Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach (1801.10578v1)

Abstract: The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed towards a comprehensive measure of robustness. In this paper, we provide a theoretical justification for converting robustness analysis into a local Lipschitz constant estimation problem, and propose to use the Extreme Value Theory for efficient evaluation. Our analysis yields a novel robustness metric called CLEVER, which is short for Cross Lipschitz Extreme Value for nEtwork Robustness. The proposed CLEVER score is attack-agnostic and computationally feasible for large neural networks. Experimental results on various networks, including ResNet, Inception-v3 and MobileNet, show that (i) CLEVER is aligned with the robustness indication measured by the $\ell_2$ and $\ell_\infty$ norms of adversarial examples from powerful attacks, and (ii) defended networks using defensive distillation or bounded ReLU indeed achieve better CLEVER scores. To the best of our knowledge, CLEVER is the first attack-independent robustness metric that can be applied to any neural network classifier.

• The paper introduces a novel, attack-independent CLEVER metric that estimates local Lipschitz constants using Extreme Value Theory to quantify robustness.
• The paper validates the CLEVER score on architectures such as ResNet and Inception-v3, showing strong correlation with ℓ2 and ℓ∞ adversarial benchmarks.
• The paper demonstrates that defensive techniques like defensive distillation enhance CLEVER scores, indicating improved resilience against adversarial attacks.

Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach

Overview

The paper introduces a novel method for evaluating the robustness of neural networks against adversarial examples, applying Extreme Value Theory (EVT) to propose a robustness metric termed CLEVER (Cross Lipschitz Extreme Value for nEtwork Robustness). This approach transforms the robustness assessment into a problem of estimating local Lipschitz constants, characterizing the difficulty of crafting adversarial examples.

The CLEVER Metric

The robustness of neural networks has been a critical area of research due to security threats posed by adversarial examples—inputs crafted to deceive models without noticeable changes to the input data. Prior evaluations often relied on attack-specific benchmarks, which might not provide a comprehensive robustness measure. The paper aims to address this by introducing an attack-independent metric applicable to any neural network architecture.

The introduction of the CLEVER score is premised on the following:

• Theoretical Basis: The paper addresses the robustness problem of neural networks by leveraging the concept of Lipschitz continuity. The task is converted into finding lower bounds on the minimum distortion required to create adversarial perturbations.
• Use of EVT: EVT is employed to estimate the local Lipschitz constants. This method capitalizes on the probability distributions of maximum gradient norms in a defined neighborhood around an input, using these distributions to estimate an upper boundary for robustness metrics.

Results and Contributions

The paper details experiments that validate the CLEVER score across several neural network architectures, including ResNet, Inception-v3, and MobileNet:

1. Alignment with Attack-specific Metrics: The CLEVER score correlates well with robustness indications derived from specific $\ell_2$ and $\ell_\infty$ norms of adversarial examples in contemporary attack scenarios. These results affirm the CLEVER score captures inherent robustness without reliance on specific adversarial strategies.
2. Defensive Techniques: Neural networks utilizing defense mechanisms such as defensive distillation and bounded ReLU functions achieve higher CLEVER scores, suggesting an improvement in resilience against adversarial perturbations.
3. Efficiency: Unlike previously proposed verification methods involving high computational complexity, the CLEVER approach proves computational feasibility even for large networks.

Implications and Future Directions

The CLEVER metric offers an important step towards standardizing adversarial robustness across various architectures:

• Practical Impact: It holds significant implications for deploying neural networks in security-sensitive applications, where a guaranteed level of resilience is critical.
• Theoretical Significance: By separating robustness metrics from attack methodologies, the paper redirects focus towards intrinsic properties of neural networks, possibly guiding future designs of more inherently robust architectures.
• Future Work: Extending this work could involve applying the CLEVER framework to new network structures or combining it with other verification methods to enhance robustness guarantees. Further paper may also delve into optimizing EVT parameters for more accurate estimations and broader applicability.

Through the CLEVER score, this paper paves the way for more reliable and generalized assessments of neural network robustness, shifting the discourse from reactive attack-counteraction tactics to inherent architectural resilience.