On the Effect of Bit-Level Parameter Perturbations in Machine Learning and Deep Learning Models

Chain-of-thought monitoring as an approach for AI oversight and control is threatened by the possibility of steganographic reasoning, where LLMs conceal their reasoning inside innocuous-looking text. Two neighbouring capabilities, steganographic messaging (passing a concealed message) and encoded reasoning (reasoning in an illegible but unconcealed format), have already been shown to emerge under training pressures that occur in real pipelines, such as reinforcement learning against monitors. This suggests that steganographic reasoning too might arise as an unintended side effect of training. Here, we compare how easily models learn steganographic reasoning and these two neighbouring capabilities across three elicitation methods: reinforcement learning, in-context learning, and supervised fine-tuning (SFT). For most tasks, models learn steganographic reasoning only under SFT, while they learn steganographic messaging and encoded reasoning under all three elicitation methods. Even under SFT, steganographic reasoning requires at least twice as much training as messaging, and for several model-task combinations it is not learned at all. However, on a cover task that makes hiding information especially convenient, steganographic reasoning can be successfully learned under all three elicitation methods. Steganographic reasoning is thus much harder than steganographic messaging and encoded reasoning, and learning the latter two does not imply learning the former. Yet it lies within reach: an easy version is learned under every elicitation method, when the cover task is convenient for hiding information.

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, 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 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.

Large language models can be fine-tuned to encode prompt-borne secrets into fluent, seemingly benign outputs. This creates a steganographic exfiltration risk that is difficult to detect with output-level steganalysis. Recent work proposes mechanistic detection using linear probes that recover the secret from internal activations. We show that this defense can be systematically evaded, but that detectability can be recovered through a targeted data-level intervention. First, we extend the detection setup to include a non-linear MLP probe. We then adversarially fine-tune steganographic trojans across five base models: Qwen3-8B, Llama-3.1-8B, Ministral-8B, Qwen3-14B, and Phi-4-14B. The resulting models retain $58$--$79\%$ exact-match secret recovery while evading both ridge and held-out MLP probes, with $1$--$8\%$ average capability degradation across six benchmarks. We then give an information-theoretic characterization of this evasion. Successful evasion preserves recoverability while reducing low-order extractability of the secret from the content-aligned representation, forcing the payload into synergistic interaction with residual degrees of freedom. This motivates a recontextualization dataset that restricts these residual degrees of freedom. On this distribution, both ridge and MLP detectability are restored across all five evasive trojans. Overall, our findings show that activation-based steganography detection is vulnerable to adaptive evasion, but also that theory-guided evaluation distributions can expose otherwise hidden payloads.