# Adversary Detection in Neural Networks via Persistent Homology

arXiv: https://arxiv.org/abs/1711.10056 · HTML: https://mlsanity.com/paper/1711.10056/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2017.

## Built on by (most cited first, 12 of 12)

- [Topological Detection of Trojaned Neural Networks](https://mlsanity.com/paper/2106.06469/) (2021)
- [Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs](https://mlsanity.com/paper/2105.04404/) (2021)
- [Topology and geometry of data manifold in deep learning](https://mlsanity.com/paper/2204.08624/) (2022)
- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [An Adversarial Robustness Perspective on the Topology of Neural Networks](https://mlsanity.com/paper/2211.02675/) (2022)
- [A topological classifier to characterize brain states: When shape matters more than variance](https://mlsanity.com/paper/2303.04231/) (2023)
- [Be Persistent: Towards a Unified Solution for Mitigating Shortcuts in Deep Learning](https://mlsanity.com/paper/2402.11237/) (2024)
- [Topology of Out-of-Distribution Examples in Deep Neural Networks](https://mlsanity.com/paper/2501.12522/) (2025)
- [Leveraging The Topological Consistencies of Learning in Deep Neural Networks](https://mlsanity.com/paper/2111.15651/) (2021)
- [Characterization of topological structures in different neural network architectures](https://mlsanity.com/paper/2407.06286/) (2024)
- [TopoReformer: Mitigating Adversarial Attacks Using Topological Purification in OCR Models](https://mlsanity.com/paper/2511.15807/) (2025)
- [How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rule](https://mlsanity.com/paper/2608.01268/) (2026)

## Abstract (arXiv)

We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs induced by different inputs. Specifically, by applying persistent homology to these induced graphs, we observe that the structure of the most persistent subgraphs which generate the first homology group differ between adversarial and unperturbed inputs. Based on this observation, we build a detection algorithm that depends only on the topological information extracted during training. We test our algorithm on MNIST and achieve 98% detection adversary accuracy with F1-score 0.98.