# Testing Deep Neural Networks

arXiv: https://arxiv.org/abs/1803.04792 · HTML: https://mlsanity.com/paper/1803.04792/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2018.

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

- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Taxonomy of Machine Learning Safety: A Survey and Primer](https://mlsanity.com/paper/2106.04823/) (2021)
- [Distribution-Aware Testing of Neural Networks Using Generative Models](https://mlsanity.com/paper/2102.13602/) (2021)
- [Attack as Defense: Characterizing Adversarial Examples using Robustness](https://mlsanity.com/paper/2103.07633/) (2021)
- [Minimal Multi-Layer Modifications of Deep Neural Networks](https://mlsanity.com/paper/2110.09929/) (2021)
- [A Search-Based Testing Approach for Deep Reinforcement Learning Agents](https://mlsanity.com/paper/2206.07813/) (2022)
- [MDPFuzz: Testing Models Solving Markov Decision Processes](https://mlsanity.com/paper/2112.02807/) (2021)
- [Revisiting Neuron Coverage for DNN Testing: A Layer-Wise and Distribution-Aware Criterion](https://mlsanity.com/paper/2112.01955/) (2021)
- [DeepGD: A Multi-Objective Black-Box Test Selection Approach for Deep Neural Networks](https://mlsanity.com/paper/2303.04878/) (2023)
- [Increasing the Confidence of Deep Neural Networks by Coverage Analysis](https://mlsanity.com/paper/2101.12100/) (2021)
- [Customizable Reference Runtime Monitoring of Neural Networks using Resolution Boxes](https://mlsanity.com/paper/2104.14435/) (2021)
- [Fairness Testing of Deep Image Classification with Adequacy Metrics](https://mlsanity.com/paper/2111.08856/) (2021)
- [Online Safety Analysis for LLMs: a Benchmark, an Assessment, and a Path Forward](https://mlsanity.com/paper/2404.08517/) (2024)
- [Software Testing for Machine Learning](https://mlsanity.com/paper/2205.00210/) (2022)
- [Corner case data description and detection](https://mlsanity.com/paper/2101.02494/) (2021)
- [LUNA: A Model-Based Universal Analysis Framework for Large Language Models](https://mlsanity.com/paper/2310.14211/) (2023)
- [Neuron Sensitivity Guided Test Case Selection for Deep Learning Testing](https://mlsanity.com/paper/2307.11011/) (2023)
- [A Survey of Neural Network Robustness Assessment in Image Recognition](https://mlsanity.com/paper/2404.08285/) (2024)
- [Targeted Deep Learning System Boundary Testing](https://mlsanity.com/paper/2408.06258/) (2024)
- [Abstraction and Symbolic Execution of Deep Neural Networks with Bayesian Approximation of Hidden Features](https://mlsanity.com/paper/2103.03704/) (2021)
- [Fixed-Point Code Synthesis For Neural Networks](https://mlsanity.com/paper/2202.02095/) (2022)
- [Is Neuron Coverage Needed to Make Person Detection More Robust?](https://mlsanity.com/paper/2204.10027/) (2022)
- [D-Score: A White-Box Diagnosis Score for CNNs Based on Mutation Operators](https://mlsanity.com/paper/2304.00697/) (2023)
- [Feature Map Testing for Deep Neural Networks](https://mlsanity.com/paper/2307.11563/) (2023)
- [Safe AI -- How is this Possible?](https://mlsanity.com/paper/2201.10436/) (2022)
- [Testing the Channels of Convolutional Neural Networks](https://mlsanity.com/paper/2303.03400/) (2023)
- [Path Analysis for Effective Fault Localization in Deep Neural Networks](https://mlsanity.com/paper/2310.18987/) (2023)
- [Beyond Accuracy: An Empirical Study on Unit Testing in Open-source Deep Learning Projects](https://mlsanity.com/paper/2402.16546/) (2024)
- [DeepKnowledge: Generalisation-Driven Deep Learning Testing](https://mlsanity.com/paper/2403.16768/) (2024)

## Abstract (arXiv)

Deep neural networks (DNNs) have a wide range of applications, and software employing them must be thoroughly tested, especially in safety-critical domains. However, traditional software test coverage metrics cannot be applied directly to DNNs. In this paper, inspired by the MC/DC coverage criterion, we propose a family of four novel test criteria that are tailored to structural features of DNNs and their semantics. We validate the criteria by demonstrating that the generated test inputs guided via our proposed coverage criteria are able to capture undesired behaviours in a DNN. Test cases are generated using a symbolic approach and a gradient-based heuristic search. By comparing them with existing methods, we show that our criteria achieve a balance between their ability to find bugs (proxied using adversarial examples) and the computational cost of test case generation. Our experiments are conducted on state-of-the-art DNNs obtained using popular open source datasets, including MNIST, CIFAR-10 and ImageNet.