# The Distributed Detectability Band Against Marginal-Preserving Attacks

arXiv: https://arxiv.org/abs/2606.10456 · HTML: https://mlsanity.com/paper/2606.10456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [Alignment faking in large language models](https://mlsanity.com/paper/2412.14093/) (2024)
- [Frontier Models are Capable of In-context Scheming](https://mlsanity.com/paper/2412.04984/) (2024)
- [Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety](https://mlsanity.com/paper/2507.11473/) (2025)
- [AI Control: Improving Safety Despite Intentional Subversion](https://mlsanity.com/paper/2312.06942/) (2023)
- [Sycophancy to Subterfuge: Investigating Reward-Tampering in Large Language Models](https://mlsanity.com/paper/2406.10162/) (2024)
- [Natural Emergent Misalignment from Reward Hacking in Production RL](https://mlsanity.com/paper/2511.18397/) (2025)
- [Sabotage Evaluations for Frontier Models](https://mlsanity.com/paper/2410.21514/) (2024)
- [LLMs Can Covertly Sandbag on Capability Evaluations Against Chain-of-Thought Monitoring](https://mlsanity.com/paper/2508.00943/) (2025)

## Abstract (arXiv)

AI-control monitors score individual agent actions to detect misbehavior, but real harm can be distributed across many benign-looking steps, each individually below any per-step alarm. We construct a marginal-preserving, correlation-encoded distributed-sabotage attack using a Gaussian-copula AR(1) construction: the per-step monitor-score marginal is held exactly equal to benign, so mean, max, top-k tail, and threshold monitors (Monitor A) are defeated by construction, while harm is encoded in the temporal correlation structure. We sequence the paper around three reviewer-mandated gates. (1) Realizability gate: the stealthy attack achieves KS-distance to benign of 0.013 (effectively zero) at all tested harm levels up to 3.0, confirming that harm is fully decoupled from the per-step marginal and realizability is not harm-limited. (2) Monitor-A-vs-B reconciliation: we show formally that the attack, built against Monitor A's score marginal, remains marginal-preserving under a different-score Monitor B (the correlation/sequence family: CUSUM, SPRT, HMM-LR, runs test, autocorrelation, windowed logistic), and scope worst-case claims to score functions that admit a temporal signature. (3) Non-empty detectability band: Monitor A achieves AUC 0.52 (chance); Monitor B spans AUC 0.79-0.97 at the same 1% FPR target, and as harm is amortized over more steps Monitor A collapses to chance while Monitor B holds at AUC ~0.95. These results demonstrate a non-empty detectability band and characterize the sub-threshold sabotage frontier: distribution-shape monitors fail by construction; temporal-correlation monitors can detect but are not trivially optimal.