Towards High Semantic Fidelity: Hyperdimensional Symbolic Messages in Multi-Agent Communication

Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic information model comprising Lsem-definable state sets linked by computable enabling maps, and define the semantic channel as a composition of Markov kernels whose supports respect the enabling structure. A fixed proof system induces an irredundant semantic core and a derivation-depth stratification, enabling four distortion measures of increasing semantic depth: Hamming, closure, depth, and a parameterized composite. Six families of computable semantic channel invariants are defined and their inter-relationships established, including a data processing bound, a semantic Fano bound, and an ideal-channel collapse theorem. The central quantitative result is a deductive compression gain: under closure-based fidelity, the minimum block length is determined by the irredundant core size rather than the full knowledge-base size. We instantiate the framework for heterogeneous multi-agent communication, introducing an overlap decomposition that yields necessary and sufficient conditions for closure-reliable communication. A semantic bottleneck phenomenon is identified in broadcast settings: vocabulary mismatch imposes irreducible fidelity limitations even over noiseless carriers. All results are verified on an explicit Datalog instance.

Communication protocol design is a central challenge in large language model-based multi-agent systems. Existing single-channel approaches face an inherent communication trilemma: text-based methods are interpretable but verbose, while latent-space methods are efficient but opaque and limited to unidirectional workflows. Inspired by multi-channel communication theory, we propose HyLaT, a hybrid latent-text communication protocol that transmits elaborate cognitive signals through a latent channel for efficiency, while expressing concise critical signals in natural language to preserve interpretability and precision. We introduce a two-stage training framework combining single-agent hybrid generation learning and multi-agent interactive co-training, enabling agents to generate and interpret hybrid messages across multiple rounds of interaction. Experiments demonstrate that HyLaT reduces communication overhead significantly while maintaining competitive task performance, with strong generalization and robustness across diverse settings.

When 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 $19\times$ relative to the counting bound, and a shrinking-distortion sweep matches the regime of the asymptotic converse.