Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dist2Cycle: A Simplicial Neural Network for Homology Localization   Simplicial complexes can be viewed as high dimensional generalizations of
graphs that explicitly encode multi-way ordered relations between vertices at
different resolutions, all at once. This concept is central towards detection
of higher dimensional topological features of data, features to which graphs,
encoding only pairwise relationships, remain oblivious. While attempts have
been made to extend Graph Neural Networks (GNNs) to a simplicial complex
setting, the methods do not inherently exploit, or reason about, the underlying
topological structure of the network. We propose a graph convolutional model
for learning functions parametrized by the $k$-homological features of
simplicial complexes. By spectrally manipulating their combinatorial
$k$-dimensional Hodge Laplacians, the proposed model enables learning
topological features of the underlying simplicial complexes, specifically, the
distance of each $k$-simplex from the nearest "optimal" $k$-th homology
generator, effectively providing an alternative to homology localization.

33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci