# Expediting Neural Network Verification via Network Reduction

arXiv: https://arxiv.org/abs/2308.03330 · HTML: https://mlsanity.com/paper/2308.03330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 7 Aug 2023.

## Builds on (most cited first, 29 of 29)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [An Abstraction-Based Framework for Neural Network Verification](https://mlsanity.com/paper/1910.14574/) (2019)
- [The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification](https://mlsanity.com/paper/2006.14076/) (2020)
- [Neural Network Branching for Neural Network Verification](https://mlsanity.com/paper/1912.01329/) (2019)
- [Scaling Polyhedral Neural Network Verification on GPUs](https://mlsanity.com/paper/2007.10868/) (2020)
- [Fastened CROWN: Tightened Neural Network Robustness Certificates](https://mlsanity.com/paper/1912.00574/) (2019)
- [The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Results](https://mlsanity.com/paper/2212.10376/) (2022)
- [Lagrangian Decomposition for Neural Network Verification](https://mlsanity.com/paper/2002.10410/) (2020)
- [Abstraction based Output Range Analysis for Neural Networks](https://mlsanity.com/paper/2007.09527/) (2020)
- [Improving Neural Network Verification through Spurious Region Guided Refinement](https://mlsanity.com/paper/2010.07722/) (2020)
- [An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks](https://mlsanity.com/paper/2201.01978/) (2022)
- [DNNV: A Framework for Deep Neural Network Verification](https://mlsanity.com/paper/2105.12841/) (2021)
- [Abstract Neural Networks](https://mlsanity.com/paper/2009.05660/) (2020)
- [Debona: Decoupled Boundary Network Analysis for Tighter Bounds and Faster Adversarial Robustness Proofs](https://mlsanity.com/paper/2006.09040/) (2020)
- [Fully Automatic Neural Network Reduction for Formal Verification](https://mlsanity.com/paper/2305.01932/) (2023)

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

- [SimCert: Probabilistic Certification for Behavioral Similarity in Deep Neural Network Compression](https://mlsanity.com/paper/2603.14818/) (2026)

## Abstract (arXiv)

A wide range of verification methods have been proposed to verify the safety properties of deep neural networks ensuring that the networks function correctly in critical applications. However, many well-known verification tools still struggle with complicated network architectures and large network sizes. In this work, we propose a network reduction technique as a pre-processing method prior to verification. The proposed method reduces neural networks via eliminating stable ReLU neurons, and transforming them into a sequential neural network consisting of ReLU and Affine layers which can be handled by the most verification tools. We instantiate the reduction technique on the state-of-the-art complete and incomplete verification tools, including alpha-beta-crown, VeriNet and PRIMA. Our experiments on a large set of benchmarks indicate that the proposed technique can significantly reduce neural networks and speed up existing verification tools. Furthermore, the experiment results also show that network reduction can improve the availability of existing verification tools on many networks by reducing them into sequential neural networks.