Semantic Transferability of Generative Rate-Distortion-Perception Systems

Generative lossy compression combines a rate-limited representation with a stochastic decoder that preserves source-dependent information while generating unresolved detail. We ask what remains reusable when a rate-distortion-perception (RDP) system selected for one operating point is transferred to a prescribed conditional-generation task. We distinguish the single-letter RDP factorization from its block-code implementation and compare Full Redesign with three increasingly restrictive transfer strategies. Renderer-Only Transfer retains only the renderer and redesigns semantic steering. Representation-Induced Transfer additionally retains the semantic latent law induced by the original representation. Full-Model Transfer retains a compatible RDP code, marginalizing over the task conditional law to form its semantic encoder. For finite alphabets, we characterize Renderer-Only Transfer's exact compression-common-randomness rate region, renderer-hull controllability condition, and compression-rate penalty relative to Full Redesign. Under unlimited common randomness, this penalty is the minimum residual semantic information $I(S;U|X)$ forced by the inherited renderer. Representation-Induced Transfer is exact if and only if the semantic condition depends on the source only through the recurrent-class label $C$ of the end-to-end RDP test channel. Every compatible RDP code reused under Full-Model Transfer preserves $C$ and supports every task satisfying $X-C-S$. Any additionally transferable within-class semantic dependence must satisfy $I(S;X|C)\le R_0-H(C)$, where $R_0$ is the inherited compression rate. The bound is exact when $R_0=H(C)$. A scalar Gaussian specialization yields a renderer-noise controllability threshold, a closed-form transfer penalty, and examples of identical Gaussian RDP test channels with different Renderer-Only Transfer capabilities.