CayleyPy-Holography: Mathematical and String Theory Methods for AI

par Alexander Chervov (Institute for Theoretical and Experimental Physics, Moscow)

jeudi 16 juil. 2026, 14:00 → 15:00 Europe/Paris

Bâtiment Alix et Marwan Lahoud (IHES)

We present a new approach to one of the central problems in AI: the construction of embeddings (latent representations) inspired by ideas from holographic string dualities, in particular the AdS/CFT correspondence. Our central conjecture is that, for a broad class of graphs, there exists a dual polygon together with a map ("holography") that sends graph vertices to lattice paths inside the polygon in such a way that graph distances are well approximated by the areas enclosed between the corresponding lattice paths. This can be viewed as a combinatorial analogue of the "Complexity = Volume" principle proposed by L. Susskind and collaborators in 2014 in the context of AdS/CFT, and later explored for Cayley graphs by H. Lin, D. Melnikov, and others. From the perspective of AI, this suggests that effective embeddings of graph vertices may be realized as their holographic images. Understanding such holographic representations for natural language and other AI systems could provide a new mathematical framework for constructing more powerful latent representations and, ultimately, more effective AI architectures. As mathematical applications of the conjecture, we explain how it naturally leads to variants of the famous Babai conjecture predicting an n² upper bound on the diameters of S_n Cayley graphs and conjecture of quasi-polynomiality of the diameters and word metrics. We also discuss connections with limit shapes of Young diagrams, integrable systems, and the description of conformal dimensions in conformal field theories arising as large-size limits of graph families. The talk is based on the CayleyPy series of papers, in particular CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks (https://arxiv.org/abs/2603.22195).

The talk will be accessible to mathematicians. No prior background in artificial intelligence or string theory will be assumed.

 

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