Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global versus Localized Generative Adversarial Nets   In this paper, we present a novel localized Generative Adversarial Net (GAN)
to learn on the manifold of real data. Compared with the classic GAN that {\em
globally} parameterizes a manifold, the Localized GAN (LGAN) uses local
coordinate charts to parameterize distinct local geometry of how data points
can transform at different locations on the manifold. Specifically, around each
point there exists a {\em local} generator that can produce data following
diverse patterns of transformations on the manifold. The locality nature of
LGAN enables local generators to adapt to and directly access the local
geometry without need to invert the generator in a global GAN. Furthermore, it
can prevent the manifold from being locally collapsed to a dimensionally
deficient tangent subspace by imposing an orthonormality prior between
tangents. This provides a geometric approach to alleviating mode collapse at
least locally on the manifold by imposing independence between data
transformations in different tangent directions. We will also demonstrate the
LGAN can be applied to train a robust classifier that prefers locally
consistent classification decisions on the manifold, and the resultant
regularizer is closely related with the Laplace-Beltrami operator. Our
experiments show that the proposed LGANs can not only produce diverse image
transformations, but also deliver superior classification performances.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an