# Algebraic Adversarial Attacks on Explainability Models

arXiv: https://arxiv.org/abs/2503.12683 · HTML: https://mlsanity.com/paper/2503.12683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 30 of 34)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Efficient Decision-based Black-box Adversarial Attacks on Face Recognition](https://mlsanity.com/paper/1904.04433/) (2019)
- [Summary of ChatGPT-Related Research and Perspective Towards the Future of Large Language Models](https://mlsanity.com/paper/2304.01852/) (2023)
- [Feature Importance-aware Transferable Adversarial Attacks](https://mlsanity.com/paper/2107.14185/) (2021)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- ["How do I fool you?": Manipulating User Trust via Misleading Black Box Explanations](https://mlsanity.com/paper/1911.06473/) (2019)
- [Improving Adversarial Transferability via Neuron Attribution-Based Attacks](https://mlsanity.com/paper/2204.00008/) (2022)
- [How Important Is a Neuron?](https://mlsanity.com/paper/1805.12233/) (2018)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [The Unreasonable Effectiveness of Deep Learning in Artificial Intelligence](https://mlsanity.com/paper/2002.04806/) (2020)
- [Robust Explainability: A Tutorial on Gradient-Based Attribution Methods for Deep Neural Networks](https://mlsanity.com/paper/2107.11400/) (2021)
- [Adversarial attacks and defenses in explainable artificial intelligence: A survey](https://mlsanity.com/paper/2306.06123/) (2023)
- [Towards the Unification and Robustness of Perturbation and Gradient Based Explanations](https://mlsanity.com/paper/2102.10618/) (2021)
- [Explainable Artificial Intelligence Applications in Cyber Security: State-of-the-Art in Research](https://mlsanity.com/paper/2208.14937/) (2022)
- [Bridging Adversarial Robustness and Gradient Interpretability](https://mlsanity.com/paper/1903.11626/) (2019)
- [The Manifold Hypothesis for Gradient-Based Explanations](https://mlsanity.com/paper/2206.07387/) (2022)
- [Approximate Manifold Defense Against Multiple Adversarial Perturbations](https://mlsanity.com/paper/2004.02183/) (2020)
- [Algebraic Adversarial Attacks on Integrated Gradients](https://mlsanity.com/paper/2407.16233/) (2024)

## Abstract (arXiv)

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.