# Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

arXiv: https://arxiv.org/abs/2603.25266 · HTML: https://mlsanity.com/paper/2603.25266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Synthesizing the preferred inputs for neurons in neural networks via deep generator networks](https://mlsanity.com/paper/1605.09304/) (2016)
- [Interpretable Convolutional Neural Networks](https://mlsanity.com/paper/1710.00935/) (2017)
- [Interpreting Deep Visual Representations via Network Dissection](https://mlsanity.com/paper/1711.05611/) (2017)
- [Interpreting CNN Knowledge via an Explanatory Graph](https://mlsanity.com/paper/1708.01785/) (2017)
- [Rule Extraction Algorithm for Deep Neural Networks: A Review](https://mlsanity.com/paper/1610.05267/) (2016)

## Abstract (arXiv)

Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to analyse density distribution flow of all possible inputs of a neural network when a network has uncountably many or countable but infinitely many inputs. We show how this theoretical framework works in neural networks and then discuss different abstract domains and corresponding Moore-Penrose pseudo-inverses together with abstract transformers used in the framework. We also present experimental examples to show how this framework helps to analyse real world problems.