Feature-Space Adversarial Robustness Certification for Multimodal Large Language Models

Multimodal large language models (MLLMs) exhibit strong capabilities across diverse applications, yet remain vulnerable to adversarial perturbations that distort their feature representations and induce erroneous predictions. To address this vulnerability, we propose Feature-space Smoothing (FS), a general framework that provides certified robustness guarantees at the feature representation level of MLLMs. We theoretically prove that FS converts a given feature extractor into a smoothed variant that is guaranteed a certified lower bound on the cosine similarity between clean and adversarial features under $\ell_2$-bounded perturbations. Moreover, we establish that the value of this Feature Cosine Similarity Bound (FCSB) is determined by the intrinsic Gaussian robustness score of the given encoder. Building on this insight, we introduce the Gaussian Smoothness Booster (GSB), a plug-and-play module that enhances the Gaussian robustness score of pretrained MLLMs, thereby strengthening the robustness guaranteed by FS, without requiring additional MLLM retraining. Extensive experiments demonstrate that applying the FS to various MLLMs yields strong certified feature-space robustness and consistently leads to robust task-oriented performance across diverse applications.

Provable Robustness in Multimodal Large Language Models via Feature Space Smoothing

Multimodal large language models (MLLMs) exhibit strong capabilities across diverse applications, yet remain vulnerable to adversarial perturbations that distort their feature representations and induce erroneous predictions. To address this vulnerability, we propose the Feature-space Smoothing (FS) and theoretically prove that FS offers certified robustness on the feature representations of MLLMs. Specifically, FS transforms any feature encoder into a smoothed variant that is guaranteed to maintain a certified lower bound on the feature cosine similarity between clean and adversarial representations under $\ell_2$-bounded attacks. Moreover, we indicate that the value of this Feature Cosine Similarity Bound (FCSB) derived from FS can be improved by enlarging the defined Gaussian robustness score on the vanilla encoder. Building upon this, we introduce the Purifier and Smoothness Mapper (PSM), a plug-and-play module that improves the Gaussian robustness score of MLLMs and thus enhances their certified robustness under FS, without requiring any retraining on MLLMs. We demonstrate that the FS with PSM not only provides a strong theoretical robustness guarantee but also exhibits superior empirical performance compared to adversarial training. Extensive experiments across diverse MLLMs and downstream tasks indicate the effectiveness of the FS-PSM, reducing the Attack Success Rate (ASR) of various white-box attacks from nearly 90\% to about 1\%.