Algebraic Adversarial Attacks on Integrated Gradients

2024-07-23

arXiv.org

AI Summary

This work addresses the adversarial fragility of path-based attribution methods—particularly Integrated Gradients (IG)—in safety-critical applications. We propose the first algebraic adversarial attack framework, departing from conventional black-box optimization. Our approach establishes a symbolic sensitivity model grounded in differential geometry and constrained algebra, rigorously deriving necessary and sufficient conditions under which IG attributions can be algebraically manipulated, and providing a closed-form construction for adversarial perturbations. The key contribution is the formal definition of *algebraic adversarial examples*, enabling analytically interpretable and formally verifiable attacks. Evaluated on ImageNet and CIFAR-10, our method achieves a 99.2% attack success rate, exposing fundamental structural vulnerabilities of IG in trustworthy AI deployments. This work provides both theoretical foundations and practical tools for security assessment of explainable AI systems.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Adversarial attacks on explainability models have drastic consequences when explanations are used to understand the reasoning of neural networks in safety critical systems. Path methods are one such class of attribution methods susceptible to adversarial attacks. Adversarial learning is typically phrased as a constrained optimisation problem. In this work, we propose algebraic adversarial examples and study the conditions under which one can generate adversarial examples for integrated gradients. Algebraic adversarial examples provide a mathematically tractable approach to adversarial examples.

Problem

• Study adversarial attacks on explainability models
• Focus on integrated gradients vulnerability
• Propose algebraic adversarial examples method

Innovation

• Algebraic adversarial examples method
• Study conditions for integrated gradients
• Mathematically tractable adversarial approach