Beyond Sharpness: A Flatness Decomposition Framework for Efficient Continual Learning

TL;DR

This paper introduces FLAD, a new optimization framework for continual learning that decomposes sharpness-aware perturbations, focusing on noise components to improve generalization while reducing computational costs.

Contribution

FLAD decomposes sharpness regularization into components, retaining only the noise part, and introduces a scheduling scheme for efficient continual learning.

Findings

FLAD outperforms standard optimizers in diverse settings.

Retaining noise components enhances generalization.

FLAD is computationally efficient and adaptable.

Abstract

Continual Learning (CL) aims to enable models to sequentially learn multiple tasks without forgetting previous knowledge. Recent studies have shown that optimizing towards flatter loss minima can improve model generalization. However, existing sharpness-aware methods for CL suffer from two key limitations: (1) they treat sharpness regularization as a unified signal without distinguishing the contributions of its components. and (2) they introduce substantial computational overhead that impedes practical deployment. To address these challenges, we propose FLAD, a novel optimization framework that decomposes sharpness-aware perturbations into gradient-aligned and stochastic-noise components, and show that retaining only the noise component promotes generalization. We further introduce a lightweight scheduling scheme that enables FLAD to maintain significant performance gains even under constrained training time. FLAD can be seamlessly integrated into various CL paradigms and consistently outperforms standard and sharpness-aware optimizers in diverse experimental settings, demonstrating its effectiveness and practicality in CL.