# Get Global Guarantees: On the Probabilistic Nature of Perturbation Robustness

arXiv: https://arxiv.org/abs/2508.19183 · HTML: https://mlsanity.com/paper/2508.19183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [PEGASUS: Pre-training with Extracted Gap-sentences for Abstractive Summarization](https://mlsanity.com/paper/1912.08777/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Protein-Ligand Scoring with Convolutional Neural Networks](https://mlsanity.com/paper/1612.02751/) (2016)
- [An SMT-Based Approach for Verifying Binarized Neural Networks](https://mlsanity.com/paper/2011.02948/) (2020)
- [Fast Certified Robust Training with Short Warmup](https://mlsanity.com/paper/2103.17268/) (2021)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Analyzing Deep Neural Networks with Symbolic Propagation: Towards Higher Precision and Faster Verification](https://mlsanity.com/paper/1902.09866/) (2019)
- [PRoA: A Probabilistic Robustness Assessment against Functional Perturbations](https://mlsanity.com/paper/2207.02036/) (2022)
- [No driver, No Regulation? --Online Legal Driving Behavior Monitoring for Self-driving Vehicles](https://mlsanity.com/paper/2212.04156/) (2022)
- [Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors](https://mlsanity.com/paper/2405.11547/) (2024)
- [Adapting and evaluating a deep learning language model for clinical why-question answering](https://mlsanity.com/paper/1911.05604/) (2019)
- [An Ensemble Deep Learning-based Cyber-Attack Detection in Industrial Control System](https://mlsanity.com/paper/2005.00936/) (2020)
- [How Does Bayes Error Limit Probabilistic Robust Accuracy](https://mlsanity.com/paper/2405.14923/) (2024)
- [Towards Precise Observations of Neural Model Robustness in Classification](https://mlsanity.com/paper/2404.16457/) (2024)

## Abstract (arXiv)

In safety-critical deep learning applications, robustness measures the ability of neural models that handle imperceptible perturbations in input data, which may lead to potential safety hazards. Existing pre-deployment robustness assessment methods typically suffer from significant trade-offs between computational cost and measurement precision, limiting their practical utility. To address these limitations, this paper conducts a comprehensive comparative analysis of existing robustness definitions and associated assessment methodologies. We propose tower robustness to evaluate robustness, which is a novel, practical metric based on hypothesis testing to quantitatively evaluate probabilistic robustness, enabling more rigorous and efficient pre-deployment assessments. Our extensive comparative evaluation illustrates the advantages and applicability of our proposed approach, thereby advancing the systematic understanding and enhancement of model robustness in safety-critical deep learning applications.