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arXiv · 2605.12876

Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing

Blaise Delattre·Hengyu Wu·Paul Caillon·Wei Yang Bryan Lim·Yang Cao
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Abstract

Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal models, where decisions depend on cross-modal semantics and adversaries can jointly perturb heterogeneous inputs, rendering unimodal certificates insufficient. We introduce a unified randomized smoothing framework for mixed discrete--continuous inputs based on an analytically tractable Neyman--Pearson formulation of the joint worst-case problem. By analyzing the joint likelihood ordering induced by factorized discrete and continuous noise, our approach yields a closed-form, one-dimensional certificate that strictly generalizes both Gaussian (image-only) and discrete (text-only) randomized smoothing. We validate the framework on multimodal safety filtering, providing, to our knowledge, the first model-agnostic Neyman--Pearson certificate for joint discrete-token and continuous-image perturbations in interaction-dependent text--image safety filtering.

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Blaise Delattre, Hengyu Wu, Paul Caillon, Wei Yang Bryan Lim, Yang Cao. 2026-05-13. Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing. https://arxiv.org/abs/2605.12876

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