zwilling@mitre.org (Daniel Zwillinger) (03/22/90)
A report is available from the authors of this mail message that documents a year-long MITRE study in feedback neural networks. The report is lengthy (100+ pages), so in the interest of forest preservation, please request it only if you are really interested. Be sure to include your US mail address. Here is the abstract: This report analyzes the usefulness of solving quadratic optimization problems using feedback neural networks. We review the existing literature on feedback neural networks, compare and contrast existing neural network models, discuss implementation issues, and describe how quadratic optimization problems have been mapped onto neural networks. We have developed our own model for mapping a quadratic optimization problem onto a neural network that has dynamics that are easily analyzed Additionally, we describe important neural network characteristics that we have discovered. Some of these characteristics are that the underlying differential equations describing a neural network are often stiff (i.e., the equations evolve on more than one time scale), that an imprecise implementation of the transfer function can lead to multiple solutions and/or unacceptable convergence properties, and that linear constraints often exist on the final values produced by the neural network. These conclusions are documented by several theoretical analyses and small examples. Because of these characteristics, simple-minded numerical simulations of neural networks are invalid. Accurate numerical methods must be used to determine the true output of a neural network. A robust numerical integrator is described that will determine precisely the trajectories of the neurons. Another concern addressed in this volume is representation issues (i.e., how the network contains the information related to a specific problem). Our emphasis has been on obtaining digital output from the network. A common technique used to obtain digital output is to represent desired quantities by weighted sums of neurons. This volume also includes two extensive case studies: a discrete system and a continuous system. The three main aspects of feedback neural networks that we discuss, namely formulation, dynamics, and representation, are applied to these case studies. Joe J. Rushanan & Dan Zwillinger Technical Staff, MITRE ----------------------------------------------------------------------- Daniel Zwillinger ARPANET: zwilling@linus.mitre.org (author of "Handbook of Differential Equations") The MITRE Corporation work: 617/271-7017 FAX: 617/271-2184 Bedford, Mass 01730 home: 617/646-8565 -----------------------------------------------------------------------