# Randomized Smoothing Meets Vision-Language Models

arXiv: https://arxiv.org/abs/2509.16088 · HTML: https://mlsanity.com/paper/2509.16088/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in MLLM jailbreaks and adversarial robustness, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Placed in

- Multimodal LLMs / vision-language models / [MLLM jailbreaks and adversarial robustness](https://mlsanity.com/mllm/mllm-jailbreaks-and-adversarial-robustness/)

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [An Introduction to Vision-Language Modeling](https://mlsanity.com/paper/2405.17247/) (2024)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Certified Defense to Image Transformations via Randomized Smoothing](https://mlsanity.com/paper/2002.12463/) (2020)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [Advancing the Robustness of Large Language Models through Self-Denoised Smoothing](https://mlsanity.com/paper/2404.12274/) (2024)
- [Input-Specific Robustness Certification for Randomized Smoothing](https://mlsanity.com/paper/2112.12084/) (2021)
- [Treatment of Statistical Estimation Problems in Randomized Smoothing for Adversarial Robustness](https://mlsanity.com/paper/2406.17830/) (2024)
- [Estimating the Robustness Radius for Randomized Smoothing with 100× Sample Efficiency](https://mlsanity.com/paper/2404.17371/) (2024)

## Built on by (most cited first, 1 of 1)

- [Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing](https://mlsanity.com/paper/2605.12876/) (2026)

## Abstract (arXiv)

Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its application to generative models is unclear, since their outputs are sequences rather than labels. We resolve this by connecting generative outputs to an oracle classification task and showing that RS can still be enabled: the final response can be classified as a discrete action (e.g., service-robot commands in VLAs), as harmful vs. harmless (content moderation or toxicity detection in VLMs), or even applying oracles to cluster answers into semantically equivalent ones. Provided that the error rate for the oracle classifier comparison is bounded, we develop the theory that associates the number of samples with the corresponding robustness radius. We further derive improved scaling laws analytically relating the certified radius and accuracy to the number of samples, showing that the earlier result of 2 to 3 orders of magnitude fewer samples sufficing with minimal loss remains valid even under weaker assumptions. Together, these advances make robustness certification both well-defined and computationally feasible for state-of-the-art VLMs, as validated against recent jailbreak-style adversarial attacks.