# Harnessing Neuron Stability to Improve DNN Verification

arXiv: https://arxiv.org/abs/2401.14412 · HTML: https://mlsanity.com/paper/2401.14412/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 83 references that are in the map.
- First posted on arXiv 19 Jan 2024.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [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)
- [Safety-Enhanced Autonomous Driving Using Interpretable Sensor Fusion Transformer](https://mlsanity.com/paper/2207.14024/) (2022)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (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)
- [Guiding Deep Learning System Testing using Surprise Adequacy](https://mlsanity.com/paper/1808.08444/) (2018)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)](https://mlsanity.com/paper/2301.05815/) (2023)
- [Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition](https://mlsanity.com/paper/2104.06718/) (2021)
- [Scaling Polyhedral Neural Network Verification on GPUs](https://mlsanity.com/paper/2007.10868/) (2020)
- [The Third International Verification of Neural Networks Competition (VNN-COMP 2022): Summary and Results](https://mlsanity.com/paper/2212.10376/) (2022)
- [DeepHyperion: Exploring the Feature Space of Deep Learning-Based Systems through Illumination Search](https://mlsanity.com/paper/2107.06997/) (2021)
- [DNNV: A Framework for Deep Neural Network Verification](https://mlsanity.com/paper/2105.12841/) (2021)
- [End-to-End Deep Learning of Lane Detection and Path Prediction for Real-Time Autonomous Driving](https://mlsanity.com/paper/2102.04738/) (2021)
- [Can pruning improve certified robustness of neural networks?](https://mlsanity.com/paper/2206.07311/) (2022)
- [Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustness](https://mlsanity.com/paper/2206.07839/) (2022)

## Built on by (most cited first, 13 of 13)

- [SoundnessBench: A Soundness Benchmark for Neural Network Verifiers](https://mlsanity.com/paper/2412.03154/) (2024)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [A Survey of Neural Network Robustness Assessment in Image Recognition](https://mlsanity.com/paper/2404.08285/) (2024)
- [ZonoGPT: Towards An Abstract Domain for Verifying Large GPT Models](https://mlsanity.com/paper/2609.34457/) (2026)
- [A Guide to Failure in Machine Learning: Reliability and Robustness from Foundations to Practice](https://mlsanity.com/paper/2503.00563/) (2025)
- [Language Models That Walk the Talk: A Framework for Formal Fairness Certificates](https://mlsanity.com/paper/2505.12767/) (2025)
- [Efficient Certified Reasoning for Binarized Neural Networks](https://mlsanity.com/paper/2507.02916/) (2025)
- [Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees](https://mlsanity.com/paper/2507.17453/) (2025)
- [From Decoupled to Coupled: Robustness Verification for Learning-based Keypoint Detection with Joint Specifications](https://mlsanity.com/paper/2603.05604/) (2026)
- [Lipschitz-Based Robustness Certification Under Floating-Point Execution](https://mlsanity.com/paper/2603.13334/) (2026)
- [Repurposing CLIP to Localize at Pixel Level](https://mlsanity.com/paper/2607.05253/) (2026)
- [Verifying Neural Networks with Reinforcement Learning](https://mlsanity.com/paper/2609.34553/) (2026)
- [CLAD: Constrained Abstract Domain for Neural Network Verification](https://mlsanity.com/paper/2609.34628/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interests in developing effective and scalable DNN verification techniques and tools. In this paper, we present VeriStable, a novel extension of recently proposed DPLL-based constraint DNN verification approach. VeriStable leverages the insight that while neuron behavior may be non-linear across the entire DNN input space, at intermediate states computed during verification many neurons may be constrained to have linear behavior - these neurons are stable. Efficiently detecting stable neurons reduces combinatorial complexity without compromising the precision of abstractions. Moreover, the structure of clauses arising in DNN verification problems shares important characteristics with industrial SAT benchmarks. We adapt and incorporate multi-threading and restart optimizations targeting those characteristics to further optimize DPLL-based DNN verification. We evaluate the effectiveness of VeriStable across a range of challenging benchmarks including fully-connected feedforward networks (FNNs), convolutional neural networks (CNNs) and residual networks (ResNets) applied to the standard MNIST and CIFAR datasets. Preliminary results show that VeriStable is competitive and outperforms state-of-the-art DNN verification tools, including α-β-CROWN and MN-BaB, the first and second performers of the VNN-COMP, respectively.