Resolution Information: Limits of Ambiguity Resolution for Generative Communication

TL;DR

This paper explores the limits of ambiguity resolution in generative communication, introducing the concept of resolution information and analyzing how posterior geometry affects semantic ambiguity reduction.

Contribution

It formalizes resolution information as a measure of minimal information needed to resolve ambiguity and reveals fundamental limits imposed by generative model constraints.

Findings

Resolution information reduces to binary divergence in ideal cases.

Ambiguity decays exponentially with the resolution information.

Geometric constraints can create irreducible ambiguity floors.

Abstract

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.