Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational autoencoders in the presence of low-dimensional data:
  landscape and implicit bias   Variational Autoencoders (VAEs) are one of the most commonly used generative
models, particularly for image data. A prominent difficulty in training VAEs is
data that is supported on a lower dimensional manifold. Recent work by Dai and
Wipf (2019) suggests that on low-dimensional data, the generator will converge
to a solution with 0 variance which is correctly supported on the ground truth
manifold.
  In this paper, via a combination of theoretical and empirical results, we
show that the story is more subtle. Precisely, we show that for linear
encoders/decoders, the story is mostly true and VAE training does recover a
generator with support equal to the ground truth manifold, but this is due to
the implicit bias of gradient descent rather than merely the VAE loss itself.
  In the nonlinear case, we show that the VAE training frequently learns a
higher-dimensional manifold which is a superset of the ground truth manifold.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph