Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation Learning on Unit Ball with 3D Roto-Translational
  Equivariance   Convolution is an integral operation that defines how the shape of one
function is modified by another function. This powerful concept forms the basis
of hierarchical feature learning in deep neural networks. Although performing
convolution in Euclidean geometries is fairly straightforward, its extension to
other topological spaces---such as a sphere ($\mathbb{S}^2$) or a unit ball
($\mathbb{B}^3$)---entails unique challenges. In this work, we propose a novel
`\emph{volumetric convolution}' operation that can effectively model and
convolve arbitrary functions in $\mathbb{B}^3$. We develop a theoretical
framework for \emph{volumetric convolution} based on Zernike polynomials and
efficiently implement it as a differentiable and an easily pluggable layer in
deep networks. By construction, our formulation leads to the derivation of a
novel formula to measure the symmetry of a function in $\mathbb{B}^3$ around an
arbitrary axis, that is useful in function analysis tasks. We demonstrate the
efficacy of proposed volumetric convolution operation on one viable use case
i.e., 3D object recognition.

3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: stat