# Statistically Robust Neural Network Classification

arXiv: https://arxiv.org/abs/1912.04884 · HTML: https://mlsanity.com/paper/1912.04884/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2019.

## Built on by (most cited first, 16 of 16)

- [SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretability](https://mlsanity.com/paper/2208.09418/) (2022)
- [Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurance](https://mlsanity.com/paper/2112.00646/) (2021)
- [ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbation](https://mlsanity.com/paper/2402.15429/) (2024)
- [Hierarchical Distribution-Aware Testing of Deep Learning](https://mlsanity.com/paper/2205.08589/) (2022)
- [PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks](https://mlsanity.com/paper/2408.09262/) (2024)
- [What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systems](https://mlsanity.com/paper/2307.11784/) (2023)
- [When to Trust AI: Advances and Challenges for Certification of Neural Networks](https://mlsanity.com/paper/2309.11196/) (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)
- [Investigating the Corruption Robustness of Image Classifiers with Random Lp-norm Corruptions](https://mlsanity.com/paper/2305.05400/) (2023)
- [Reachability Verification Based Reliability Assessment for Deep Reinforcement Learning Controlled Robotics and Autonomous Systems](https://mlsanity.com/paper/2210.14991/) (2022)
- [Utilizing Class Separation Distance for the Evaluation of Corruption Robustness of Machine Learning Classifiers](https://mlsanity.com/paper/2206.13405/) (2022)
- [PRBench: A Standardized Probabilistic Robustness Benchmark](https://mlsanity.com/paper/2511.01724/) (2025)
- [Non-Parametric Probabilistic Robustness: A Conservative Risk Estimator under Unknown Perturbation Distributions](https://mlsanity.com/paper/2511.17380/) (2025)
- [Stylized Synthetic Augmentation further improves Corruption Robustness](https://mlsanity.com/paper/2512.15675/) (2025)
- [Probabilistic Adversarial Training](https://mlsanity.com/paper/2609.39798/) (2026)

## Abstract (arXiv)

Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being generated by an explicit adversary, while the poor train--test generalization of adversarial metrics can limit their usage to simple problems. Motivated by this, we develop a probabilistic robust risk framework, the statistically robust risk (SRR), which considers pointwise corruption distributions, as opposed to worst-case adversaries. The SRR provides a distinct and complementary measure of robust performance, compared to natural and adversarial risk. We show that the SRR admits estimation and training schemes which are as simple and efficient as for the natural risk: these simply require noising the inputs, but with a principled derivation for exactly how and why this should be done. Furthermore, we demonstrate both theoretically and experimentally that it can provide superior generalization performance compared with adversarial risks, enabling application to high-dimensional datasets.