Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to
  Represent Algebraic Structures   One of the central problems in the interface of deep learning and mathematics
is that of building learning systems that can automatically uncover underlying
mathematical laws from observed data. In this work, we make one step towards
building a bridge between algebraic structures and deep learning, and introduce
\textbf{AIDN}, \textit{Algebraically-Informed Deep Networks}. \textbf{AIDN} is
a deep learning algorithm to represent any finitely-presented algebraic object
with a set of deep neural networks. The deep networks obtained via
\textbf{AIDN} are \textit{algebraically-informed} in the sense that they
satisfy the algebraic relations of the presentation of the algebraic structure
that serves as the input to the algorithm. Our proposed network can robustly
compute linear and non-linear representations of most finitely-presented
algebraic structures such as groups, associative algebras, and Lie algebras. We
evaluate our proposed approach and demonstrate its applicability to algebraic
and geometric objects that are significant in low-dimensional topology. In
particular, we study solutions for the Yang-Baxter equations and their
applications on braid groups. Further, we study the representations of the
Temperley-Lieb algebra. Finally, we show, using the Reshetikhin-Turaev
construction, how our proposed deep learning approach can be utilized to
construct new link invariants. We believe the proposed approach would tread a
path toward a promising future research in deep learning applied to algebraic
and geometric structures.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys