  In this article, we propose the approach to structural optimization of neural
networks, based on the braid theory. The paper describes the basics of braid
theory as applied to the description of graph structures of neural networks. It
is shown how networks of various topologies can be built using braid structures
between layers of neural networks. The operation of a neural network based on
the braid theory is compared with a homogeneous deep neural network and a
network with random intersections between layers that do not correspond to the
ordering of the braids. Results are obtained showing the advantage of
braid-based networks over comparable architectures in classification problems.
