面向随机预测函数的聚类随机平滑方法
Clustered Randomized Smoothing for Stochastic Prediction Functions
- Delft University of Technology（代尔夫特理工大学）
- University of Stuttgart（斯图加特大学）
- AI4I
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对随机多模态回归中随机平滑的模式崩溃问题，提出聚类α-平滑框架，在两个基准实验中较现有方法显著降低了Wasserstein距离与碰撞率。
AI中文摘要：
现代随机预测器能够对丰富的多模态结果分布进行建模，但这种表达能力带来了确保预测鲁棒性的挑战，而鲁棒性是安全关键领域的关键要求。随机平滑是提升鲁棒性的领先技术，尤其针对对抗性扰动。然而在随机多模态回归场景中，随机平滑常因模式崩溃失效，产生的平均预测无法反映潜在分布。为解决该局限，本文提出聚类α-平滑（clustered α-smoothing）框架：（1）使用任意聚类算法划分带噪样本；（2）在每个簇内局部应用α-平滑；（3）将所得预测组合为混合分布。通过将平滑分布解释为α-平滑器的混合，本文推导了平滑预测落入对应不同模式的紧致区域并集的概率下界。在两个基准上的实验表明，本文框架较现有方法有显著提升：在驾驶模拟器数据集的随机轨迹预测任务中，本文方法较α-平滑平均降低了27%的Wasserstein距离；在四旋翼控制任务中（模式对应到达目标的不同可行路径），本文方法较现有随机平滑降低了81%的碰撞率。
英文摘要：
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.
