# Reachability Analysis of Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2106.12074 · HTML: https://mlsanity.com/paper/2106.12074/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 30 of 39)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [SparseFool: a few pixels make a big difference](https://mlsanity.com/paper/1811.02248/) (2018)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [Automatic Instrument Segmentation in Robot-Assisted Surgery Using Deep Learning](https://mlsanity.com/paper/1803.01207/) (2018)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)

## Built on by (most cited first, 4 of 4)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks](https://mlsanity.com/paper/2201.01978/) (2022)
- [Neural Network Repair with Reachability Analysis](https://mlsanity.com/paper/2108.04214/) (2021)
- [Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes](https://mlsanity.com/paper/2503.10840/) (2025)

## Abstract (arXiv)

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address this challenge, we propose an approach to compute the exact reachable sets of a network given an input domain, where the reachable set is represented by the face lattice structure. Besides the computation of reachable sets, our approach is also capable of backtracking to the input domain given an output reachable set. Therefore, a full analysis of a network's behavior can be realized. In addition, an approach for fast analysis is also introduced, which conducts fast computation of reachable sets by considering selected sensitive neurons in each layer. The exact pixel-level reachability analysis method is evaluated on a CNN for the CIFAR10 dataset and compared to related works. The fast analysis method is evaluated over a CNN CIFAR10 dataset and VGG16 architecture for the ImageNet dataset.