论文信息 - P-ADIC DYNAMICAL SYSTEMS AND NEURAL NETWORKS

P-ADIC DYNAMICAL SYSTEMS AND NEURAL NETWORKS

A p-adic model which describes a large class of neural networks is presented. In this model the states of neurons are described by digits in the canonical expansion of a p-adic number. Thus each p-adic number represents a configuration of firing and non firing neurons. The process of recognition of patterns is investigated in the P-adic framework. We study heteroassociative and autoassociative nets. P-adic dynamical systems are used to describe a feedback process for autoassociative nets.

Andrei Khrennikov | Brunello Tirozzi | Sergio Albeverio | Sergio Albeverio

[1] Sergio Albeverio,et al. A Regularization of Quantum Field Hamiltonians with the Aid of p–adic Numbers , 1998 .

[2] Igor Volovich,et al. p-adic quantum mechanics , 1989 .

[3] Sergio Albeverio,et al. p-ADIC HILBERT SPACE REPRESENTATION OF QUANTUM SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM , 1996 .

[4] Sergio Albeverio,et al. An Introduction to the Mathematical Theory of Neural Networks , 1997 .

[5] Edward Witten,et al. ADELIC STRING AMPLITUDES , 1987 .

[6] J J Hopfield,et al. Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[7] Giorgio Parisi,et al. On the p-adic five-point function , 1988 .

[8] Y. Miyashita,et al. Neuronal correlate of pictorial short-term memory in the primate temporal cortexYasushi Miyashita , 1988, Nature.

[9] Y. Miyashita. Neuronal correlate of visual associative long-term memory in the primate temporal cortex , 1988, Nature.

[10] Roberto Cianci,et al. p-adic numbers and renormalization of eigenfunctions in quantum mechanics , 1994 .