Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation (1705.08475v2)

Abstract: Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high confidence. This raises concerns that such classifiers are vulnerable to attacks and calls into question their usage in safety-critical systems. We show in this paper for the first time formal guarantees on the robustness of a classifier by giving instance-specific lower bounds on the norm of the input manipulation required to change the classifier decision. Based on this analysis we propose the Cross-Lipschitz regularization functional. We show that using this form of regularization in kernel methods resp. neural networks improves the robustness of the classifier without any loss in prediction performance.

• The paper introduces a method that computes instance-specific lower bounds on perturbations needed to change classifier decisions.
• It employs localized Lipschitz constants and a Cross-Lipschitz regularizer to boost robustness in kernel methods and neural networks.
• Empirical tests on MNIST and CIFAR10 confirm improved robustness and accuracy over traditional defensive techniques.

Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation

The paper by Matthias Hein and Maksym Andriushchenko addresses a significant issue in machine learning: the vulnerability of classifiers to adversarial manipulations. It introduces formal robustness guarantees for classifiers, focusing on calculating instance-specific lower bounds for the magnitude of input changes required to alter classifier decisions. This provides a novel angle on ensuring the safety of machine learning systems, particularly in safety-critical environments.

Overview

The authors highlight a critical challenge where state-of-the-art classifiers can be easily misled by minor adversarial perturbations. Such vulnerabilities have severe implications, especially in safety-critical applications like autonomous driving. Traditional methods, such as adversarial training or the use of universal perturbations, offer no absolute assurance against adversarial attacks.

In response, the paper presents a new method for providing formal guarantees on classifier robustness. It achieves this by computing lower bounds on the norm of necessary input manipulation to alter a classification decision. These bounds imply that within certain limits around an input instance, the classifier decision remains unchanged.

Methodology

The paper focuses on kernel methods and neural networks, proposing a Cross-Lipschitz regularization functional to enhance classifier robustness. This functional is utilized to derive improved robustness guarantees while maintaining prediction performance.

The approach involves calculating local Lipschitz constants for each class difference function, instead of relying on global estimates, which tend to be overly conservative. This localized assessment leads to more effective robustness guarantees.

The Cross-Lipschitz regularizer is integrated into the learning process, formulating an objective that simultaneously maximizes class difference and minimizes gradient dissimilarities across classes. This dual focus inherently enhances robustness against adversarial manipulations.

Results

Empirical results demonstrate the effectiveness of Cross-Lipschitz regularization in both kernel methods and neural networks. For MNIST and CIFAR10 datasets, classifiers regularized with Cross-Lipschitz surpass those trained with traditional techniques like weight decay and dropout in terms of robustness and prediction accuracy.

For example, neural networks trained with this regularization achieve significantly higher resistance against adversarial samples, and the robustness guarantees are similarly improved.

Implications and Future Directions

The paper's findings have substantial implications for designing more secure machine learning systems. The proposed formal guarantees pave the way for developing classifiers that can be reliably deployed in applications demanding high safety standards.

However, the paper opens several avenues for future research:

1. Scalability to Deep Networks: Extending these formal guarantees to deeper networks remains challenging.
2. Efficient Computation: Optimization of these robustness measures for faster computation in complex models.
3. Broadening Applications: Applying these principles to a wider range of classifiers and ensuring robustness across diverse datasets.

In conclusion, this paper provides a structured pathway toward embedding formal robustness guarantees in machine learning systems, ensuring their safe and reliable deployment in critical real-world applications.