Bounding Subliminal Preference Transfer: An Information-Theoretic Rate-Distortion Analysis of Steganographic Capacity in Synthetic Training Data

This paper derives an information-theoretic ceiling on Subliminal Preference Transfer (SPT), a companion framework hypothesizing that a teacher language model's latent behavioural preferences may become implicitly embedded within semantically neutral synthetic data and influence a student model trained on it. Recasting SPT as a capacity-constrained communication problem, this work models the teacher's generation process as a channel whose preference-conditioned output distribution must remain within a bounded Kullback-Leibler divergence of a neutral reference distribution. Drawing on rate-distortion theory and information-theoretic steganography, it derives rigorous upper bounds on the mutual information between a latent preference variable and a finite synthetic corpus, and on the information recoverable by a student model after training via the data-processing inequality. A heuristic translation of this bound into the original framework's Preference Alignment Score is also proposed and illustrated numerically. This work does not claim SPT occurs empirically; rather, it establishes the maximum information-theoretic budget available to the phenomenon, offering calibration targets for representation-level auditing tools such as SubtleNet. This paper is a direct companion to the original SPT framework: https://doi.org/10.5281/zenodo.21922425