# Revisiting Neuron Coverage for DNN Testing: A Layer-Wise and Distribution-Aware Criterion

arXiv: https://arxiv.org/abs/2112.01955 · HTML: https://mlsanity.com/paper/2112.01955/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 3 Dec 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNet](https://mlsanity.com/paper/1904.00760/) (2019)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [DRIT++: Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1905.01270/) (2019)
- [Guiding Deep Learning System Testing using Surprise Adequacy](https://mlsanity.com/paper/1808.08444/) (2018)
- [Glow: Graph Lowering Compiler Techniques for Neural Networks](https://mlsanity.com/paper/1805.00907/) (2018)
- [TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing](https://mlsanity.com/paper/1807.10875/) (2018)
- [TVM: An Automated End-to-End Optimizing Compiler for Deep Learning](https://mlsanity.com/paper/1802.04799/) (2018)
- [Testing Deep Neural Networks](https://mlsanity.com/paper/1803.04792/) (2018)
- [Exploring Disentangled Feature Representation Beyond Face Identification](https://mlsanity.com/paper/1804.03487/) (2018)
- [Reducing DNN Labelling Cost using Surprise Adequacy: An Industrial Case Study for Autonomous Driving](https://mlsanity.com/paper/2006.00894/) (2020)
- [Interpreting and Disentangling Feature Components of Various Complexity from DNNs](https://mlsanity.com/paper/2006.15920/) (2020)

## Built on by (most cited first, 11 of 11)

- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [Understanding the Effectiveness of Coverage Criteria for Large Language Models: A Special Angle from Jailbreak Attacks](https://mlsanity.com/paper/2408.15207/) (2024)
- [Efficient Input-level Backdoor Defense on Text-to-Image Synthesis via Neuron Activation Variation](https://mlsanity.com/paper/2503.06453/) (2025)
- [Exposing the Ghost in the Transformer: Abnormal Detection for Large Language Models via Hidden State Forensics](https://mlsanity.com/paper/2504.00446/) (2025)
- [Precise and Generalized Robustness Certification for Neural Networks](https://mlsanity.com/paper/2306.06747/) (2023)
- [A3Rank: Augmentation Alignment Analysis for Prioritizing Overconfident Failing Samples for Deep Learning Models](https://mlsanity.com/paper/2407.14114/) (2024)
- [DANDI: Diffusion as Normative Distribution for Deep Neural Network Input](https://mlsanity.com/paper/2502.02910/) (2025)
- [Robust Black-box Testing of Deep Neural Networks using Co-Domain Coverage](https://mlsanity.com/paper/2408.06766/) (2024)
- [Towards Understanding Deep Learning Model in Image Recognition via Coverage Test](https://mlsanity.com/paper/2505.08814/) (2025)
- [Learnable Weighting of Intra-Attribute Distances for Categorical Data Clustering with Nominal and Ordinal Attributes](https://mlsanity.com/paper/2607.05464/) (2026)
- [RepTran: Search-Based Repair of Transformer Models](https://mlsanity.com/paper/2607.11193/) (2026)

## Abstract (arXiv)

Various deep neural network (DNN) coverage criteria have been proposed to assess DNN test inputs and steer input mutations. The coverage is characterized via neurons having certain outputs, or the discrepancy between neuron outputs. Nevertheless, recent research indicates that neuron coverage criteria show little correlation with test suite quality. In general, DNNs approximate distributions, by incorporating hierarchical layers, to make predictions for inputs. Thus, we champion to deduce DNN behaviors based on its approximated distributions from a layer perspective. A test suite should be assessed using its induced layer output distributions. Accordingly, to fully examine DNN behaviors, input mutation should be directed toward diversifying the approximated distributions. This paper summarizes eight design requirements for DNN coverage criteria, taking into account distribution properties and practical concerns. We then propose a new criterion, NeuraL Coverage (NLC), that satisfies all design requirements. NLC treats a single DNN layer as the basic computational unit (rather than a single neuron) and captures four critical properties of neuron output distributions. Thus, NLC accurately describes how DNNs comprehend inputs via approximated distributions. We demonstrate that NLC is significantly correlated with the diversity of a test suite across a number of tasks (classification and generation) and data formats (image and text). Its capacity to discover DNN prediction errors is promising. Test input mutation guided by NLC results in a greater quality and diversity of exposed erroneous behaviors.