# Clustered Randomized Smoothing for Stochastic Prediction Functions

arXiv: https://arxiv.org/abs/2608.12037 · HTML: https://mlsanity.com/paper/2608.12037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 30 of 34)

- [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)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [Boosting the Transferability of Adversarial Attacks with Reverse Adversarial Perturbation](https://mlsanity.com/paper/2210.05968/) (2022)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Data-Dependent Randomized Smoothing](https://mlsanity.com/paper/2012.04351/) (2020)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)
- [Probabilistic Mixture-of-Experts for Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2104.09122/) (2021)
- [Wasserstein Smoothing: Certified Robustness against Wasserstein Adversarial Attacks](https://mlsanity.com/paper/1910.10783/) (2019)
- [Intriguing Properties of Input-dependent Randomized Smoothing](https://mlsanity.com/paper/2110.05365/) (2021)
- [Diffusion Policy Attacker: Crafting Adversarial Attacks for Diffusion-based Policies](https://mlsanity.com/paper/2405.19424/) (2024)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programming](https://mlsanity.com/paper/2306.10742/) (2023)
- [CluCERT: Certifying LLM Robustness via Clustering-Guided Denoising Smoothing](https://mlsanity.com/paper/2512.08967/) (2025)
- [TrajFlow: Learning Distributions over Trajectories for Human Behavior Prediction](https://mlsanity.com/paper/2304.05166/) (2023)
- [RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothing](https://mlsanity.com/paper/2405.08892/) (2024)

## Abstract (arXiv)

Modern stochastic predictors can model rich, multi-modal outcome distributions. However, this expressive power comes with challenges in ensuring robust predictions - a critical requirement in safety-critical domains. Randomized smoothing is a leading technique for improving robustness, particularly against adversarial perturbations. Yet, in stochastic multi-modal regression settings, randomized smoothing often fails due to mode collapse, yielding averaged predictions that do not reflect the underlying distribution. To address this limitation, we propose clustered α-smoothing, a framework that (1) partitions noisy samples using an arbitrary clustering algorithm, (2) applies α-smoothing locally within each cluster, and (3) combines the resulting predictions into a mixture distribution. By interpreting the smoothing distribution as a mixture of α-smoothers, we derive a lower bound on the probability that the smoothed prediction lies within a union of compact regions corresponding to distinct modes. We empirically evaluate our framework on two benchmarks, demonstrating substantial improvements over state-of-the-art methods. In stochastic trajectory prediction on a driving simulator dataset, our approach achieves, on average, a 27% lower Wasserstein distance to the ground-truth distribution compared to α-smoothing. In quadrotor control, where modes correspond to distinct feasible paths to a target, our method reduces the collision rate by 81% relative to the state-of-the-art randomized smoothing.