Chandru, V and Vidyasagar, M and Vinay, V
(1997)
*Tractable theories for the synthesis of neural networks.*
[Book Chapter]

## Abstract

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Item Type: | Book Chapter |
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Series.: | Operations research/computer science interfaces series |

Publisher: | Kluwer Academic Publishers |

Additional Information: | Copyright of this article belongs to Kluwer Academic Publishers. |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 15 Mar 2012 09:09 |

Last Modified: | 15 Mar 2012 09:09 |

URI: | http://eprints.iisc.ac.in/id/eprint/43963 |

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