Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convolutional Neural Networks on the HEALPix sphere: a pixel-based
  algorithm and its application to CMB data analysis   We describe a novel method for the application of Convolutional Neural
Networks (CNNs) to fields defined on the sphere, using the HEALPix tessellation
scheme. Specifically, We have developed a pixel-based approach to implement
convolutional layers on the spherical surface, similarly to what is commonly
done for CNNs in Euclidian space. The algorithm is fully integrable with
existing libraries for NNs (e.g., PyTorch or TensorFlow). We present two
applications: (i) recognition of handwritten digits projected on the sphere;
(ii) estimation of cosmological parameter from Cosmic Microwave Background
(CMB) simulated maps. We have built a simple NN architecture, consisting in
four convolutional+pooling layers, and have used it for all the applications
explored herein. For what concerns the handwritten digits, our CNN reaches an
accuracy of about 95%, comparable with other existing spherical CNNs. For CMB
applications, we have tested the CNN on the estimation of a "mock" parameter,
defining the angular scale at which the power spectrum of a Gaussian field
projected on the sphere peaks. We have estimated this parameter directly from
maps, in several cases: temperature and polarization, presence of noise and
partial sky coverage. In all the cases, the NN performances are comparable with
those from standard spectrum-based bayesian methods. We demonstrate, for the
first time, the capability of CNNs to extract information from polarization
fields and to distinguish between E and B-modes. Lastly, we have applied our
CNN to the estimation of the Thomson scattering optical depth at reionization
(tau) from simulated CMB maps. Even without any specific optimization of the NN
architecture, we reach an accuracy comparable with standard bayesian methods.
This work represents a first step towards the exploitation of NNs in CMB
parameter estimation and demonstrates the feasibility of our approach.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin