Fast curvature matrix-vector products for second-order gradient descent

We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniq...

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Vydáno v:Neural computation Ročník 14; číslo 7; s. 1723
Hlavní autor: Schraudolph, Nicol N
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 01.07.2002
Témata:
Acceleration
Algorithms
Neural Networks (Computer)
Stochastic Processes
ISSN:0899-7667
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Shrnutí:We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this approach. Since both were originally derived by very different routes, this offers fresh insight into their operation, resulting in further improvements to SMD.
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ISSN:0899-7667
DOI:10.1162/08997660260028683