Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Deterministic Gradient-Based Approach to Avoid Saddle Points   Loss functions with a large number of saddle points are one of the major
obstacles for training modern machine learning models efficiently. First-order
methods such as gradient descent are usually the methods of choice for training
machine learning models. However, these methods converge to saddle points for
certain choices of initial guesses. In this paper, we propose a modification of
the recently proposed Laplacian smoothing gradient descent [Osher et al.,
arXiv:1806.06317], called modified Laplacian smoothing gradient descent
(mLSGD), and demonstrate its potential to avoid saddle points without
sacrificing the convergence rate. Our analysis is based on the attraction
region, formed by all starting points for which the considered numerical scheme
converges to a saddle point. We investigate the attraction region's dimension
both analytically and numerically. For a canonical class of quadratic
functions, we show that the dimension of the attraction region for mLSGD is
floor((n-1)/2), and hence it is significantly smaller than that of the gradient
descent whose dimension is n-1.

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg