Adversarial Examples Are a Natural Consequence of Test Error in Noise (1901.10513v1)

Abstract: Over the last few years, the phenomenon of adversarial examples --- maliciously constructed inputs that fool trained machine learning models --- has captured the attention of the research community, especially when the adversary is restricted to small modifications of a correctly handled input. Less surprisingly, image classifiers also lack human-level performance on randomly corrupted images, such as images with additive Gaussian noise. In this paper we provide both empirical and theoretical evidence that these are two manifestations of the same underlying phenomenon, establishing close connections between the adversarial robustness and corruption robustness research programs. This suggests that improving adversarial robustness should go hand in hand with improving performance in the presence of more general and realistic image corruptions. Based on our results we recommend that future adversarial defenses consider evaluating the robustness of their methods to distributional shift with benchmarks such as Imagenet-C.

• The paper demonstrates that adversarial examples emerge as a natural consequence of noise-induced test errors through linear models and the Gaussian isoperimetric inequality.
• Empirical results on CIFAR-10 and ImageNet reveal that both adversarial training and Gaussian augmentation variably improve robustness against diverse types of corruption.
• The findings imply that adopting unified defense strategies addressing both adversarial and corruption robustness can enhance overall model performance against distributional shifts.

Overview of "Adversarial Examples Are a Natural Consequence of Test Error in Noise"

This paper presents a detailed examination of the relationship between adversarial examples in machine learning and robustness to noise-induced corruption of inputs, particularly within the context of image classification. The authors, Ford, Gilmer, Carlini, and Cubuk, provide both empirical evidence and theoretical analysis to draw a connection between these two phenomena, proposing that they are manifestations of the same underlying issue in model robustness. They posit that improving adversarial robustness may concurrently enhance a model's performance against more general noise corruption, thus suggesting a unified approach to tackling these issues.

Key Findings and Analysis

The authors start by highlighting that adversarial examples—minor, targeted perturbations that cause misclassification—are analogous to errors caused by random noise, such as Gaussian noise. State-of-the-art models are shown to be susceptible not only to adversarial attacks but also to various types of noise, including blur and pixelation, which deviate from the model's training data distribution.

The core of the paper establishes that adversarial errors can be explained by the test errors present in noisy image distributions. This insight is grounded in two main analyses:

1. Theoretical Framework: The authors employ a linear model to demonstrate that adversarial examples emerge naturally as a linear response to Gaussian noise perturbations. They show that the distance from an input to its nearest adversarial perturbation aligns with theoretical predictions based on simple error models.
2. Isoperimetric Inequality for Gaussian Distributions: They leverage the Gaussian isoperimetric inequality to formalize the relationship between test error in noise and adversarial robustness. This mathematical tool provides bounds on the distance that randomly corrupted inputs must be from the decision boundary, supporting the notion that non-zero test errors naturally lead to adversarial vulnerabilities.

Empirical Evidence

The empirical portion of the paper evaluates models trained on the CIFAR-10 and ImageNet datasets with various training paradigms, including adversarial training and noise augmentation. The findings suggest that:

• Both adversarial training and Gaussian data augmentation improve robustness to noise, although their effects vary depending on the type of corruption and noise level.
• Models trained with these methods exhibit performance improvements on benchmark datasets evaluating corruption robustness, which includes a variety of non-adversarial corruptions.
• The paper further critiques prior defense methods shown ineffective by revealing their failure to provide noise robustness, underscoring the importance of evaluating both adversarial and corruption robustness.

Practical and Theoretical Implications

The implications of these findings are twofold. Practically, they suggest that efforts to improve machine learning model robustness should not be siloed between adversarial robustness and corruption robustness. Instead, an integrative defense strategy might be more effective and pragmatic. Theoretically, they offer a perspective that adversarial vulnerability might not necessarily be intrinsic to neural networks or an anomalous flaw but rather a natural outcome of the existing model errors in corrupted distributions.

Future Directions

The authors recommend that future research in adversarial defenses also considers robustness to more general distributional shifts as a baseline for evaluation. This broader set of considerations could lead to improvements in model robustness across both adversarial and non-adversarial contexts, potentially diffusing the current singular focus on small perturbation adversarial robustness that may overlook broader vulnerabilities to distributional shifts.

In summary, this paper contributes to a more nuanced understanding of adversarial examples by reframing them in the context of noise-induced test errors, offering a holistic approach to tackling the broader challenge of achieving robustness in machine learning models. This unified perspective could guide future research to more effectively address the vulnerabilities inherent in contemporary models.