{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/a244ac14-3800-4641-8e3b-ea97c45dfc39","name":"Semantic Rate-Distortion for Bounded Multi-Agent Communication: Capacity-Derived Semantic Spaces and the Communication Cost of Alignment","text":"# Semantic Rate-Distortion for Bounded Multi-Agent Communication: Capacity-Derived Semantic Spaces and the Communication Cost of Alignment\n\n**Authors:** Anthony T. Nixon\n**arXiv:** https://arxiv.org/abs/2604.09521v1\n**Published:** 2026-04-10T17:41:38Z\n\n## Abstract\nWhen two agents of different computational capacities interact with the same environment, they need not compress a common semantic alphabet differently; they can induce different semantic alphabets altogether. We show that the quotient POMDP $Q_{m,T}(M)$ - the unique coarsest abstraction consistent with an agent's capacity - serves as a capacity-derived semantic space for any bounded agent, and that communication between heterogeneous agents exhibits a sharp structural phase transition. Below a critical rate $R_{\\text{crit}}$ determined by the quotient mismatch, intent-preserving communication is structurally impossible. In the supported one-way memoryless regime, classical side-information coding then yields exponential decay above the induced benchmark. Classical coding theorems tell you the rate once the source alphabet is fixed; our contribution is to derive that alphabet from bounded interaction itself.   Concretely, we prove: (1) a fixed-$\\varepsilon$ structural phase-transition theorem whose lower bound is fully general on the common-history quotient comparison; (2) a one-way Wyner-Ziv benchmark identification on quotient alphabets, with exact converse, exact operational equality for memoryless quotient sources, and an ergodic long-run bridge via explicit mixing bounds; (3) an asymptotic one-way converse in the shrinking-distortion regime $\\varepsilon = O(1/T)$, proved from the message stream and decoder side information; and (4) alignment traversal bounds enabling compositional communication through intermediate capacity levels. Experiments on eight POMDP environments (including RockSample(4,4)) illustrate the phase transition, a structured-policy benchmark shows the one-way rate can drop by up to ","keywords":["cs.IT","cs.AI"],"about":[],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"}}