both fixed-length and Chinchilla-style training settings, at various model scales (including billion-parameter scale). On the whole, our work highlights the importance of more precise characterizations of sharpness in broadening the applicability of curvature regularization to large language models (LLMs).