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Computing homotopy groups of spheres has long been a fundamental objective inalgebraic topology. Various theoretical and algorithmic approaches have beendeveloped to tackle this problem. In this paper we take a step towards the goalof comprehending the group-theoretic structure of the generators of thesehomotopy groups by leveraging the power of machine learning. Specifically, inthe simplicial group setting of Wu's formula, we reformulate the problem ofgenerating simplicial cycles as a problem of sampling from the intersection ofalgorithmic datasets related to Dyck languages. We present and evaluatelanguage modelling approaches that employ multi-label information for inputsequences, along with the necessary group-theoretic toolkit and non-neuralbaselines.

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