Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight Sharing is Crucial to Succesful Optimization   Exploiting the great expressive power of Deep Neural Network architectures,
relies on the ability to train them. While current theoretical work provides,
mostly, results showing the hardness of this task, empirical evidence usually
differs from this line, with success stories in abundance. A strong position
among empirically successful architectures is captured by networks where
extensive weight sharing is used, either by Convolutional or Recurrent layers.
Additionally, characterizing specific aspects of different tasks, making them
"harder" or "easier", is an interesting direction explored both theoretically
and empirically. We consider a family of ConvNet architectures, and prove that
weight sharing can be crucial, from an optimization point of view. We explore
different notions of the frequency, of the target function, proving necessity
of the target function having some low frequency components. This necessity is
not sufficient - only with weight sharing can it be exploited, thus
theoretically separating architectures using it, from others which do not. Our
theoretical results are aligned with empirical experiments in an even more
general setting, suggesting viability of examination of the role played by
interleaving those aspects in broader families of tasks.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol