# On existence, uniqueness and scalability of adversarial robustness measures for AI classifiers

arXiv: https://arxiv.org/abs/2310.14421 · HTML: https://mlsanity.com/paper/2310.14421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [HopSkipJumpAttack: A Query-Efficient Decision-Based Attack](https://mlsanity.com/paper/1904.02144/) (2019)
- [Adversarial Attacks and Defenses in Images, Graphs and Text: A Review](https://mlsanity.com/paper/1909.08072/) (2019)
- [Adversarial Policies Beat Superhuman Go AIs](https://mlsanity.com/paper/2211.00241/) (2022)
- [Robust learning of data anomalies with analytically-solvable entropic outlier sparsification](https://mlsanity.com/paper/2112.11768/) (2021)

## Built on by (most cited first, 1 of 1)

- [An entropy-optimal path to humble AI](https://mlsanity.com/paper/2506.17940/) (2025)

## Abstract (arXiv)

Simply-verifiable mathematical conditions for existence, uniqueness and explicit analytical computation of minimal adversarial paths (MAP) and minimal adversarial distances (MAD) for (locally) uniquely-invertible classifiers, for generalized linear models (GLM), and for entropic AI (EAI) are formulated and proven. Practical computation of MAP and MAD, their comparison and interpretations for various classes of AI tools (for neuronal networks, boosted random forests, GLM and EAI) are demonstrated on the common synthetic benchmarks: on a double Swiss roll spiral and its extensions, as well as on the two biomedical data problems (for the health insurance claim predictions, and for the heart attack lethality classification). On biomedical applications it is demonstrated how MAP provides unique minimal patient-specific risk-mitigating interventions in the predefined subsets of accessible control variables.