# Distribution-Aware Testing of Neural Networks Using Generative Models

arXiv: https://arxiv.org/abs/2102.13602 · HTML: https://mlsanity.com/paper/2102.13602/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 28 of 28)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Machine Learning Testing: Survey, Landscapes and Horizons](https://mlsanity.com/paper/1906.10742/) (2019)
- [DeepGauge: Multi-Granularity Testing Criteria for Deep Learning Systems](https://mlsanity.com/paper/1803.07519/) (2018)
- [Efficient GAN-Based Anomaly Detection](https://mlsanity.com/paper/1802.06222/) (2018)
- [TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing](https://mlsanity.com/paper/1807.10875/) (2018)
- [DLFuzz: Differential Fuzzing Testing of Deep Learning Systems](https://mlsanity.com/paper/1808.09413/) (2018)
- [Concolic Testing for Deep Neural Networks](https://mlsanity.com/paper/1805.00089/) (2018)
- [Testing Deep Neural Networks](https://mlsanity.com/paper/1803.04792/) (2018)
- [Distribution Matching in Variational Inference](https://mlsanity.com/paper/1802.06847/) (2018)
- [Toward Low-Flying Autonomous MAV Trail Navigation using Deep Neural Networks for Environmental Awareness](https://mlsanity.com/paper/1705.02550/) (2017)
- [Combinatorial Testing for Deep Learning Systems](https://mlsanity.com/paper/1806.07723/) (2018)

## Built on by (most cited first, 22 of 22)

- [When and Why Test Generators for Deep Learning Produce Invalid Inputs: an Empirical Study](https://mlsanity.com/paper/2212.11368/) (2022)
- [Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurance](https://mlsanity.com/paper/2112.00646/) (2021)
- [DeepMetis: Augmenting a Deep Learning Test Set to Increase its Mutation Score](https://mlsanity.com/paper/2109.07514/) (2021)
- [Hierarchical Distribution-Aware Testing of Deep Learning](https://mlsanity.com/paper/2205.08589/) (2022)
- [Generating and Detecting True Ambiguity: A Forgotten Danger in DNN Supervision Testing](https://mlsanity.com/paper/2207.10495/) (2022)
- [What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systems](https://mlsanity.com/paper/2307.11784/) (2023)
- [Decictor: Towards Evaluating the Robustness of Decision-Making in Autonomous Driving Systems](https://mlsanity.com/paper/2402.18393/) (2024)
- [Bridging the Gap between Real-world and Synthetic Images for Testing Autonomous Driving Systems](https://mlsanity.com/paper/2408.13950/) (2024)
- [Benchmarking Generative AI Models for Deep Learning Test Input Generation](https://mlsanity.com/paper/2412.17652/) (2024)
- [Hierarchical Testing with Rabbit Optimization for Industrial Cyber-Physical Systems](https://mlsanity.com/paper/2507.04100/) (2025)
- [Characterizing and Understanding the Behavior of Quantized Models for Reliable Deployment](https://mlsanity.com/paper/2204.04220/) (2022)
- [White-box Testing of NLP models with Mask Neuron Coverage](https://mlsanity.com/paper/2205.05050/) (2022)
- [Provably Valid and Diverse Mutations of Real-World Media Data for DNN Testing](https://mlsanity.com/paper/2112.01956/) (2021)
- [LaF: Labeling-Free Model Selection for Automated Deep Neural Network Reusing](https://mlsanity.com/paper/2204.03994/) (2022)
- [Topological Parallax: A Geometric Specification for Deep Perception Models](https://mlsanity.com/paper/2306.11835/) (2023)
- [A3Rank: Augmentation Alignment Analysis for Prioritizing Overconfident Failing Samples for Deep Learning Models](https://mlsanity.com/paper/2407.14114/) (2024)
- [HOMRS: High Order Metamorphic Relations Selector for Deep Neural Networks](https://mlsanity.com/paper/2107.04863/) (2021)
- [Understanding the Complexity and Its Impact on Testing in ML-Enabled Systems](https://mlsanity.com/paper/2301.03837/) (2023)
- [Adopting Two Supervisors for Efficient Use of Large-Scale Remote Deep Neural Networks](https://mlsanity.com/paper/2304.02654/) (2023)
- [Generating Realistic, Diverse, and Fault-Revealing Inputs with Latent Space Interpolation for Testing Deep Neural Networks](https://mlsanity.com/paper/2503.17630/) (2025)
- [Effort-Optimized, Accuracy-Driven Labelling and Validation of Test Inputs for DL Systems: A Mixed-Integer Linear Programming Approach](https://mlsanity.com/paper/2507.04990/) (2025)
- [Latent Anchor-Driven Test Generation for Deep Neural Networks](https://mlsanity.com/paper/2606.04310/) (2026)

## Abstract (arXiv)

The reliability of software that has a Deep Neural Network (DNN) as a component is urgently important today given the increasing number of critical applications being deployed with DNNs. The need for reliability raises a need for rigorous testing of the safety and trustworthiness of these systems. In the last few years, there have been a number of research efforts focused on testing DNNs. However the test generation techniques proposed so far lack a check to determine whether the test inputs they are generating are valid, and thus invalid inputs are produced. To illustrate this situation, we explored three recent DNN testing techniques. Using deep generative model based input validation, we show that all the three techniques generate significant number of invalid test inputs. We further analyzed the test coverage achieved by the test inputs generated by the DNN testing techniques and showed how invalid test inputs can falsely inflate test coverage metrics. To overcome the inclusion of invalid inputs in testing, we propose a technique to incorporate the valid input space of the DNN model under test in the test generation process. Our technique uses a deep generative model-based algorithm to generate only valid inputs. Results of our empirical studies show that our technique is effective in eliminating invalid tests and boosting the number of valid test inputs generated.