Resolution Information: Limits of Ambiguity Resolution for Generative Communication
For researchers in generative communication and information theory, this work reveals a fundamental limit on resolvability distinct from classical channel coding, highlighting that model-induced posterior geometry can prevent ambiguity resolution regardless of information rate.
The paper introduces resolution information as a measure of the minimum information needed to resolve semantic ambiguity in generative communication, showing that in unconstrained settings ambiguity decays exponentially with this measure, but under practical constraints geometry can create irreducible ambiguity floors that prevent asymptotic resolution.
In generative communication, the transmitter sends a compact generative description, such as model parameters or a latent representation, rather than raw data. The receiver uses this description to form a posterior belief over the underlying state and to resolve semantic ambiguity: which interpretation, decision, or action is supported by the received representation? Inspired by Shannon's geometric view of communication as uncertainty resolution, we introduce resolution information as the minimum information update, measured in nats, required to move the receiver's posterior belief into a low-ambiguity semantic region. Our work yields three main results. First, when the receiver can form any posterior belief, corresponding to the ideal unconstrained case, resolution information reduces to a binary divergence that depends only on each region's prior probability. In this case, the shape of the regions is irrelevant. Under repeated sampling, ambiguity decays exponentially with an exponent equal to the resolution information, giving it an operational meaning as an ambiguity exponent. Second, when the generative representation constrains the posterior family, as in practice, geometry becomes operational and can create irreducible ambiguity floors: half-spaces remain resolvable, whereas polytope-type regions can exhibit residual ambiguity that no amount of additional information can remove. These results reveal a fundamental departure from classical channel coding. In Shannon theory, codes can be designed so that decoding regions separate messages and error probability vanishes below capacity. In generative communication, the model itself induces a constrained posterior geometry that may prevent asymptotic ambiguity resolution. The resulting limit is not on rate, but on resolvability itself.