We study strategic Gaussian semantic compression under rate and compute constraints, where an encoder and decoder optimize distinct quadratic objectives. A latent Gaussian state generates a task dependent semantic variable, and the decoder best responds via MMSE estimation, reducing the encoder's problem to posterior covariance design under an information rate constraint. We characterize the strategic rate distortion function in direct, remote, and full information regimes, derive semantic waterfilling and rate constrained Gaussian persuasion solutions, and establish Gaussian optimality under misaligned objectives. We further show that architectural compute limits act as implicit rate constraints, yielding exponential improvements in semantic accuracy with model depth and inference time compute, while multimodal observation eliminates the geometric mean penalty inherent to remote encoding. These results provide information theoretic foundations for data and energy efficient AI and offer a principled interpretation of modern multimodal language models as posterior design mechanisms under resource constraints.

翻译：本文研究在速率与计算约束下的策略性高斯语义压缩问题，其中编码器与解码器分别优化不同的二次目标函数。一个潜在高斯状态生成任务相关的语义变量，解码器通过最小均方误差估计进行最优响应，从而将编码器问题转化为信息速率约束下的后验协方差设计。我们刻画了直接、远程与完全信息三种机制下的策略性率失真函数，推导出语义注水解与速率约束的高斯说服解，并在目标错配条件下证明了高斯最优性。进一步研究表明，架构计算限制可作为隐式速率约束，使得语义精度随模型深度与推理时间计算量呈指数级提升，而多模态观测则消除了远程编码固有的几何平均惩罚。这些结果为数据与能量高效的人工智能提供了信息理论基础，并为现代多模态语言模型在资源约束下作为后验设计机制提供了原理性解释。