Center Manifold Analysis of Plateau Phenomena Caused by Degeneration of Three-Layer Perceptron
Keyword(s):
A hierarchical neural network usually has many singular regions in the parameter space due to the degeneration of hidden units. Here, we focus on a three-layer perceptron, which has one-dimensional singular regions comprising both attractive and repulsive parts. Such a singular region is often called a Milnor-like attractor. It is empirically known that in the vicinity of a Milnor-like attractor, several parameters converge much faster than the rest and that the dynamics can be reduced to smaller-dimensional ones. Here we give a rigorous proof for this phenomenon based on a center manifold theory. As an application, we analyze the reduced dynamics near the Milnor-like attractor and study the stochastic effects of the online learning.
1997 ◽
Vol 119
(2)
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pp. 158-165
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2018 ◽
Vol 28
(11)
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pp. 1850139
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2019 ◽
Vol 28
(15)
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pp. 1950173
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Keyword(s):
2010 ◽
Vol 20
(04)
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pp. 1255-1259
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