Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sub-Riemannian Landmark Matching and its interpretation as residual
  neural networks   The problem of finding a time-dependent vector field which warps an initial
set of points to a target set is common in shape analysis. It is an example of
a problem in the diffeomorphic shape matching regime and can be thought of as a
type of spatial discretization of the more general LDDMM framework as it
transforms into a finite-dimensional Hamiltonian system. In this paper, we
consider landmark matching modified by restricting the set of available vector
fields in the sense that vector fields are parametrized by a set of controls.
We determine the geometric setting of the problem, referred to as
sub-Riemannian landmark matching, and derive equations of motions for the
controls. We provide two computational algorithms and demonstrate them in
numerical examples. In particular, the experiments highlight the importance of
the regularization term. The reason why this is of interest is that
sub-Riemannian landmark matching is demonstrated to have connections with
neural networks, in particular the interpretation of residual neural networks
as time discretizations of continuous control problems. It allows shape
analysis practitioners to think about neural networks in terms of shape
analysis, thereby providing a bridge between the two fields.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th