MMA Training: Direct Input Space Margin Maximization through Adversarial Training (1812.02637v4)

Abstract: We study adversarial robustness of neural networks from a margin maximization perspective, where margins are defined as the distances from inputs to a classifier's decision boundary. Our study shows that maximizing margins can be achieved by minimizing the adversarial loss on the decision boundary at the "shortest successful perturbation", demonstrating a close connection between adversarial losses and the margins. We propose Max-Margin Adversarial (MMA) training to directly maximize the margins to achieve adversarial robustness. Instead of adversarial training with a fixed $\epsilon$, MMA offers an improvement by enabling adaptive selection of the "correct" $\epsilon$ as the margin individually for each datapoint. In addition, we rigorously analyze adversarial training with the perspective of margin maximization, and provide an alternative interpretation for adversarial training, maximizing either a lower or an upper bound of the margins. Our experiments empirically confirm our theory and demonstrate MMA training's efficacy on the MNIST and CIFAR10 datasets w.r.t. $\ell_\infty$ and $\ell_2$ robustness. Code and models are available at https://github.com/BorealisAI/mma_training.

• The paper introduces MMA training that dynamically adjusts perturbation magnitude to maximize individual sample margins and improve adversarial robustness.
• It employs gradient-based optimization to approximate the shortest successful perturbations, achieving stable performance on MNIST and CIFAR10.
• Empirical results demonstrate MMA's insensitivity to initial perturbations and lower computational cost compared to standard adversarial training.

An Examination of Max-Margin Adversarial Training: Analytical and Empirical Insights

The focus of the paper is the development of Max-Margin Adversarial (MMA) training which leverages margin maximization for enhancing neural network robustness against adversarial attacks. This methodological innovation is predicated on associating margins, defined as the distance from inputs to a classifier's decision boundary, with adversarial robustness, culminating in a framework that simultaneously maximizes margins relative to each data point by dynamically adjusting the perturbation magnitude $\epsilon$. This is in contrast to traditional adversarial training where $\epsilon$ is fixed throughout.

The authors provide a rigorous analysis of how MMA approximates margin maximization, linking the notion of finding the "shortest successful perturbation" to gradient-based optimization of the loss function with respect to model parameters. Through the lens of this MMA training, a nuanced view is afforded where the strategy actively adapts the defense mechanism, targeting individual example-specific robustness—a significant change from static adversarial defense techniques.

Strong Numerical Results

The paper's experimental section demonstrates the efficacy and stability of MMA training across varied datasets including MNIST and CIFAR10, under $\ell_\infty$ and $\ell_2$ norm constraints. The experimental results on CIFAR10 showed that MMA trained models, especially those trained with higher $\epsilon$, achieved notably balanced resilience across various attack lengths by maintaining robust average accuracies on adversarial examples. Additionally, the proposed MMA schemes showed insensitivity to the initial perturbation magnitude, which contrasts with the sensitivity of standard adversarial training to the perturbation length $\epsilon$, emphasizing MMA's robustness.

A distinctive contribution to the discussion is the empirical validation on CIFAR10-$$, where MMA displays the capability to enhance average margin, providing a tangible empirical indicator of robustness improvement. MMA training was able to not only match, but in several cases surpass the performance of carefully chosen adversarial training ensembles, with a lower computational cost at both training and inference phases.

Theoretical and Practical Implications

Theoretically, the authors have extended the discourse on adversarial training frameworks by offering a margin-oriented interpretation of conventional adversarial training. This is encapsulated in the paper's conclusion that for small perturbation magnitudes, standard adversarial training maximizes a lower bound of the margin, while larger perturbation magnitudes do not necessarily result in margin maximization.

Practically, the results advocate for MMA training as a more reliable defense mechanism when there's uncertainty about the attack's perturbation length. This adaptability not only enhances the classifier's robustness but also obviates the need for exhaustive empirical tuning typical of existing methods.

Speculations on Future AI Development

The paper presents compelling implications for future research paths in AI robustness. Future research could build on the theoretical foundation laid by this work, potentially exploring the integration of the MMA framework with other model architectures or augmenting it with alternative loss functions or perturbation techniques. Another forthcoming direction could be evaluating MMA's performance in adversarial transfer learning scenarios or in conjunction with other defensive strategies such as randomized smoothing or certificate-based approaches which are gaining traction.

In conclusion, the paper represents a significant step towards understanding the dynamics between input space margin maximization and model robustness, challenging and refining the traditional paradigms of adversarial machine learning by aligning defensive strategies with the intrinsic properties of data distributions and decision boundaries. The insights presented offer the community valuable guidance on constructing inherently robust models, adaptable to the evolving adversarial landscapes.