Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: VolterraNet: A higher order convolutional network with group
  equivariance for homogeneous manifolds   Convolutional neural networks have been highly successful in image-based
learning tasks due to their translation equivariance property. Recent work has
generalized the traditional convolutional layer of a convolutional neural
network to non-Euclidean spaces and shown group equivariance of the generalized
convolution operation. In this paper, we present a novel higher order Volterra
convolutional neural network (VolterraNet) for data defined as samples of
functions on Riemannian homogeneous spaces. Analagous to the result for
traditional convolutions, we prove that the Volterra functional convolutions
are equivariant to the action of the isometry group admitted by the Riemannian
homogeneous spaces, and under some restrictions, any non-linear equivariant
function can be expressed as our homogeneous space Volterra convolution,
generalizing the non-linear shift equivariant characterization of Volterra
expansions in Euclidean space. We also prove that second order functional
convolution operations can be represented as cascaded convolutions which leads
to an efficient implementation. Beyond this, we also propose a dilated
VolterraNet model. These advances lead to large parameter reductions relative
to baseline non-Euclidean CNNs. To demonstrate the efficacy of the VolterraNet
performance, we present several real data experiments involving classification
tasks on spherical-MNIST, atomic energy, Shrec17 data sets, and group testing
on diffusion MRI data. Performance comparisons to the state-of-the-art are also
presented.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph