# Depth, Not Breadth: Best-of-N Jailbreaking Beyond Surface Noise

arXiv: https://arxiv.org/abs/2607.26639 · HTML: https://mlsanity.com/paper/2607.26639/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Jailbreaking, one of 12 directions in LLM safety and security.
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [LLM Self Defense: By Self Examination, LLMs Know They Are Being Tricked](https://mlsanity.com/paper/2308.07308/) (2023)
- [Defense Against the Dark Prompts: Mitigating Best-of-N Jailbreaking with Prompt Evaluation](https://mlsanity.com/paper/2502.00580/) (2025)
- [Statistical Estimation of Adversarial Risk in Large Language Models under Best-of-N Sampling](https://mlsanity.com/paper/2601.22636/) (2026)
- [The Great Pretender: A Stochasticity Problem in LLM Jailbreak](https://mlsanity.com/paper/2605.14418/) (2026)
- [ContextualJailbreak: Evolutionary Red-Teaming via Simulated Conversational Priming](https://mlsanity.com/paper/2605.02647/) (2026)
- [Compositional Jailbreaking: An Empirical Analysis of Mutator Chain Interactions in Aligned LLMs](https://mlsanity.com/paper/2605.15598/) (2026)

## Abstract (arXiv)

Best-of-N jailbreaking spends a query budget on surface variation, scrambling and recasing a request until one draw lands. We ask what the same search buys when it wraps a structural encoding instead. Against SAGE, a published self-check defense, best-of-N over a code-completion encoding reaches 67, 22 and 15% of behaviors on three open-weight targets, where that encoding fired once reaches at most 4.7% and the published character search at full budget at most 3.0%: 9 to 68 times the sum of the parts, with bootstrap intervals clearing both ingredients on every target. We report the operative figure beside the headline rather than the headline alone: at the actionable severity threshold those cells read 24, 8 and 1 behaviors (95% interval [13, 28], [3, 13], [0, 3]). A 2x2 on Llama-3.1-8B holding encoding and variation apart shows that SAGE and a classifier gate fail to different factors: SAGE is broken by the depth of the encoding (7 -> 67 behaviors at fixed variation) and the gate by the breadth of the variation (13 -> 57 at fixed encoding). Per-draw reporting also overstates robustness, because an attacker who may try N times experiences the maximum over draws while safety results are reported as means: on one target SAGE stops 99.8% of individual draws yet loses at least as many behaviors to a repeat attacker (12) as a classifier gate that stops 95.6% (10). Removing the target's sampling shrinks SAGE's coverage, relative to its own level, by 59, 76, 82 and 29 percentage points more than an undefended control's, against 25, -5, 8 and 2 for a defense whose verdict comes from a fixed shadow model. The design that loses is the one fusing screening and answering into a single generation, so every attacker draw redraws the safety decision as well. The prescription is architectural, not free: do not fuse screening with generation.