# A Statistical Approach to Assessing Neural Network Robustness

arXiv: https://arxiv.org/abs/1811.07209 · HTML: https://mlsanity.com/paper/1811.07209/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2018.

## Built on by (most cited first, 30 of 54)

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- [SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretability](https://mlsanity.com/paper/2208.09418/) (2022)
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- [Provable Preimage Under-Approximation for Neural Networks (Full Version)](https://mlsanity.com/paper/2305.03686/) (2023)
- [From Robustness to Explainability and Back Again](https://mlsanity.com/paper/2306.03048/) (2023)
- [Towards Practical Robustness Analysis for DNNs based on PAC-Model Learning](https://mlsanity.com/paper/2101.10102/) (2021)
- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networks](https://mlsanity.com/paper/2212.11138/) (2022)
- [Assessing the Reliability of Deep Learning Classifiers Through Robustness Evaluation and Operational Profiles](https://mlsanity.com/paper/2106.01258/) (2021)
- [Scaling the Convex Barrier with Sparse Dual Algorithms](https://mlsanity.com/paper/2101.05844/) (2021)
- [RoMA: a Method for Neural Network Robustness Measurement and Assessment](https://mlsanity.com/paper/2110.11088/) (2021)
- [Improving the Robustness of Transformer-based Large Language Models with Dynamic Attention](https://mlsanity.com/paper/2311.17400/) (2023)
- [ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbation](https://mlsanity.com/paper/2402.15429/) (2024)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [QEBVerif: Quantization Error Bound Verification of Neural Networks](https://mlsanity.com/paper/2212.02781/) (2022)
- [ε-weakened Robustness of Deep Neural Networks](https://mlsanity.com/paper/2110.15764/) (2021)
- [Hierarchical Distribution-Aware Testing of Deep Learning](https://mlsanity.com/paper/2205.08589/) (2022)
- [TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Models](https://mlsanity.com/paper/2308.05985/) (2023)
- [PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks](https://mlsanity.com/paper/2408.09262/) (2024)
- [Risk Verification of Stochastic Systems with Neural Network Controllers](https://mlsanity.com/paper/2209.09881/) (2022)
- [What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systems](https://mlsanity.com/paper/2307.11784/) (2023)
- [Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Survey](https://mlsanity.com/paper/2409.18214/) (2024)
- [Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guide](https://mlsanity.com/paper/2502.14833/) (2025)
- [Hierarchical Testing with Rabbit Optimization for Industrial Cyber-Physical Systems](https://mlsanity.com/paper/2507.04100/) (2025)
- [Certifiable Deep Importance Sampling for Rare-Event Simulation of Black-Box Systems](https://mlsanity.com/paper/2111.02204/) (2021)
- [Reachability Verification Based Reliability Assessment for Deep Reinforcement Learning Controlled Robotics and Autonomous Systems](https://mlsanity.com/paper/2210.14991/) (2022)

## Abstract (arXiv)

We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.