Adversarial vulnerability for any classifier (1802.08686v2)

Abstract: Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the data is generated with a smooth generative model. We derive fundamental upper bounds on the robustness to perturbations of any classification function, and prove the existence of adversarial perturbations that transfer well across different classifiers with small risk. Our analysis of the robustness also provides insights onto key properties of generative models, such as their smoothness and dimensionality of latent space. We conclude with numerical experimental results showing that our bounds provide informative baselines to the maximal achievable robustness on several datasets.

• The paper derives upper bounds on classifier robustness, showing that even smooth generative models are susceptible to minimal adversarial perturbations.
• It demonstrates that adversarial perturbations can transfer across different classifiers, highlighting shared vulnerabilities among models.
• The paper contrasts in-distribution and unconstrained robustness, offering a theoretical framework for developing more resilient classifiers.

Adversarial Vulnerability for Any Classifier: An In-Depth Analysis

The paper "Adversarial vulnerability for any classifier" explores a critical facet of machine learning: adversarial robustness. Despite impressive advancements in classifier models, a notable vulnerability persists—adversarial perturbations. These are minute, often imperceptible changes in input data that can lead to significant misclassifications. This paper provides a thorough theoretical exploration of this vulnerability within the context of smooth generative models.

The paper begins by establishing the significance of its undertaking: modern deep neural networks, while achieving state-of-the-art outcomes in diverse fields like bioinformatics and computer vision, are notably fragile against adversarial attacks. The vulnerability has spurred a substantial body of work aimed at enhancing the resilience of such classifiers. Yet, improvements in robustness are consistently overshadowed by evolving robust perturbation techniques.

The researchers leverage a smooth generative model for data distribution—a mapping from latent representations to images—to theoretically explore adversarial robustness. The principal contributions of the work are threefold:

1. Upper Bounds on Robustness: The authors derive fundamental upper bounds on any classifier’s robustness against adversarial perturbations. A significant insight is that any classifier, when employed on high-dimensional latent space data distributions, is susceptible to adversarial perturbations. The relationship drawn between the classifier's vulnerability and its linearity in the latent space is critical. The authors underscore that even linear decision boundaries could potentially lead to robustness if the latent space is accommodated accordingly.
2. Transferability of Adversarial Perturbations: An additional theoretical result established within this paper is the existence of adversarial perturbations transferable across different classifiers. This aligns with empirical findings suggesting that perturbations effective against one model often exploit similar vulnerabilities in others. The implications are substantial, indicating potential vulnerabilities across versatile applications with shared adversarial examples.
3. Contrasts in Robustness Definitions: The paper differentiates between in-distribution robustness and unconstrained robustness, demonstrating the practical import of both. Notably, the researchers prove that for any classifier with in-distribution robustness r, one can construct another classifier achieving unconstrained robustness of at least r/2. This result provides a pathway for more robust model constructions in the future.

The empirical evaluation uses the SVHN and CIFAR-10 datasets, showcasing the application of their theoretical bounds against real-world scenarios. The generation of adversarial examples/perturbations highlights that the bound offers a realistic robustness baseline—though it leaves room for further refinement and empirical adjustment. The complexities observed in high-dimensional datasets suggest ongoing potential for enhancing classifier resilience.

The implications of this work extend into pivotal theoretical and practical arenas. Theoretically, it questions the limitations of smooth, high-dimensional generative models to accurately simulate natural image distributions while maintaining adversarial robustness. Practically, the need for crafting robust classifiers becomes more poignant, as does the significance of considering both smoothness and dimensionality dimensions in generative models.

In synopsis, the paper provides vital insights into the robustness mechanisms and adversarial vulnerabilities of classifiers, supporting a landscape where more robust, adaptable machine learning models are vital for technological efficacy. Future advancements likely necessitate addressing the theoretical constraints outlined in this paper while broadening the empirical scope to accommodate evolving complexities in machine learning environments.