OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 8 — Mar. 10, 1996
  • pp: 1328–1343

Convergence of backward-error-propagation learning in photorefractive crystals

Gregory C. Petrisor, Adam A. Goldstein, B. Keith Jenkins, Edward J. Herbulock, and Armand R. Tanguay, Jr  »View Author Affiliations


Applied Optics, Vol. 35, Issue 8, pp. 1328-1343 (1996)
http://dx.doi.org/10.1364/AO.35.001328


View Full Text Article

Enhanced HTML    Acrobat PDF (462 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We analytically determine that the backward-error-propagation learning algorithm has a well-defined region of convergence in neural learning-parameter space for two classes of photorefractive-based optical neural-network architectures. The first class uses electric-field amplitude encoding of signals and weights in a fully coherent system, whereas the second class uses intensity encoding of signals and weights in an incoherent/coherent system. Under typical assumptions on the grating formation in photorefractive materials used in adaptive optical interconnections, we compute weight updates for both classes of architectures. Using these weight updates, we derive a set of conditions that are sufficient for such a network to operate within the region of convergence. The results are verified empirically by simulations of the XOR sample problem. The computed weight updates for both classes of architectures contain two neural learning parameters: a learning-rate coefficient and a weight-decay coefficient. We show that these learning parameters are directly related to two important design parameters: system gain and exposure energy. The system gain determines the ratio of the learning-rate parameter to decay-rate parameter, and the exposure energy determines the size of the decay-rate parameter. We conclude that convergence is guaranteed (assuming no spurious local minima in the error function) by using a sufficiently high gain and a sufficiently low exposure energy per weight update.

© 1996 Optical Society of America

History
Original Manuscript: June 23, 1995
Revised Manuscript: October 30, 1995
Published: March 10, 1996

Citation
Gregory C. Petrisor, Adam A. Goldstein, B. Keith Jenkins, Edward J. Herbulock, and Armand R. Tanguay, "Convergence of backward-error-propagation learning in photorefractive crystals," Appl. Opt. 35, 1328-1343 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-8-1328

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited