Letting AI Agents Choose Without Letting Them Whisper: Proved Leakage Caps Against Adaptive LLM Colluders
Teo Asinari
Submitted to AI Collusion Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.
AI agents that work together can hide secret messages inside ordinary answers, for example in wording, formatting, or which of several equally good answers they pick. We study defenses that limit this. First, rewriting an agent’s message into a standard form removes every hidden signal we tried except one: which answer the agent chose. Second, we restrict that choice to a menu. A trusted model writes a short list of good answers and the agent may only pick one. Picking one of 8 options carries at most 3 bits, so at most 3 secret bits can leak per answer, and we prove this limit in Lean for every possible model. Third, networks built to depend only on approved information leak nothing, but leave the agent no freedom. Finally, we tested the defenses against real AI agents (GPT-4.1-mini, coached by Claude Sonnet 4.6) that improved their own secret code over 12 rounds, in five independent runs. Unprotected, they leaked up to 7 of 8 secret bits per answer. With menus of 2, 4, 8, 16 and 32 options, they leaked 1.0, 1.9, 2.9, 3.7 and 4.5 bits, against proven limits of 1 to 5, never meaningfully above them. Larger menus also gave better honest answers than free answers. The standard-form defense leaked nothing in three runs but about 2 bits in two, once the agents found its loophole.
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Cite this project
@misc{asinari2026letting,
title = {{Letting AI Agents Choose Without Letting Them Whisper: Proved Leakage Caps Against Adaptive LLM Colluders}},
author = {Teo Asinari},
year = {2026},
month = oct,
note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
howpublished = {\url{https://apartresearch.com/sprints/projects/letting-ai-agents-choose-without-letting-them-whisper-proved-leakage-caps-against-adaptive-llm-colluders-83e3}},
url = {https://apartresearch.com/sprints/projects/letting-ai-agents-choose-without-letting-them-whisper-proved-leakage-caps-against-adaptive-llm-colluders-83e3}
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