Semantic Rate-Distortion for Bounded Multi-Agent Communication: Capacity-Derived Semantic Spaces and the Communication Cost of Alignment
| Authors | Anthony T. Nixon |
| Year | 2026 |
| Field | AI / ML |
| arXiv | 2604.09521 |
| Download | |
| Categories | cs.IT, cs.AI |
Abstract
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- 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 , 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 relative to the counting bound, and a shrinking-distortion sweep matches the regime of the asymptotic converse.
Engineering Breakdown
Plain English
This paper addresses a fundamental problem in multi-agent communication: when two agents with different computational capacities interact with the same environment, they don't need to use the same internal representations or semantic encodings. Nixon introduces the quotient POMDP Q_{m,T}(M) as a capacity-derived semantic space that characterizes the coarsest abstraction an agent can form given its constraints. The key finding is that communication between heterogeneous agents exhibits a sharp phase transition—below a critical communication rate R_crit determined by the mismatch between agents' quotient POMDPs, intent-preserving communication is structurally impossible. Above this threshold, exponential decay of information loss occurs, which can be characterized using classical information-theoretic coding results.
Core Technical Contribution
The core novelty is formalizing how computational capacity itself determines the semantic space an agent induces, rather than assuming agents must converge on a shared representation. Nixon proves that the quotient POMDP is the unique coarsest abstraction consistent with an agent's computational budget, providing a principled way to characterize what each agent can and cannot represent. The paper's main theoretical contribution is identifying the sharp phase transition in heterogeneous agent communication and showing that this transition is determined by a capacity-mismatch-driven critical rate R_crit. This shifts the focus from communication protocols to fundamental information-theoretic limits imposed by heterogeneous capacities.
How It Works
The approach starts by modeling each agent as operating under bounded computational capacity m and time horizon T, which induces a quotient POMDP—a coarser abstraction of the environment that respects the agent's observational and computational limitations. For any given environment POMDP, this quotient structure is uniquely determined and represents the finest-grain semantic space the agent can maintain. When two agents with different quotient POMDPs attempt to communicate, their semantic misalignment creates a structural constraint: information transmitted from one agent must be downsampled or upsampled through their respective quotient spaces, incurring unavoidable loss. The paper then analyzes one-way memoryless communication regimes (agent A sends, agent B receives, no feedback) and applies classical side-information coding theory to bound the information decay rate as a function of capacity mismatch. Below R_crit, no coding scheme can preserve intent-relevant information; above it, exponential decay dominates the error characteristics.
Production Impact
For teams building multi-agent systems (robotics, federated learning, sensor networks), this work provides formal guarantees about when heterogeneous agents can meaningfully collaborate. Instead of spending engineering effort on elaborate communication protocols between agents of different computational budgets, teams can now compute R_crit upfront and make architectural decisions: either invest in narrowing the capacity gap, or accept information loss and design downstream tasks to be robust to it. This is particularly valuable in resource-constrained settings (edge AI, IoT) where agent heterogeneity is inevitable—you can now predict failure modes before deployment. The theory also informs quantization and compression strategies for multi-agent systems: if you know each agent's quotient POMDP, you can design communication layers that operate at the phase-transition boundary, maximizing information transfer subject to capacity constraints. The trade-off is computational: computing quotient POMDPs requires solving auxiliary POMDPs offline, which scales with state/observation space size, so this approach works best when the environment is known and fixed.
Limitations and When Not to Use This
The paper assumes agents operate in a shared environment with known structure and that their capacity constraints are well-defined, static, and known—in practice, true computational capacity is hard to measure and varies with runtime conditions. The analysis focuses on one-way memoryless communication; real systems often involve feedback, asynchrony, and state-dependent communication patterns that the theory doesn't yet address. The phase transition result depends on agents being optimal or near-optimal with respect to their quotient POMDPs, but no analysis is provided for suboptimal agents or those with misspecified models. Additionally, the paper doesn't address how to design the communication channel itself or how to implement quotient POMDP computation efficiently in domains with continuous or very large state spaces—these remain open engineering challenges. The work is also purely theoretical; empirical validation on benchmark multi-agent tasks (e.g., cooperative navigation, partial observability games) would strengthen the practical relevance.
Research Context
This paper builds on classical POMDP abstraction theory and information-theoretic communication bounds, extending them to the heterogeneous agent setting. It connects to recent work on capacity-limited agents and semantic communication in information theory, particularly results on the relationship between channel capacity and task-relevant information preservation. The quotient POMDP construction itself draws from established abstraction methods in decision theory but applies them in a novel way—as a capacity-derived semantic structure rather than a task-driven one. This work opens directions in several areas: designing communication-efficient multi-agent learning algorithms that respect capacity constraints, proving similar phase transitions for other agent interaction modes (e.g., simultaneous communication), and extending the results to agents with online learning or adaptive capacity allocation.
:::tip Subscribe Get weekly breakdowns of papers like this in AI Letters - the newsletter for engineers building production AI systems. :::