# Laplace-Bridged Randomized Smoothing for Fast Certified Robustness

arXiv: https://arxiv.org/abs/2604.24993 · HTML: https://mlsanity.com/paper/2604.24993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 63 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 30 of 43)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [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)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [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)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Adversarial Risk and the Dangers of Evaluating Against Weak Attacks](https://mlsanity.com/paper/1802.05666/) (2018)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius](https://mlsanity.com/paper/2001.02378/) (2020)
- [A Comprehensive Study on Robustness of Image Classification Models: Benchmarking and Rethinking](https://mlsanity.com/paper/2302.14301/) (2023)
- [On Certifying Robustness against Backdoor Attacks via Randomized Smoothing](https://mlsanity.com/paper/2002.11750/) (2020)
- [Consistency Regularization for Certified Robustness of Smoothed Classifiers](https://mlsanity.com/paper/2006.04062/) (2020)
- [Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothing](https://mlsanity.com/paper/1912.09899/) (2019)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Random Smoothing Might be Unable to Certify ℓ_∞ Robustness for High-Dimensional Images](https://mlsanity.com/paper/2002.03517/) (2020)

## Abstract (arXiv)

Randomized Smoothing (RS) offers formal ℓ2 guarantees for arbitrary base classifiers but faces two key practical bottlenecks: (i) it often relies on noise-augmented training to achieve nontrivial certificates, which increases training cost, can reduce clean accuracy, and weakens RS as a genuinely post-hoc defense; and (ii) certification is computationally expensive, typically requiring tens of thousands of noisy forward passes per input, which hinders deployment, especially on resource-constrained edge devices. To address both limitations, we propose Laplace-Bridged Smoothing (LBS), an analytic reformulation of RS that replaces high-dimensional input-space Monte Carlo (MC) sampling with efficient computations in a low-dimensional probability space. LBS preserves formal robustness guarantees without requiring noise-augmented training while substantially reducing certification burden. On CIFAR-10 and ImageNet, LBS attains stronger certified robustness than RS and reduces per-sample certification cost by nearly an order of magnitude. Notably, on NVIDIA Jetson Orin Nano and Raspberry Pi 4, LBS achieves speedups of up to 494×, enabling practical certified deployment on real-world edge devices. Finally, we provide theoretical justification for the analytic formulation and certificate validity of LBS.