Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compressive Phase Retrieval: Optimal Sample Complexity with Deep
  Generative Priors   Advances in compressive sensing provided reconstruction algorithms of sparse
signals from linear measurements with optimal sample complexity, but natural
extensions of this methodology to nonlinear inverse problems have been met with
potentially fundamental sample complexity bottlenecks. In particular, tractable
algorithms for compressive phase retrieval with sparsity priors have not been
able to achieve optimal sample complexity. This has created an open problem in
compressive phase retrieval: under generic, phaseless linear measurements, are
there tractable reconstruction algorithms that succeed with optimal sample
complexity? Meanwhile, progress in machine learning has led to the development
of new data-driven signal priors in the form of generative models, which can
outperform sparsity priors with significantly fewer measurements. In this work,
we resolve the open problem in compressive phase retrieval and demonstrate that
generative priors can lead to a fundamental advance by permitting optimal
sample complexity by a tractable algorithm in this challenging nonlinear
inverse problem. We additionally provide empirics showing that exploiting
generative priors in phase retrieval can significantly outperform sparsity
priors. These results provide support for generative priors as a new paradigm
for signal recovery in a variety of contexts, both empirically and
theoretically. The strengths of this paradigm are that (1) generative priors
can represent some classes of natural signals more concisely than sparsity
priors, (2) generative priors allow for direct optimization over the natural
signal manifold, which is intractable under sparsity priors, and (3) the
resulting non-convex optimization problems with generative priors can admit
benign optimization landscapes at optimal sample complexity, perhaps
surprisingly, even in cases of nonlinear measurements.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg