Abstract
I will elaborate on construction of an Unsupervised ML classifier algorithm based on ideas from Algebraic Geometry, specially category theory. We will show that this construction has many advantages! As an example: it outperforms commercial products in domain of Natural Language Processing, e.g. Google sequence to sequence classifiers, such as Google search engine in certain tasks, or google translate app. Furthermore if time permits, in this talk or a sequel, I will elaborate on construction of an auto-encoder/ decoder ML generative algorithm which mounts on top of the categorifier. It is called RG-categorifier and its construction borrows ideas from the theory of Renormalization Group Flows in Quantum field theory. Once again in order to show usefulness of implementation of such ideas, we elaborate on a proof of concept algorithm in domain of “sequence to function mapping” in bio-informatics, which can be used to classify and predict cancer mutations or new Viruses. These algorithms can all be optimized even further to more robust classifier-generative models, using optimal transport theory, and the latter leads to construction of generative diffusion based auto-encoder/decoder models.
Speaker Intro
Artan Sheshmani is a Professor of pure Mathematics, specialized in Algebraic geometry, Enumerative and Derived Geometry, and Mathematics of String Theory. He is a Professor at Yanqi Lake Beijing Institute of Mathematical Sciences and Applications in Beijing, and a senior personnel (Professor) at Simons Collaboration Program on Homological Mirror Symmetry ( Harvard University Center for Mathematical Sciences and Applications), and an Affiliate Faculty Member at Harvard University- MIT IAiFi (Institute for Artificial Intelligence and Fundamental Interactions). Between 2020 and 2023, he jointly held the visiting professor position at Institute for the Mathematical Sciences of the Americas at University of Miami, where he was part of the research collaboration program on "Hodge theory and its applications". During the past 5 years while at Harvard CMSA he was also a visiting professor at Harvard Physics department (2020-2021), and an Associate Professor of Mathematics at Institut for Mathematik (formerly the Center for Quantum Geometry of Moduli Spaces) at Aarhus University in Denmark (2016-2022). His work is mainly focused on Gromov Witten theory, Donaldson Thomas theory, Calabi-Yau geometries, and mathematical aspects of String theory. He studies geometry of moduli spaces of sheaves and curves on Calabi Yau spaces, some of which arise in the study of mathematics of string theory. In his research he has worked on understanding dualities between geometry of such moduli spaces over complex varieties of dimension 2,3,4 and currently he is working on extension of these projects from derived geometry and geometric representation theory point of view. In joint work with Shing-Tung Yau (BIMSA, YMSC, Tsinghua, Harvard Math, Harvard CMSA, and Harvard Physics departments), Cody Long (Harvard Physics), and Cumrun Vafa (Harvard Math and Physics departments) he worked on geometry moduli spaces of sheaves with non-homolomorphic support and their associated non-BPS (non-holomorphic) counting invariants. In 2019 he was one of the 30 winners of the IRFD "Research Leader" grant (approx 1M USD) on his project "Embedded surfaces, dualities and quantum number theory". The project was additionally co-financed by Harvard University CMSA and Aarhus University (Approx total. 400K USD). Detail of IRFD "Research Leader" grant: https://dff.dk/en/grants/research-leaders-2018.
