为不同算力的智能体设计可适配的语义通信空间，揭示通信失败的临界速率。
Semantic Rate-Distortion for Bounded Multi-Agent Communication: Capacity-Derived Semantic Spaces and the Communication Cost of Alignment
- 基于环境交互抽象出容量自适应的语义空间，取代固定语义集。
- 发现通信存在临界速率 $R_{\text{crit}}$，低于该值则无法保留意图。
- 适用于异构智能体协作、强化学习中的高效通信设计。
当算力不同的两个智能体与同一环境交互时，无需对共同语义字母表进行不同压缩，而是可以各自生成不同的语义字母表。我们证明，商POMDP $Q_{m,T}(M)$——即与智能体能力一致的最粗粒度抽象——可作为任意有限能力智能体的容量自适应语义空间；异构智能体间的通信表现出明显的结构相变。当通信速率低于由商不匹配决定的临界速率 $R_{\text{crit}}$ 时，意图保持的通信在结构上不可能实现。在单向无记忆通信场景中，经典侧信息编码理论表明速率可呈指数下降。传统编码定理假设源字母表固定，而本文贡献在于从有限交互本身推导出字母表。具体地，我们证明：(1) 一个固定误差 $\ε$ 的结构性相变定理，其下界对共历史商比较具有完全普遍性；(2) 在商字母表上识别出单向Wyner-Ziv基准，具备精确逆定理、无记忆商源下的操作等价性，以及通过显式混合界连接长时程平稳性的路径；(3) 在收缩失真率 $\ε = O(1/T)$ 下的渐近单向逆定理，从消息流与解码器侧信息角度证明；(4) 对齐遍历边界，支持通过中间能力层级实现组合通信。在八个POMDP环境（包括RockSample(4,4)）上的实验验证了相变现象，结构化策略基准显示单向通信速率可比计数界降低高达19倍，收缩失真扫面结果与渐近逆定理相符。
原文摘要 · Abstract (English)
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.
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