Research map / Adversarial robustness and security / Certified and empirical robustness

Clustered Randomized Smoothing for Stochastic Prediction Functions

NeurIPS 2026 · Adversarial robustness and security › Certified and empirical robustness · approach: Randomized smoothing certification · 0 citations (OpenAlex)

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Proposes clustered α-smoothing, which clusters noisy predictor outputs, α-trims within each cluster, and combines the locally smoothed predictions as a mixture, with probabilistic robustness certificates for multi-modal stochastic regressors.

Problem

Randomized smoothing for regression collapses multi-modal outputs of stochastic neural predictors into an averaged, uninformative prediction, which hurts safety-critical trajectory prediction and robust control.

Approach

Partition noisy prediction samples by clustering in output space, apply alpha-trimmed smoothing within each cluster, and combine per-cluster predictions as a mixture weighted by cluster size; certify via Neyman-Pearson bounds, union bound, and Clopper-Pearson estimates of cluster probabilities.

Key results

• On 200 L-GAP inputs, clustered alpha-smoothing reduces mean 2-Wasserstein distance to the noisy predictor by 27% vs alpha-smoothing (3.80 vs 5.18).
• Safety analysis risk rate on L-GAP: 2.5% for clustered smoothing vs 16.5% for alpha-smoothing and 7.5% for RS-Reg.
• In quadrotor control, clustered smoothing reduces collision rate by 81% relative to the state-of-the-art randomized smoothing (9 vs 48 crashes out of 100 for alpha-smoothing).

Surprising findings

• Certified lower bounds become more conservative as new clusters are added, requiring smaller radius or larger noise in highly multi-modal settings.

Limitations

• Certified sets must be disjoint convex regions, which is restrictive for non-separable clusters.
• Certification is with respect to the smoothed predictor, not the base predictor, which can break parity in simulations.
• Randomized smoothing requires repeated inference, costly for large networks; bounds become conservative with more clusters.

Experimental setup

Datasets: L-GAP NuScenes

Benchmarks: L-GAP trajectory prediction quadrotor navigation benchmark

Metrics: 2-Wasserstein distance risk rate collision rate certified probability lower bound

Baselines: alpha-smoothing RS-Reg nominal policy

Builds on: randomized smoothing alpha-smoothing Clopper-Pearson Neyman-Pearson lemma

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