Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularization of Persistent Homology Gradient Computation   Persistent homology is a method for computing the topological features
present in a given data. Recently, there has been much interest in the
integration of persistent homology as a computational step in neural networks
or deep learning. In order for a given computation to be integrated in such a
way, the computation in question must be differentiable. Computing the
gradients of persistent homology is an ill-posed inverse problem with
infinitely many solutions. Consequently, it is important to perform
regularization so that the solution obtained agrees with known priors. In this
work we propose a novel method for regularizing persistent homology gradient
computation through the addition of a grouping term. This has the effect of
helping to ensure gradients are defined with respect to larger entities and not
individual points.

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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph