Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neural Group Actions   We introduce an algorithm for designing Neural Group Actions, collections of
deep neural network architectures which model symmetric transformations
satisfying the laws of a given finite group. This generalizes involutive neural
networks $\mathcal{N}$, which satisfy $\mathcal{N}(\mathcal{N}(x))=x$ for any
data $x$, the group law of $\mathbb{Z}_2$. We show how to optionally enforce an
additional constraint that the group action be volume-preserving. We
conjecture, by analogy to a universality result for involutive neural networks,
that generative models built from Neural Group Actions are universal
approximators for collections of probabilistic transitions adhering to the
group laws. We demonstrate experimentally that a Neural Group Action for the
quaternion group $Q_8$ can learn how a set of nonuniversal quantum gates
satisfying the $Q_8$ group laws act on single qubit quantum states.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph