Towards a Mathematical Theory of Semantic Communication


This talk is an attempt to answer the question “How can intelligent machines efficiently communicate?” which is one of the main goals of the so-called “Semantic Communication”. I will present a joint work with Daniel Bennequin which shows our progresses towards a mathematical theory of semantic communication, inspired by the foundational works of Claude Shannon and Alexander Grothendieck. To communicate efficiently we need a language. Using category theory, we can define a category transporting the semantics of a language. We will see then that the notion of semantics depends on many aspects that can be found in machine learning: Sampling (the data), structures (a kind of presemantic that will be carefully defined), the language itself .

Some important mathematical notions as Grothendieck Toposes and Stacks will be introduced through simple examples and we will see how neural networks can be modelled this way). Finally, after showing how a language is transported through the layers of a neural network, we will give a definition of semantic information measures which are not scalar quantities as in Shannon information theory, but spaces. Some examples will show the validity of such a definition. We will also start proposing some semantic coding theorems.


Jean-Claude Belfiore graduated from Ecole Supérieure d'Electricité (Supelec), got his PhD from Telecom Paris and the Habilitation from Université Pierre et Marie Curie (UPMC). Until 2015, he has been with Telecom Paris as a full Professor in the Communications & Electronics department. In 2015, he joined the Mathematical and Algorithmic Sciences Lab of Huawei as the head of the Communication Science Department and now the Director of WTLab, Paris. Jean-Claude Belfiore has made pioneering contributions in modulation and coding for wireless systems (especially space-time coding) by using tools of number theory. He is also one of the co-inventors of the celebrated Golden Code of the Wi-Max standard. Jean-Claude Belfiore is author or co-author of more than 200 technical papers and communications and has served as an advisor for more than 30 Ph.D. students. He was Associate Editor of the IEEE Transactions on Information Theory for Coding Theory and has been the recipient of the 2007 Blondel Medal. In Huawei, he has been involved in 5G standardization process, essentially in Channel Coding (Polar Codes for 5G). He is now working in wireless 6G, on artificial reasoning and future wireless networks for intelligent machines.