Sharpness-Aware Minimization (SAM) has substantially improved the generalization of neural networks under various settings. Despite the success, its effectiveness remains poorly understood. In this work, we discover an intriguing phenomenon in the training dynamics of SAM, shedding lights on understanding its implicit bias towards flatter minima over Stochastic Gradient Descent (SGD). We conjecture that the optimization method chosen in the late phase is more crucial in shaping the final solution's properties. Based on this viewpoint, we extend our findings from SAM to Adversarial Training. We provide source code in supplementary materials and will release checkpoints in future. Recently, it has been observed that the generalization of neural networks is closely tied to the sharpness of the loss landscape (Keskar et al., 2017; Zhang et al., 2017; Neyshabur et al., 2017; Jiang et al., 2020). This has led to the development of many gradient-based optimization algorithms that explicitly/implicitly regularize the sharpness of solutions. In particular, Foret et al. (2021) proposed Sharpness-Aware Minimization (SAM), which has substantially improved the generalization and robustness (Zhang et al., 2024) of neural networks across many tasks, including computer vision (Foret et al., 2021; Chen et al., 2022; Kaddour et al., 2022) and natural language processing (Bahri et al., 2022). Despite the empirical success of SAM, its effectiveness is not yet fully understood. Andriushchenko & Flammarion (2022) has shown that existing theoretical justifications based on PAC-Bayes generalization bounds (Foret et al., 2021; Wu et al., 2020a) are incomplete in explaining the superior performance of SAM.

The Lookahead optimizer improves the training stability of deep neural networks by having a set of fast weights that "look ahead" to guide the descent direction. Here, we combine this idea with sharpness-aware minimization (SAM) to stabilize its multi-step variant and improve the loss-sharpness trade-off. We propose Lookbehind, which computes $k$ gradient ascent steps ("looking behind") at each iteration and combine the gradients to bias the descent step toward flatter minima. We apply Lookbehind on top of two popular sharpness-aware training methods -- SAM and adaptive SAM (ASAM) -- and show that our approach leads to a myriad of benefits across a variety of tasks and training regimes. Particularly, we show increased generalization performance, greater robustness against noisy weights, and higher tolerance to catastrophic forgetting in lifelong learning settings.

Sharpness-Aware Minimization (SAM) and adaptive sharpness-aware minimization (ASAM) aim to improve the model generalization. And in this project, we proposed three experiments to valid their generalization from the sharpness aware perspective. And our experiments show that sharpness aware-based optimization techniques could help to provide models with strong generalization ability. Our experiments also show that ASAM could improve the generalization performance on un-normalized data, but further research is needed to confirm this.

Models trained in federated settings often suffer from degraded performances and fail at generalizing, especially when facing heterogeneous scenarios. In this work, we investigate such behavior through the lens of geometry of the loss and Hessian eigenspectrum, linking the model's lack of generalization capacity to the sharpness of the solution. Motivated by prior studies connecting the sharpness of the loss surface and the generalization gap, we show that i) training clients locally with Sharpness-Aware Minimization (SAM) or its adaptive version (ASAM) and ii) averaging stochastic weights (SWA) on the server-side can substantially improve generalization in Federated Learning and help bridging the gap with centralized models. By seeking parameters in neighborhoods having uniform low loss, the model converges towards flatter minima and its generalization significantly improves in both homogeneous and heterogeneous scenarios. Empirical results demonstrate the effectiveness of those optimizers across a variety of benchmark vision datasets (e.g.

Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a drawback in sensitivity to parameter re-scaling which leaves the loss unaffected, leading to weakening of the connection between sharpness and generalization gap. In this paper, we introduce the concept of adaptive sharpness which is scale-invariant and propose the corresponding generalization bound. We suggest a novel learning method, adaptive sharpness-aware minimization (ASAM), utilizing the proposed generalization bound. Experimental results in various benchmark datasets show that ASAM contributes to significant improvement of model generalization performance.