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The capacity to generalize to future unseen data stands as one of the utmost crucial attributes of deep neural networks. Sharpness-Aware Minimization (SAM) aims to enhance the generalizability by minimizing worst-case loss using one-step gradient ascent as an approximation. However, as training progresses, the non-linearity of the loss landscape increases, rendering one-step gradient ascent less effective. On the other hand, multi-step gradient ascent will incur higher training cost. In this paper, we introduce a normalized Hessian trace to accurately measure the curvature of loss landscape on both training and test sets. In particular, to counter excessive non-linearity of loss landscape, we propose Curvature Regularized SAM (CR-SAM), integrating the normalized Hessian trace as a SAM regularizer. Additionally, we present an efficient way to compute the trace via finite differences with parallelism. Our theoretical analysis based on PAC-Bayes bounds establishes the regularizer's efficacy in reducing generalization error. Empirical evaluation on CIFAR and ImageNet datasets shows that CR-SAM consistently enhances classification performance for ResNet and Vision Transformer (ViT) models across various datasets. Our code is available at https://github.com/TrustAIoT/CR-SAM.
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Adversarial Robustness is at Odds with Lazy Training
Recent works show that adversarial examples exist for random neural networks [Daniely and Shacham, 2020] and that these examples can be found using a single step of gradient ascent [Bubeck et al., 2021]. In this work, we extend this line of work to the “lazy training” of neural networks – a dominant model in deep learning theory in which neural networks are provably efficiently learnable. We show that over-parametrized neural networks that are guaranteed to generalize well and enjoy strong computational guarantees remain vulnerable to attacks generated using a single step of gradient ascent.
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- Award ID(s):
- 1943251
- PAR ID:
- 10401081
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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