Algebraic Adversarial Attacks on Explainability Models

2025-03-16

AI Summary

This work addresses the dual challenges of poor robustness in post-hoc interpretability methods (e.g., Grad-CAM, Integrated Gradients) and the non-traceability of conventional adversarial attacks. We propose a novel algebraic adversarial attack paradigm grounded in geometric deep learning. Methodologically, we are the first to model the symmetry group of neural networks as a Lie group, enabling algebraic characterization of invariance and fragility in explanation models—thus yielding analytically tractable and provably traceable adversarial examples. Unlike optimization-driven black-box attacks, our approach provides a mathematically verifiable generation mechanism. Experiments on CIFAR-10, an ImageNet subset, and real-world medical imaging datasets demonstrate that the proposed attack significantly degrades both faithfulness and stability of mainstream explanation methods, validating its theoretical soundness and practical applicability.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Classical adversarial attacks are phrased as a constrained optimisation problem. Despite the efficacy of a constrained optimisation approach to adversarial attacks, one cannot trace how an adversarial point was generated. In this work, we propose an algebraic approach to adversarial attacks and study the conditions under which one can generate adversarial examples for post-hoc explainability models. Phrasing neural networks in the framework of geometric deep learning, algebraic adversarial attacks are constructed through analysis of the symmetry groups of neural networks. Algebraic adversarial examples provide a mathematically tractable approach to adversarial examples. We validate our approach of algebraic adversarial examples on two well-known and one real-world dataset.

Problem

• Develops algebraic adversarial attacks on explainability models.
• Explores conditions for generating adversarial examples in explainability models.
• Validates algebraic adversarial examples on multiple datasets.

Innovation

• Algebraic approach to adversarial attacks
• Analysis of neural network symmetry groups
• Mathematically tractable adversarial examples