Applying language models to algebraic topology: generating simplicial
  cycles using multi-labeling in Wu's formula
Kirill Brilliantov Fedor Pavutnitskiy Dmitry Pasechnyuk German Magai
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.