Sharpness-Aware Minimization for Efficiently Improving Generalization (2010.01412v3)

Abstract: In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at \url{https://github.com/google-research/sam}.

• The paper introduces SAM, which reformulates neural network training as a min-max problem to minimize both loss and sharpness, significantly improving generalization.
• The authors validate SAM empirically on datasets like CIFAR-10/100 and ImageNet, achieving state-of-the-art improvements and robustness to label noise.
• By open-sourcing the SAM implementation, the paper paves the way for future research on optimizing loss landscapes in deep learning models.

Sharpness-Aware Minimization for Efficiently Improving Generalization

The paper "Sharpness-Aware Minimization for Efficiently Improving Generalization" introduces a novel method called Sharpness-Aware Minimization (SAM) that targets the optimization of neural network training by reducing the sharpness of the loss landscape in order to enhance generalization. This approach is motivated by the understanding that simply minimizing the training loss does not guarantee optimal generalization, especially in heavily overparameterized models. SAM aims to address this by simultaneously minimizing both the loss value and the sharpness of the loss function, resulting in improved performance across various models and datasets.

Key Contributions

1. Introduction of SAM: The primary contribution is the development of SAM, which seeks model parameters that lie in neighborhoods having uniformly low loss values. This is formulated as a min-max optimization problem, which can be efficiently addressed using gradient descent approaches.
2. Empirical Validation: The paper presents robust empirical evidence demonstrating that SAM improves generalization performance across a variety of widely used computer vision datasets and models. Noteworthy improvements are observed in state-of-the-art models on CIFAR-10, CIFAR-100, ImageNet, and other fine-tuning tasks.
3. Robustness to Label Noise: SAM is shown to inherently provide robustness against label noise, matching or surpassing the performance of specialized procedures designed for learning with noisy labels.
4. m-sharpness Concept: Emphasizes a new notion of sharpness, termed m-sharpness, which is crucial in understanding the method's effectiveness and the deeper connection between loss surface geometry and generalization.
5. Open Source Implementation: The authors have also open-sourced the SAM implementation, facilitating its adoption and further research within the community.

Mathematical Formulation

SAM reformulates the objective function to incorporate both the loss and its sharpness, leading to an optimization problem:

$$\min_{\boldsymbol{w}} \max_{\|\boldsymbol{\epsilon}\|_p \leq \rho} L_\mathcal{S}(\boldsymbol{w} + \boldsymbol{\epsilon})$$

Here, $\rho$ is the neighborhood size, and $p$ specifies the norm. Efficient computation of the gradient in this min-max setting is achieved through approximation and gradient descent.

Numerical Results

The numerical results across several datasets and architectures are compelling. For instance:

• On CIFAR-100, using PyramidNet with ShakeDrop regularization, SAM achieved a test error of 10.3%, a state-of-the-art result.
• For ImageNet, ResNet-152 combined with SAM showed significant improvement, reducing the top-1 error rate from 20.3% to 18.4% when trained for 400 epochs.
• In scenarios with label noise, a model trained with SAM demonstrates robustness comparable to specialized noisy label methods, evidencing the versatility and applicability of SAM beyond standard settings.

Practical and Theoretical Implications

Practical Implications:

• Enhanced Model Performance: SAM offers a straightforward yet powerful method for improving model generalization, making it suitable for a range of applications in computer vision and potentially other domains.
• Robustness to Noisy Data: The intrinsic robustness to label noise suggests SAM's utility in real-world settings where data imperfections are common.

Theoretical Implications:

• Generalization Bound: The introduction of m-sharpness enriches the theoretical landscape for understanding generalization. This concept can refine generalization bounds by considering local sharpness rather than global measures.
• Future Research Directions: The promising results and insights from SAM open up new avenues for exploring loss landscape properties and their impact on model performance, particularly through metrics like m-sharpness and adaptations of SAM to other optimization problems.

Speculation on Future Developments in AI

The introduction of SAM is likely to inspire further research into optimization techniques that go beyond traditional loss minimization. Future developments may focus on:

• Adaptive Sharpness Minimization: Dynamic adjustment of the neighborhood size $\rho$ during training to further refine generalization capabilities.
• Cross-Domain Applications: Extending SAM to natural language processing, reinforcement learning, and other AI fields to test its universality and effectiveness across different problem spaces.
• Hybrid Methods: Combining SAM with other regularization techniques or architectural innovations to multiply its benefits.

In sum, Sharpness-Aware Minimization represents a significant advancement in the optimization of deep learning models. By efficiently addressing both the loss value and sharpness, SAM not only achieves superior performance but also provides a robust and generalizable framework for future AI research and applications.