Disentangling Adversarial Robustness and Generalization (1812.00740v2)

Abstract: Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and generalization are conflicting goals. In an effort to clarify the relationship between robustness and generalization, we assume an underlying, low-dimensional data manifold and show that: 1. regular adversarial examples leave the manifold; 2. adversarial examples constrained to the manifold, i.e., on-manifold adversarial examples, exist; 3. on-manifold adversarial examples are generalization errors, and on-manifold adversarial training boosts generalization; 4. regular robustness and generalization are not necessarily contradicting goals. These assumptions imply that both robust and accurate models are possible. However, different models (architectures, training strategies etc.) can exhibit different robustness and generalization characteristics. To confirm our claims, we present extensive experiments on synthetic data (with known manifold) as well as on EMNIST, Fashion-MNIST and CelebA.

• The paper demonstrates that on-manifold adversarial robustness aligns with generalization by exploiting the data’s low-dimensional structure.
• It distinguishes between regular adversarial examples, which deviate from the manifold, and on-manifold examples that preserve true class labels.
• The study shows that using data augmentation and adversarial training enables models to achieve both robustness and high accuracy.

Disentangling Adversarial Robustness and Generalization: A Detailed Examination

The paper "Disentangling Adversarial Robustness and Generalization" by Stutz et al. addresses the intricate relationship between adversarial robustness and generalization in deep neural networks, challenging the prevalent hypothesis that these two properties are inherently conflicting. The authors embark on a methodical exploration, proposing that under certain conditions, both robust and accurate models are achievable.

The document proposes a unique perspective by considering the data distribution as lying on a low-dimensional manifold. The authors classify adversarial examples into two distinct types: regular adversarial examples, which leave the manifold, and on-manifold adversarial examples, which remain constrained to the manifold. Through an incisive examination, four critical points are asserted:

1. Regular Adversarial Examples and the Manifold: The paper provides empirical evidence that regular adversarial examples, typically generated through standard attacks, indeed deviate from the data manifold. This observation supports the argument that these examples exploit non-manifold structures, a result in line with previous insights but substantiated with rigorous experimental evaluation on synthetic datasets and real-world image datasets such as EMNIST and Fashion-MNIST.
2. Existence of On-Manifold Adversarial Examples: Contrary to the idea that adversarial robustness and accuracy are conflicting due to adversarial examples exploiting non-manifold perturbations, the paper demonstrates the existence of on-manifold adversarial examples. These pertain to alterations confined to the manifold that do not change the true class label under the data distribution, as evidenced by experiments using variational autoencoder-generative adversarial networks (VAE-GANs) to approximate the manifold.
3. On-Manifold Robustness as Generalization: The authors propose that robustness against on-manifold adversarial examples equates to generalization. They theorize that better generalization performance typically reduces the on-manifold adversarial success rate, essentially correlating robustness in this context with improved learning performance.
4. Independence of Regular Robustness and Generalization: In a bold divergence from previous assertions in the literature, the paper posits that regular robustness does not necessarily conflict with generalization when appropriate training practices such as data augmentation and adversarial training are employed. This is especially marked when adversarial examples are incorporated into the training regimen, particularly as the amount of training data grows.

The comprehensive experiments conducted throughout the paper substantiate these arguments across various datasets and attack models, including both white-box and black-box attacks. The application of adversarial training in a bid to affirm its effect on robustness and generalization further reinforces the viability of achieving these characteristics in tandem. The investigation meticulously explores different architectures, such as convolutional networks and multi-layer perceptrons, asserting the robustness of the findings across architectural nuances.

The implications of this research extend beyond theoretical exposition; they propose tangible advancements in developing models that do not compromise on robustness for improved accuracy or vice versa. Future work may pivot on refining manifold approximation strategies and expanding the applicability of these findings to larger, more complex datasets, potentially guiding enhancements in secure AI model development and deployment.

In summary, the paper challenges entrenched paradigms, encouraging a re-evaluation of how robustness and generalization interact within machine learning models. Through a blend of theoretical, empirical, and practical insights, it opens avenues for future exploration while providing a nuanced understanding of adversarial robustness that can drive forth innovations in AI system design.