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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 simplicialcomplex. Specifically, the teacher first maps its data into a k-ordersimplicial complex and learns its high-order correlations. For effectivecommunication and inference, the teacher seeks minimally sufficient andinvariant semantic structures prior to conveying information. These minimalsimplicial structures are found via judiciously removing simplices selected bythe Hodge Laplacians without compromising the inference query accuracy.Subsequently, the student locally runs its own set of queries based on a maskedsimplicial convolutional autoencoder (SCAE) leveraging both local and remoteteacher's knowledge. Numerical results corroborate the effectiveness of theproposed approach in terms of improving inference query accuracy underdifferent channel conditions and simplicial structures. Experiments on acoauthorship dataset show that removing simplices by ranking the Laplacianvalues yields a 85% reduction in payload size without sacrificing accuracy.Joint semantic communication and inference by masked SCAE improves queryaccuracy by 25% compared to local student based query and 15% compared toremote teacher based query. Finally, incorporating channel semantics is shownto effectively improve inference accuracy, notably at low SNR values.

Joint Semantic-Native Communication and Inference via Minimal Simplicial Structures