Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Geometry in Neural Implicits   We introduce a neural implicit framework that bridges discrete differential
geometry of triangle meshes and continuous differential geometry of neural
implicit surfaces. It exploits the differentiable properties of neural networks
and the discrete geometry of triangle meshes to approximate them as the
zero-level sets of neural implicit functions.
  To train a neural implicit function, we propose a loss function that allows
terms with high-order derivatives, such as the alignment between the principal
directions, to learn more geometric details. During training, we consider a
non-uniform sampling strategy based on the discrete curvatures of the triangle
mesh to access points with more geometric details. This sampling implies faster
learning while preserving geometric accuracy.
  We present the analytical differential geometry formulas for neural surfaces,
such as normal vectors and curvatures. We use them to render the surfaces using
sphere tracing. Additionally, we propose a network optimization based on
singular value decomposition to reduce the number of parameters.

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The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin