# Robustness Verification of Support Vector Machines

arXiv: https://arxiv.org/abs/1904.11803 · HTML: https://mlsanity.com/paper/1904.11803/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2019.

## Built on by (most cited first, 9 of 9)

- [A Review of Formal Methods applied to Machine Learning](https://mlsanity.com/paper/2104.02466/) (2021)
- [CAISAR: A platform for Characterizing Artificial Intelligence Safety and Robustness](https://mlsanity.com/paper/2206.03044/) (2022)
- [Neural Network Verification with PyRAT](https://mlsanity.com/paper/2410.23903/) (2024)
- [Abstract Interpretation-Based Feature Importance for SVMs](https://mlsanity.com/paper/2210.12456/) (2022)
- [Evaluating robustness of support vector machines with the Lagrangian dual approach](https://mlsanity.com/paper/2306.02639/) (2023)
- [Probabilistic ML Verification via Weighted Model Integration](https://mlsanity.com/paper/2402.04892/) (2024)
- [The CAISAR Platform: Extending the Reach of Machine Learning Specification and Verification](https://mlsanity.com/paper/2506.12084/) (2025)
- [Feature Engineering is Not Dead: Reviving Classical Machine Learning with Entropy, HOG, and LBP Feature Fusion for Image Classification](https://mlsanity.com/paper/2507.13772/) (2025)
- [Geometric Configurations of Perturbed Jailbreak Prompts](https://mlsanity.com/paper/2607.20581/) (2026)

## Abstract (arXiv)

We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abstract version of a given SVM classifier to be used for checking its robustness. This methodology is parametric on a given numerical abstraction of real values and, analogously to the case of neural networks, needs neither abstract least upper bounds nor widening operators on this abstraction. The standard interval domain provides a simple instantiation of our abstraction technique, which is enhanced with the domain of reduced affine forms, which is an efficient abstraction of the zonotope abstract domain. This robustness verification technique has been fully implemented and experimentally evaluated on SVMs based on linear and nonlinear (polynomial and radial basis function) kernels, which have been trained on the popular MNIST dataset of images and on the recent and more challenging Fashion-MNIST dataset. The experimental results of our prototype SVM robustness verifier appear to be encouraging: this automated verification is fast, scalable and shows significantly high percentages of provable robustness on the test set of MNIST, in particular compared to the analogous provable robustness of neural networks.