# Toward Principled LLM Safety Testing: Solving the Jailbreak Oracle Problem

arXiv: https://arxiv.org/abs/2506.17299 · HTML: https://mlsanity.com/paper/2506.17299/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Jailbreaking, one of 12 directions in LLM safety and security.
- Builds on 41 of its 53 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Jailbreaking Black Box Large Language Models in Twenty Queries](https://mlsanity.com/paper/2310.08419/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models](https://mlsanity.com/paper/2310.04451/) (2023)
- [Tree of Attacks: Jailbreaking Black-Box LLMs Automatically](https://mlsanity.com/paper/2312.02119/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [The Instruction Hierarchy: Training LLMs to Prioritize Privileged Instructions](https://mlsanity.com/paper/2404.13208/) (2024)
- [Jailbreaking Leading Safety-Aligned LLMs with Simple Adaptive Attacks](https://mlsanity.com/paper/2404.02151/) (2024)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Improving Alignment and Robustness with Circuit Breakers](https://mlsanity.com/paper/2406.04313/) (2024)
- [Defending Against Indirect Prompt Injection Attacks With Spotlighting](https://mlsanity.com/paper/2403.14720/) (2024)
- [Jailbreak Attacks and Defenses Against Large Language Models: A Survey](https://mlsanity.com/paper/2407.04295/) (2024)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [Constitutional Classifiers: Defending against Universal Jailbreaks across Thousands of Hours of Red Teaming](https://mlsanity.com/paper/2501.18837/) (2025)
- [Latent Adversarial Training Improves Robustness to Persistent Harmful Behaviors in LLMs](https://mlsanity.com/paper/2407.15549/) (2024)
- [AmpleGCG: Learning a Universal and Transferable Generative Model of Adversarial Suffixes for Jailbreaking Both Open and Closed LLMs](https://mlsanity.com/paper/2404.07921/) (2024)

## Built on by (most cited first, 4 of 4)

- [Quant Fever, Reasoning Blackholes, Schrodinger's Compliance, and More: Probing GPT-OSS-20B](https://mlsanity.com/paper/2509.23882/) (2025)
- [LLM Reinforcement in Context](https://mlsanity.com/paper/2511.12782/) (2025)
- [Invasive Context Engineering to Control Large Language Models](https://mlsanity.com/paper/2512.03001/) (2025)
- [Toward a Principled Framework for Agent Safety Measurement](https://mlsanity.com/paper/2605.01644/) (2026)

## Abstract (arXiv)

As large language models (LLMs) become increasingly deployed in safety-critical applications, the lack of systematic methods to assess their vulnerability to jailbreak attacks presents a critical security gap. We introduce the jailbreak oracle problem: given a model, prompt, and decoding strategy, determine whether a jailbreak response can be generated with likelihood exceeding a specified threshold. This formalization enables a principled study of jailbreak vulnerabilities. Answering the jailbreak oracle problem poses significant computational challenges, as the search space grows exponentially with response length. We present Boa, the first system designed for efficiently solving the jailbreak oracle problem. Boa employs a two-phase search strategy: (1) breadth-first sampling to identify easily accessible jailbreaks, followed by (2) depth-first priority search guided by fine-grained safety scores to systematically explore promising yet low-probability paths. Boa enables rigorous security assessments including systematic defense evaluation, standardized comparison of red team attacks, and model certification under extreme adversarial conditions. Code is available at https://github.com/shuyilinn/BOA/tree/mlsys2026ae