Exact solution of a layered neural network model
- 20 July 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 59 (3), 359-362
- https://doi.org/10.1103/physrevlett.59.359
Abstract
We study a deterministic parallel feed-forward neural network. Exact results for the response of the network are presented; given an initial state that has finite overlap with one stored random key pattern, we calculate the overlap on all subsequent layers (time steps). A region of good recall is separated by a first-order line from one of vanishing asymptotic overlap. Relaxation time to the limiting state is shown to diverge at the overloading transition.Keywords
This publication has 13 references indexed in Scilit:
- Statistical mechanics of neural networks near saturationAnnals of Physics, 1987
- Associative recall of memory without errorsPhysical Review A, 1987
- Structure of metastable states in the Hopfield modelJournal of Physics A: General Physics, 1986
- From basic network principles to neural architecture: emergence of spatial-opponent cells.Proceedings of the National Academy of Sciences, 1986
- Storing and Retrieving Information in a Layered Spin SystemEurophysics Letters, 1986
- Remanent magnetization of the infinite-range Ising spin glassPhysical Review B, 1986
- Random Networks of Automata: A Simple Annealed ApproximationEurophysics Letters, 1986
- Neural networks and physical systems with emergent collective computational abilities.Proceedings of the National Academy of Sciences, 1982
- First- and Second-Order Phase Transitions in Potts Models: Renormalization-Group SolutionPhysical Review Letters, 1979
- The existence of persistent states in the brainMathematical Biosciences, 1974