# Reachable Sets of Classifiers and Regression Models: (Non-)Robustness Analysis and Robust Training

arXiv: https://arxiv.org/abs/2007.14120 · HTML: https://mlsanity.com/paper/2007.14120/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2020.

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

- [Fully Automatic Neural Network Reduction for Formal Verification](https://mlsanity.com/paper/2305.01932/) (2023)

## Abstract (arXiv)

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and reliability of predictions. We answer these questions by computing reachable sets of neural networks, i.e. sets of outputs resulting from continuous sets of inputs. We provide two efficient approaches that lead to over- and under-approximations of the reachable set. This principle is highly versatile, as we show. First, we use it to analyze and enhance the robustness properties of both classifiers and regression models. This is in contrast to existing works, which are mainly focused on classification. Specifically, we verify (non-)robustness, propose a robust training procedure, and show that our approach outperforms adversarial attacks as well as state-of-the-art methods of verifying classifiers for non-norm bound perturbations. Second, we provide techniques to distinguish between reliable and non-reliable predictions for unlabeled inputs, to quantify the influence of each feature on a prediction, and compute a feature ranking.