# Extending Neural Network Verification to a Larger Family of Piece-wise Linear Activation Functions

arXiv: https://arxiv.org/abs/2311.10780 · HTML: https://mlsanity.com/paper/2311.10780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 59 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 21 of 21)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [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)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A Survey of Deep Learning Applications to Autonomous Vehicle Control](https://mlsanity.com/paper/1912.10773/) (2019)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks](https://mlsanity.com/paper/1811.12395/) (2018)
- [Scalable Object Detection using Deep Neural Networks](https://mlsanity.com/paper/1312.2249/) (2013)
- [Efficient Neural Network Analysis with Sum-of-Infeasibilities](https://mlsanity.com/paper/2203.11201/) (2022)
- [Fast Geometric Projections for Local Robustness Certification](https://mlsanity.com/paper/2002.04742/) (2020)
- [Intriguing Properties of Adversarial Examples](https://mlsanity.com/paper/1711.02846/) (2017)
- [Probabilistic Verification of Neural Networks Against Group Fairness](https://mlsanity.com/paper/2107.08362/) (2021)
- [A Survey on Activation Functions and their relation with Xavier and He Normal Initialization](https://mlsanity.com/paper/2004.06632/) (2020)
- [Optimized Symbolic Interval Propagation for Neural Network Verification](https://mlsanity.com/paper/2212.08567/) (2022)

## Abstract (arXiv)

In this paper, we extend an available neural network verification technique to support a wider class of piece-wise linear activation functions. Furthermore, we extend the algorithms, which provide in their original form exact respectively over-approximative results for bounded input sets represented as start sets, to allow also unbounded input set. We implemented our algorithms and demonstrated their effectiveness in some case studies.