Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Dictionary Learning with Gradient Descent   Randomly initialized first-order optimization algorithms are the method of
choice for solving many high-dimensional nonconvex problems in machine
learning, yet general theoretical guarantees cannot rule out convergence to
critical points of poor objective value. For some highly structured nonconvex
problems however, the success of gradient descent can be understood by studying
the geometry of the objective. We study one such problem -- complete orthogonal
dictionary learning, and provide converge guarantees for randomly initialized
gradient descent to the neighborhood of a global optimum. The resulting rates
scale as low order polynomials in the dimension even though the objective
possesses an exponential number of saddle points. This efficient convergence
can be viewed as a consequence of negative curvature normal to the stable
manifolds associated with saddle points, and we provide evidence that this
feature is shared by other nonconvex problems of importance as well.

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The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics