ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks (2102.11600v3)

Abstract: 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.

• The paper introduces adaptive sharpness-aware minimization to achieve scale-invariant learning and address SAM's re-scaling limitations.
• It incorporates weight normalization to adjust optimization regions, ensuring a robust link between loss landscape sharpness and generalization gap.
• Empirical evaluations on datasets like CIFAR and ImageNet show that ASAM outperforms traditional methods in accuracy and hyperparameter stability.

Overview of ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks

The research paper "ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks" introduces an innovative approach aimed at enhancing the generalization capacity of deep neural networks (DNNs). The paper addresses a critical issue observed in prevailing learning algorithms like Sharpness-Aware Minimization (SAM), which is the sensitivity to parameter re-scaling, compromising the relationship between sharpness and the generalization gap.

Motivation and Background

Conventionally, the sharpness of the loss landscape has served as an effective measure for estimating the generalization gap, demonstrating state-of-the-art performance in various image classification tasks. SAM, rooted in PAC-Bayesian generalization theories, seeks to minimize the sharpness of the loss landscape to infer strong generalization bounds. However, a fundamental drawback arises from SAM's scale-dependent sharpness measure, which leads to performance deterioration when model parameters are re-scaled without affecting the loss function.

The scale-dependency issue notably impairs the correlation between sharpness and the generalization gap, challenging the utility of SAM when applied to scalable or re-parametrized neural network models. Previous attempts to mitigate this issue have primarily focused on proposing generalization measures without integrating them into an effective learning algorithm.

Introduction of Adaptive Sharpness

In light of these limitations, the authors introduce adaptive sharpness, a scale-invariant notion ensuring robust generalization. This new concept leverages a normalization operator that counteracts the effect of any scaling operator, maintaining the sharpness value irrespective of parameter scaling. The adaptive sharpness consequently shows a stronger correlation with the generalization gap than conventional sharpness formulations.

Theoretical Developments and ASAM Algorithm

The paper proposes an adaptive sharpness-aware minimization (ASAM) learning algorithm, which adjusts the maximization regions in alignment with parameter scaling, thereby offering a robust solution to the scale-dependency problem identified in SAM. The authors present a maximization approach that uses this scale-invariant sharpness measure to derive a generalization bound, superior to its predecessors, by correlating closely with the actual generalization gap.

Formulated as a minimax optimization problem, ASAM seeks to minimize the generalization error upper bound through adaptive sharpness. The optimization steps are creatively modified from SAM to incorporate weight normalization and adapt to scaled parameter spaces, ensuring consistent performance improvements.

Empirical Results and Comparisons

Empirical evaluations on a variety of standard benchmarks like CIFAR-10, CIFAR-100, ImageNet, and IWSLT’14 DE-EN datasets reveal the consistent outperformance of ASAM over SGD and SAM. ASAM's ability to effectively generalize across unseen data is illustrated through superior accuracy and reduced sensitivity to hyperparameter tuning.

Importantly, experiments demonstrate that ASAM's generalization performance remains stable across different normalization strategies and p-norm settings, validating the theoretical implications of adaptive sharpness. It also exhibits robustness against label noise, further cementing its applicability to real-world scenarios where data quality cannot always be guaranteed.

Implications and Future Directions

The introduction of adaptive sharpness opens new avenues in the landscape of generalization measurement and learning algorithm design. By resolving the scale-dependency dilemma, ASAM sets a precedent for developing learning frameworks that can leverage intrinsic neural network properties for enhanced generalization.

Looking ahead, future research could explore more sophisticated normalization techniques that could enrich adaptive sharpness's alignment with generalization measures and learning dynamics. Additionally, the principles underpinning adaptive sharpness could be extended to other domains, potentially leading to breakthroughs in unsupervised learning and transfer learning paradigms, where generalized learning capabilities are even more critical.

In essence, this work not only establishes a state-of-the-art methodology but also paves the way for future innovations in the pursuit of durable and scalable neural network architectures.