# Distribution and Clusters Approximations as Abstract Domains in Probabilistic Abstract Interpretation to Neural Network Analysis

arXiv: https://arxiv.org/abs/2603.25273 · HTML: https://mlsanity.com/paper/2603.25273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Robustness of Neural Networks: A Probabilistic and Practical Approach](https://mlsanity.com/paper/1902.05983/) (2019)
- [Scalable Polyhedral Verification of Recurrent Neural Networks](https://mlsanity.com/paper/2005.13300/) (2020)

## Abstract (arXiv)

The probabilistic abstract interpretation framework of neural network analysis analyzes a neural network by analyzing its density distribution flow of all possible inputs. The grids approximation is one of abstract domains the framework uses which abstracts concrete space into grids. In this paper, we introduce two novel approximation methods: distribution approximation and clusters approximation. We show how these two methods work in theory with corresponding abstract transformers with help of illustrations of some simple examples.