Clustered Randomized Smoothing for Stochastic Prediction Functions

2026-08-12

AI Summary

This work addresses the challenge of mode collapse in randomized multimodal prediction, where conventional randomized smoothing fails to capture the true data distribution, thereby compromising robustness in safety-critical applications. The authors propose a clustered α-smoothing framework that first partitions noisy samples into clusters and then applies α-smoothing locally within each cluster, ultimately aggregating the results into a mixture distribution to preserve multimodal structure. This approach is the first to integrate clustering with local α-smoothing, effectively mitigating mode collapse through mixture-based modeling. The paper also provides a theoretical lower bound on the probability that predictions fall within multimodal regions. Empirical evaluations demonstrate significant improvements: a 27% reduction in Wasserstein distance for autonomous driving trajectory prediction and an 81% decrease in collision rates compared to existing methods in quadrotor control tasks.

Abstract

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.

Problem

• randomized smoothing
• mode collapse
• stochastic prediction
• multi-modal regression
• robustness

Innovation

• clustered randomized smoothing
• multi-modal regression
• mode collapse
• α-smoothing
• robust stochastic prediction