In this work, we study the problem of semantic communication and inference, in which a student agent (i.e. mobile device) queries a teacher agent (i.e. cloud sever) to generate higher-order data semantics living in a simplicial complex. Specifically, the teacher first maps its data into a k-order simplicial complex and learns its high-order correlations. For effective communication and inference, the teacher seeks minimally sufficient and invariant semantic structures prior to conveying information. These minimal simplicial structures are found via judiciously removing simplices selected by the Hodge Laplacians without compromising the inference query accuracy. Subsequently, the student locally runs its own set of queries based on a masked simplicial convolutional autoencoder (SCAE) leveraging both local and remote teacher's knowledge. Numerical results corroborate the effectiveness of the proposed approach in terms of improving inference query accuracy under different channel conditions and simplicial structures. Experiments on a coauthorship dataset show that removing simplices by ranking the Laplacian values yields a 85% reduction in payload size without sacrificing accuracy. Joint semantic communication and inference by masked SCAE improves query accuracy by 25% compared to local student based query and 15% compared to remote teacher based query. Finally, incorporating channel semantics is shown to effectively improve inference accuracy, notably at low SNR values.

翻译：本文研究了语义通信与推理问题，其中学生代理（如移动设备）向教师代理（如云服务器）查询，以生成位于单纯复形中的高阶数据语义。具体来说，教师首先将其数据映射至k阶单纯复形，并学习其中的高阶相关性。为实现高效的通信与推理，教师在进行信息传递前，需寻找最小充分且不变的语义结构。这些最小单纯结构通过审慎移除由Hodge拉普拉斯算子选择的单纯形来获得，且不损害推理查询精度。随后，学生基于掩码单纯卷积自编码器（SCAE），结合本地知识与教师提供的远程知识，独立执行本地查询。数值结果验证了该方法在不同信道条件与单纯复形结构下提升推理查询精度的有效性。基于合著数据集的实验表明，通过拉普拉斯值排序移除单纯形可在不牺牲精度的情况下将负载大小减少85%。与纯本地学生查询相比，基于掩码SCAE的联合语义通信与推理将查询精度提升了25%；与纯远程教师查询相比，则提升了15%。最后，研究表明融入信道语义可有效提升推理精度，尤其在低信噪比条件下表现显著。