Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalars are universal: Equivariant machine learning, structured like
  classical physics   There has been enormous progress in the last few years in designing neural
networks that respect the fundamental symmetries and coordinate freedoms of
physical law. Some of these frameworks make use of irreducible representations,
some make use of high-order tensor objects, and some apply symmetry-enforcing
constraints. Different physical laws obey different combinations of fundamental
symmetries, but a large fraction (possibly all) of classical physics is
equivariant to translation, rotation, reflection (parity), boost (relativity),
and permutations. Here we show that it is simple to parameterize universally
approximating polynomial functions that are equivariant under these symmetries,
or under the Euclidean, Lorentz, and Poincar\'e groups, at any dimensionality
$d$. The key observation is that nonlinear O($d$)-equivariant (and
related-group-equivariant) functions can be universally expressed in terms of a
lightweight collection of scalars -- scalar products and scalar contractions of
the scalar, vector, and tensor inputs. We complement our theory with numerical
examples that show that the scalar-based method is simple, efficient, and
scalable.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc