# Parallelization Techniques for Verifying Neural Networks

arXiv: https://arxiv.org/abs/2004.08440 · HTML: https://mlsanity.com/paper/2004.08440/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2020.

## Built on by (most cited first, 30 of 36)

- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks](https://mlsanity.com/paper/2210.13915/) (2022)
- [The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Results](https://mlsanity.com/paper/2212.10376/) (2022)
- [OVERT: An Algorithm for Safety Verification of Neural Network Control Policies for Nonlinear Systems](https://mlsanity.com/paper/2108.01220/) (2021)
- [Towards Scalable Verification of Deep Reinforcement Learning](https://mlsanity.com/paper/2105.11931/) (2021)
- [Verifying Learning-Based Robotic Navigation Systems](https://mlsanity.com/paper/2205.13536/) (2022)
- [VeriX: Towards Verified Explainability of Deep Neural Networks](https://mlsanity.com/paper/2212.01051/) (2022)
- [An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks](https://mlsanity.com/paper/2201.01978/) (2022)
- [Efficient Neural Network Analysis with Sum-of-Infeasibilities](https://mlsanity.com/paper/2203.11201/) (2022)
- [A DPLL(T) Framework for Verifying Deep Neural Networks](https://mlsanity.com/paper/2307.10266/) (2023)
- [Formally Explaining Neural Networks within Reactive Systems](https://mlsanity.com/paper/2308.00143/) (2023)
- [Neural Network Verification with Proof Production](https://mlsanity.com/paper/2206.00512/) (2022)
- [Pruning and Slicing Neural Networks using Formal Verification](https://mlsanity.com/paper/2105.13649/) (2021)
- [Scalable Verification of GNN-based Job Schedulers](https://mlsanity.com/paper/2203.03153/) (2022)
- [Verification-Aided Deep Ensemble Selection](https://mlsanity.com/paper/2202.03898/) (2022)
- [Minimal Multi-Layer Modifications of Deep Neural Networks](https://mlsanity.com/paper/2110.09929/) (2021)
- [DeepCert: Verification of Contextually Relevant Robustness for Neural Network Image Classifiers](https://mlsanity.com/paper/2103.01629/) (2021)
- [Constrained Reinforcement Learning for Robotics via Scenario-Based Programming](https://mlsanity.com/paper/2206.09603/) (2022)
- [Verifying Generalization in Deep Learning](https://mlsanity.com/paper/2302.05745/) (2023)
- [RoMA: a Method for Neural Network Robustness Measurement and Assessment](https://mlsanity.com/paper/2110.11088/) (2021)
- [Tighter Abstract Queries in Neural Network Verification](https://mlsanity.com/paper/2210.12871/) (2022)
- [Self-Correcting Neural Networks For Safe Classification](https://mlsanity.com/paper/2107.11445/) (2021)
- [Boosting Robustness Verification of Semantic Feature Neighborhoods](https://mlsanity.com/paper/2209.05446/) (2022)
- [DelBugV: Delta-Debugging Neural Network Verifiers](https://mlsanity.com/paper/2305.18558/) (2023)
- [PICID: Proof-Driven Clause Learning in Neural Network Verification](https://mlsanity.com/paper/2503.12083/) (2025)
- [ZoPE: A Fast Optimizer for ReLU Networks with Low-Dimensional Inputs](https://mlsanity.com/paper/2106.05325/) (2021)
- [Negative Selection Approach to support Formal Verification and Validation of BlackBox Models' Input Constraints](https://mlsanity.com/paper/2209.01411/) (2022)
- [UnbiasedNets: A Dataset Diversification Framework for Robustness Bias Alleviation in Neural Networks](https://mlsanity.com/paper/2302.12538/) (2023)
- [Boosting Few-Pixel Robustness Verification via Covering Verification Designs](https://mlsanity.com/paper/2405.10924/) (2024)

## Abstract (arXiv)

Inspired by recent successes with parallel optimization techniques for solving Boolean satisfiability, we investigate a set of strategies and heuristics that aim to leverage parallel computing to improve the scalability of neural network verification. We introduce an algorithm based on partitioning the verification problem in an iterative manner and explore two partitioning strategies, that work by partitioning the input space or by case splitting on the phases of the neuron activations, respectively. We also introduce a highly parallelizable pre-processing algorithm that uses the neuron activation phases to simplify the neural network verification problems. An extensive experimental evaluation shows the benefit of these techniques on both existing benchmarks and new benchmarks from the aviation domain. A preliminary experiment with ultra-scaling our algorithm using a large distributed cloud-based platform also shows promising results.