2023/06/01 by Kirill Brilliantov, Fedor Pavutnitskiy, Brilliantov, Kirill +5 · 1 citation
Computer Science · Mathematics · #Abstract simplicial complex #Algebra over a field #Algebraic Topology (math.AT) #Algebraic number #Algebraic topology #Combinatorics #Computer science #Discrete mathematics #FOS: Computer and information sciences #FOS: Mathematics #Group (periodic table) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Intersection (aeronautics) #Machine Learning (cs.LG) #Mathematics #Natural Language Processing Techniques #Pure mathematics #Simplicial approximation theorem #Simplicial complex #Simplicial set #Theoretical computer science #Topological and Geometric Data Analysis #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2306.16951
openalex publication_date 2023/06/01 · openalex created_date 2023/07/01 · openalex updated_date 2026/07/28
Computing homotopy groups of spheres has long been a fundamental objective in algebraic topology. Various theoretical and algorithmic approaches have been developed to tackle this problem. In this paper we take a step towards the goal of comprehending the group-theoretic structure of the generators of these homotopy groups by leveraging the power of machine learning. Specifically, in the simplicial group setting of Wu's formula, we reformulate the problem of generating simplicial cycles as a problem of sampling from the intersection of algorithmic datasets related to Dyck languages. We present and evaluate language modelling approaches that employ multi-label information for input sequences, along with the necessary group-theoretic toolkit and non-neural baselines.