Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula

• URL: http://arxiv.org/abs/2306.16951v1
• Date: Thu, 1 Jun 2023 12:23:14 GMT
• Title: Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula
• Authors: Kirill Brilliantov, Fedor Pavutnitskiy, Dmitry Pasechnyuk, German Magai
• Abstract summary: We take a step towards the goal of comprehending the group-theoretic structure of the generators of homotopy groups by leveraging the power of machine learning. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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