# Incremental Randomized Smoothing Certification

arXiv: https://arxiv.org/abs/2305.19521 · HTML: https://mlsanity.com/paper/2305.19521/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 66 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Learning to Optimize Tensor Programs](https://mlsanity.com/paper/1805.08166/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [Certified Robustness to Label-Flipping Attacks via Randomized Smoothing](https://mlsanity.com/paper/2002.03018/) (2020)
- [(De)Randomized Smoothing for Certifiable Defense against Patch Attacks](https://mlsanity.com/paper/2002.10733/) (2020)
- [Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifiers](https://mlsanity.com/paper/1906.04948/) (2019)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [Certified Robustness of Graph Neural Networks against Adversarial Structural Perturbation](https://mlsanity.com/paper/2008.10715/) (2020)
- [Efficient Robustness Certificates for Discrete Data: Sparsity-Aware Randomized Smoothing for Graphs, Images and More](https://mlsanity.com/paper/2008.12952/) (2020)
- [Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothing](https://mlsanity.com/paper/1912.09899/) (2019)
- [Certified Defense to Image Transformations via Randomized Smoothing](https://mlsanity.com/paper/2002.12463/) (2020)
- [TSS: Transformation-Specific Smoothing for Robustness Certification](https://mlsanity.com/paper/2002.12398/) (2020)
- [PointGuard: Provably Robust 3D Point Cloud Classification](https://mlsanity.com/paper/2103.03046/) (2021)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Higher-Order Certification for Randomized Smoothing](https://mlsanity.com/paper/2010.06651/) (2020)
- [Certifying Confidence via Randomized Smoothing](https://mlsanity.com/paper/2009.08061/) (2020)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networks](https://mlsanity.com/paper/2302.02829/) (2023)
- [Incremental Verification of Neural Networks](https://mlsanity.com/paper/2304.01874/) (2023)
- [Certified Robustness of Graph Classification against Topology Attack with Randomized Smoothing](https://mlsanity.com/paper/2009.05872/) (2020)
- [The cost of using exact confidence intervals for a binomial proportion](https://mlsanity.com/paper/1303.1288/) (2013)
- [Shared Certificates for Neural Network Verification](https://mlsanity.com/paper/2109.00542/) (2021)

## Built on by (most cited first, 12 of 12)

- [Treatment of Statistical Estimation Problems in Randomized Smoothing for Adversarial Robustness](https://mlsanity.com/paper/2406.17830/) (2024)
- [Fast Certification of Vision-Language Models Using Incremental Randomized Smoothing](https://mlsanity.com/paper/2311.09024/) (2023)
- [Rethinking Randomized Smoothing from the Perspective of Scalability](https://mlsanity.com/paper/2312.12608/) (2023)
- [BEAVER: An Efficient Deterministic LLM Verifier](https://mlsanity.com/paper/2512.05439/) (2025)
- [Integrating uncertainty quantification into randomized smoothing based robustness guarantees](https://mlsanity.com/paper/2410.20432/) (2024)
- [ARQ: A Mixed-Precision Quantization Framework for Accurate and Certifiably Robust DNNs](https://mlsanity.com/paper/2410.24214/) (2024)
- [Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticity](https://mlsanity.com/paper/2605.01519/) (2026)
- [Support is All You Need for Certified VAE Training](https://mlsanity.com/paper/2504.11831/) (2025)
- [PDA: Text-Augmented Defense Framework for Robust Vision-Language Models against Adversarial Image Attacks](https://mlsanity.com/paper/2604.01010/) (2026)
- [Laplace-Bridged Randomized Smoothing for Fast Certified Robustness](https://mlsanity.com/paper/2604.24993/) (2026)
- [RRISE: Robust Radius Inference via a Surrogate Estimator](https://mlsanity.com/paper/2606.02876/) (2026)
- [Uncovering the Limits of Proof Sharing for Neural Networks](https://mlsanity.com/paper/2608.19351/) (2026)

## Abstract (arXiv)

Randomized smoothing-based certification is an effective approach for obtaining robustness certificates of deep neural networks (DNNs) against adversarial attacks. This method constructs a smoothed DNN model and certifies its robustness through statistical sampling, but it is computationally expensive, especially when certifying with a large number of samples. Furthermore, when the smoothed model is modified (e.g., quantized or pruned), certification guarantees may not hold for the modified DNN, and recertifying from scratch can be prohibitively expensive. We present the first approach for incremental robustness certification for randomized smoothing, IRS. We show how to reuse the certification guarantees for the original smoothed model to certify an approximated model with very few samples. IRS significantly reduces the computational cost of certifying modified DNNs while maintaining strong robustness guarantees. We experimentally demonstrate the effectiveness of our approach, showing up to 3x certification speedup over the certification that applies randomized smoothing of the approximate model from scratch.