# Correctness Verification of Neural Networks

arXiv: https://arxiv.org/abs/1906.01030 · HTML: https://mlsanity.com/paper/1906.01030/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

## Built on by (most cited first, 7 of 7)

- [Accountability in an Algorithmic Society: Relationality, Responsibility, and Robustness in Machine Learning](https://mlsanity.com/paper/2202.05338/) (2022)
- [Verification of Image-based Neural Network Controllers Using Generative Models](https://mlsanity.com/paper/2105.07091/) (2021)
- [DeepBern-Nets: Taming the Complexity of Certifying Neural Networks using Bernstein Polynomial Activations and Precise Bound Propagation](https://mlsanity.com/paper/2305.13508/) (2023)
- [Framework for Certification of AI-Based Systems](https://mlsanity.com/paper/2302.11049/) (2023)
- [ZoPE: A Fast Optimizer for ReLU Networks with Low-Dimensional Inputs](https://mlsanity.com/paper/2106.05325/) (2021)
- [Formal and Practical Elements for the Certification of Machine Learning Systems](https://mlsanity.com/paper/2310.03217/) (2023)
- [Correctness Verification of Neural Networks Approximating Differential Equations](https://mlsanity.com/paper/2402.07621/) (2024)

## Abstract (arXiv)

We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike robustness verification, which aims to verify that the prediction of a network is stable in some local regions around labelled points, our framework provides a way to specify correctness globally in the whole target input space and verify that the network is correct for all target inputs (or find the regions where the network is not correct). We provide a specification through 1) a state space consisting of all relevant states of the world and 2) an observation process that produces neural network inputs from the states of the world. Tiling the state and input spaces with a finite number of tiles, obtaining ground truth bounds from the state tiles and network output bounds from the input tiles, then comparing the ground truth and network output bounds delivers an upper bound on the network output error for any inputs of interest. The presented framework also enables detecting illegal inputs -- inputs that are not contained in (or close to) the target input space as defined by the state space and observation process (the neural network is not designed to work on them), so that we can flag when we don't have guarantees. Results from two case studies highlight the ability of our technique to verify error bounds over the whole target input space and show how the error bounds vary over the state and input spaces.