# Smooth-Reduce: Leveraging Patches for Improved Certified Robustness

arXiv: https://arxiv.org/abs/2205.06154 · HTML: https://mlsanity.com/paper/2205.06154/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 30 of 31)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Patches Are All You Need?](https://mlsanity.com/paper/2201.09792/) (2022)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius](https://mlsanity.com/paper/2001.02378/) (2020)
- [SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustness](https://mlsanity.com/paper/2111.09277/) (2021)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [On the Certified Robustness for Ensemble Models and Beyond](https://mlsanity.com/paper/2107.10873/) (2021)
- [Improved, Deterministic Smoothing for L_1 Certified Robustness](https://mlsanity.com/paper/2103.10834/) (2021)
- [Data-Dependent Randomized Smoothing](https://mlsanity.com/paper/2012.04351/) (2020)
- [Towards Proving the Adversarial Robustness of Deep Neural Networks](https://mlsanity.com/paper/1709.02802/) (2017)
- [Intriguing Properties of Input-dependent Randomized Smoothing](https://mlsanity.com/paper/2110.05365/) (2021)
- [Provably Minimally-Distorted Adversarial Examples](https://mlsanity.com/paper/1709.10207/) (2017)
- [Defense Against the Dark Arts: An overview of adversarial example security research and future research directions](https://mlsanity.com/paper/1806.04169/) (2018)
- [Enhancing Certified Robustness via Smoothed Weighted Ensembling](https://mlsanity.com/paper/2005.09363/) (2020)

## Built on by (most cited first, 1 of 1)

- [Rethinking Randomized Smoothing from the Perspective of Scalability](https://mlsanity.com/paper/2312.12608/) (2023)

## Abstract (arXiv)

Randomized smoothing (RS) has been shown to be a fast, scalable technique for certifying the robustness of deep neural network classifiers. However, methods based on RS require augmenting data with large amounts of noise, which leads to significant drops in accuracy. We propose a training-free, modified smoothing approach, Smooth-Reduce, that leverages patching and aggregation to provide improved classifier certificates. Our algorithm classifies overlapping patches extracted from an input image, and aggregates the predicted logits to certify a larger radius around the input. We study two aggregation schemes -- max and mean -- and show that both approaches provide better certificates in terms of certified accuracy, average certified radii and abstention rates as compared to concurrent approaches. We also provide theoretical guarantees for such certificates, and empirically show significant improvements over other randomized smoothing methods that require expensive retraining. Further, we extend our approach to videos and provide meaningful certificates for video classifiers. A project page can be found at https://nyu-dice-lab.github.io/SmoothReduce/