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Energy Functions for SelfOrganizing Maps
, 1999
"... This paper is about the last issue. After people started to realize that there is no energy function for the Kohonen learning rule (in the continuous case), many attempts have been made to change the algorithm such that an energy can be defined, without drastically changing its properties. Here we w ..."
Abstract

Cited by 41 (1 self)
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This paper is about the last issue. After people started to realize that there is no energy function for the Kohonen learning rule (in the continuous case), many attempts have been made to change the algorithm such that an energy can be defined, without drastically changing its properties. Here we will review a simple suggestion, which has been proposed 2 and generalized in several different contexts. The advantage over some other attempts is its simplicity: we only need to redefine the determination of the winning ("best matching") unit. The energy function and corresponding learning algorithm are introduced in Section 2. We give two proofs that there is indeed a proper energy function. The first one, in Section 3, is based on explicit computation of derivatives. The second one, in Section 4 follows from a limiting case of a more general (free) energy function derived in a probabilistic setting. The energy formalism allows for a direct interpretation of disordered configurations in terms of local minima, two examples of which are treated in Section 5.
OnLine Learning Processes in Artificial Neural Networks
, 1993
"... We study online learning processes in artificial neural networks from a general point of view. Online learning means that a learning step takes place at each presentation of a randomly drawn training pattern. It can be viewed as a stochastic process governed by a continuoustime master equation. O ..."
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Cited by 31 (4 self)
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We study online learning processes in artificial neural networks from a general point of view. Online learning means that a learning step takes place at each presentation of a randomly drawn training pattern. It can be viewed as a stochastic process governed by a continuoustime master equation. Online learning is necessary if not all training patterns are available all the time. This occurs in many applications when the training patterns are drawn from a timedependent environmental distribution. Studying learning in a changing environment, we encounter a conflict between the adaptability and the confidence of the network's representation. Minimization of a criterion incorporating both effects yields an algorithm for online adaptation of the learning parameter. The inherent noise of online learning makes it possible to escape from undesired local minima of the error potential on which the learning rule performs (stochastic) gradient descent. We try to quantify these often made cl...
SELFORGANIZING NEUROMORPHIC SYSTEMS WITH SILICON GROWTH
, 2005
"... I would like to thank all of the people who supported me during my time here at Penn. In particular, I would like to thank my advisor, Kwabena Boahen, for his enthusiastic motivation, generous support and patient mentorship over the past few years. I would also like to thank my committee members – R ..."
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I would like to thank all of the people who supported me during my time here at Penn. In particular, I would like to thank my advisor, Kwabena Boahen, for his enthusiastic motivation, generous support and patient mentorship over the past few years. I would also like to thank my committee members – Rita BaliceGordon, Leif Finkel, Daniel Lee, and Bertram Shi – for their time and valuable advice. Finally, I would like to thank my fellow lab members – Kareem Zaghloul, Kai Hynna,