Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914561600258048 |
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| author | Delattre, Blaise Wu, Hengyu Caillon, Paul Lim, Wei Yang Bryan Cao, Yang |
| author_facet | Delattre, Blaise Wu, Hengyu Caillon, Paul Lim, Wei Yang Bryan Cao, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing Delattre, Blaise Wu, Hengyu Caillon, Paul Lim, Wei Yang Bryan Cao, Yang Machine Learning 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. |
| title | Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.12876 |