# Towards Realistic Guarantees: A Probabilistic Certificate for SmoothLLM

arXiv: https://arxiv.org/abs/2511.18721 · HTML: https://mlsanity.com/paper/2511.18721/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Jailbreaking, one of 12 directions in LLM safety and security.
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

- LLM safety and security / [Jailbreaking](https://mlsanity.com/safety/jailbreaking/)

## Builds on (most cited first, 6 of 6)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [SmoothLLM: Defending Large Language Models Against Jailbreaking Attacks](https://mlsanity.com/paper/2310.03684/) (2023)
- [Certified Defenses for Adversarial Patches](https://mlsanity.com/paper/2003.06693/) (2020)

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

- [Safety, Security, and Cognitive Risks in World Models](https://mlsanity.com/paper/2604.01346/) (2026)

## Abstract (arXiv)

The SmoothLLM defense provides a certification guarantee against jailbreaking attacks, but it relies on a strict "k-unstable" assumption that rarely holds in practice. This strong assumption can limit the trustworthiness of the provided safety certificate. In this work, we address this limitation by introducing a more realistic probabilistic framework, "(k, varepsilon)-unstable," to certify defenses against diverse jailbreaking attacks, from gradient-based (GCG) to semantic (PAIR). We derive a new, data-informed lower bound on SmoothLLM's defense probability by incorporating empirical models of attack success, providing a more trustworthy and practical safety certificate. By introducing the notion of (k, varepsilon)-unstable, our framework provides practitioners with actionable safety guarantees, enabling them to set certification thresholds that better reflect the real-world behavior of LLMs. Ultimately, this work contributes a practical and theoretically-grounded mechanism to make LLMs more resistant to the exploitation of their safety alignments, a critical challenge in secure AI deployment.