Generalizable Adversarial Training via Spectral Normalization (1811.07457v1)

Abstract: Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially-perturbed training samples, but the improved performance can still be far below the performance seen in non-adversarial settings. A significant portion of this gap can be attributed to the decrease in generalization performance due to adversarial training. In this work, we extend the notion of margin loss to adversarial settings and bound the generalization error for DNNs trained under several well-known gradient-based attack schemes, motivating an effective regularization scheme based on spectral normalization of the DNN's weight matrices. We also provide a computationally-efficient method for normalizing the spectral norm of convolutional layers with arbitrary stride and padding schemes in deep convolutional networks. We evaluate the power of spectral normalization extensively on combinations of datasets, network architectures, and adversarial training schemes. The code is available at https://github.com/jessemzhang/dl_spectral_normalization.

• The paper's main contribution is introducing spectral normalization as an effective regularizer to bridge the generalization gap in adversarial training.
• It establishes new margin-based generalization bounds for DNNs under various gradient attack schemes like FGM, PGM, and WRM.
• It offers a computationally efficient method for applying spectral normalization in convolutional layers, validated by experiments on datasets such as MNIST, CIFAR-10, and SVHN.

Generalizable Adversarial Training via Spectral Normalization

Overview of the Research

The paper "Generalizable Adversarial Training via Spectral Normalization" tackles the issue of adversarial robustness in deep neural networks (DNNs). Traditionally, DNNs have exhibited impressive performance across various supervised learning tasks. However, their vulnerability to adversarial perturbations, which are subtle changes to input data designed to mislead the model, presents a significant challenge. This vulnerability undermines the practical utility of DNNs in real-world applications.

Recent efforts to improve DNN robustness have focused on adversarial training, which involves fitting networks using adversarially-perturbed samples. While these methods enhance robustness, they often lead to poor generalization on test samples compared to non-adversarial settings. This paper argues that adversarial training significantly decreases generalization performance, thereby widening the test-train gap. The authors propose a novel regularization technique using spectral normalization (SN) to tighten this gap and improve adversarial robustness.

Detailed Contributions

1. Spectral Normalization as a Regularization Method: The authors suggest applying spectral normalization to the weight matrices of DNNs as an efficient regularization strategy during adversarial training. Spectral normalization involves bounding the spectral norm (largest singular value) of weight matrices, thus controlling the Lipschitz constant of the network and limiting capacity, leading to improved generalization.
2. Extended Margin-based Generalization Bound: Building on existing margin-based generalization analyses, the paper derives new generalization error bounds for DNNs under various gradient-based adversarial attack schemes. These include fast gradient method (FGM), projected gradient method (PGM), and Wasserstein risk minimization (WRM). The bounds indicate that effective spectral normalization can minimize the adversarial generalization component.
3. Computational Methods for SN in Convolutional Layers: A computationally efficient method for spectral normalization in convolutional layers with arbitrary stride and padding is developed, enhancing the applicability of SN across various architectures.
4. Empirical Validation: Extensive experiments are conducted using multiple datasets (MNIST, CIFAR-10, SVHN) and architectures (e.g., AlexNet, Inception, ResNet) showing that spectral normalization effectively improves generalization and test performance after adversarial training. Notably, test accuracies increase significantly post-normalization, indicating the utility of SN in adversarial contexts.

Implications and Future Directions

The introduction of spectral normalization as a regularization tool in adversarial training holds impactful implications both in theoretical understanding and practical applications of AI systems in adversarially sensitive environments. From a theoretical standpoint, SN bridges the test-train gap observed in adversarial settings, providing pathways to better theoretical models of generalization under these conditions.

Practically, the ease of implementing SN and its compatibility with existing architectures and training schemes indicate promising widespread adoption in fields requiring robust AI models—such as autonomous vehicles, health diagnostics, and cybersecurity.

Future exploration may delve into optimizing SN further, understanding its interaction with other regularization methods, or extending its framework to other adversarial attack schemes not covered in the paper. Such advancements promise heightened robustness and reliability in neural networks against adversarial threats.