Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep Learning Theory Review: An Optimal Control and Dynamical Systems
  Perspective   Attempts from different disciplines to provide a fundamental understanding of
deep learning have advanced rapidly in recent years, yet a unified framework
remains relatively limited. In this article, we provide one possible way to
align existing branches of deep learning theory through the lens of dynamical
system and optimal control. By viewing deep neural networks as discrete-time
nonlinear dynamical systems, we can analyze how information propagates through
layers using mean field theory. When optimization algorithms are further recast
as controllers, the ultimate goal of training processes can be formulated as an
optimal control problem. In addition, we can reveal convergence and
generalization properties by studying the stochastic dynamics of optimization
algorithms. This viewpoint features a wide range of theoretical study from
information bottleneck to statistical physics. It also provides a principled
way for hyper-parameter tuning when optimal control theory is introduced. Our
framework fits nicely with supervised learning and can be extended to other
learning problems, such as Bayesian learning, adversarial training, and
specific forms of meta learning, without efforts. The review aims to shed
lights on the importance of dynamics and optimal control when developing deep
learning theory.

31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex