A Decision-Theoretic Formalisation of Steganography With Applications to LLM Monitoring

TL;DR

This paper introduces a decision-theoretic framework to detect and quantify steganography in large language models by measuring asymmetries in information utility observable through agents' actions.

Contribution

It proposes a novel formalism using generalized $\

Findings

The formalism can detect steganographic reasoning in LLMs.

It quantifies the steganographic gap using a new information measure.

Empirical validation shows effectiveness in detection and mitigation.

Abstract

Large language models are beginning to show steganographic capabilities. Such capabilities could allow misaligned models to evade oversight mechanisms. Yet principled methods to detect and quantify such behaviours are lacking. Classical definitions of steganography, and detection methods based on them, require a known reference distribution of non-steganographic signals. For the case of steganographic reasoning in LLMs, knowing such a reference distribution is not feasible; this renders these approaches inapplicable. We propose an alternative, \textbf{decision-theoretic view of steganography}. Our central insight is that steganography creates an asymmetry in usable information between agents who can and cannot decode the hidden content (present within a steganographic signal), and this otherwise latent asymmetry can be inferred from the agents' observable actions. To formalise this perspective, we introduce generalised $\mathcal{V}$-information: a utilitarian framework for measuring the amount of usable information within some input. We use this to define the \textbf{steganographic gap} -- a measure that quantifies steganography by comparing the downstream utility of the steganographic signal to agents that can and cannot decode the hidden content. We empirically validate our formalism, and show that it can be used to detect, quantify, and mitigate steganographic reasoning in LLMs.