p-adic Cellular Neural Networks
Copyright policy )p-adic Cellular Neural Networks
AbstractIn this article we introduce the p-adic cellular neural networks which are mathematical generalizations of the classical cellular neural networks (CNNs) introduced by Chua and Yang. The new networks have infinitely many cells which are organized hierarchically in rooted trees, and also they have infinitely many hidden layers. Intuitively, the p-adic CNNs occur as limits of large hierarchical discrete CNNs. More precisely, the new networks can be very well approximated by hierarchical discrete CNNs. Mathematically speaking, each of the new networks is modeled by one integro-differential equation depending on several p-adic spatial variables and the time. We study the Cauchy problem associated to these integro-differential equations and also provide numerical methods for solving them.
- University of the West United States
- Instituto Politécnico Nacional Mexico
- The University of Texas Rio Grande Valley United States
- CENTRO DE INVESTIGACION Y DE ESTUDIOS AVANZADOS DEL INSTITUTO POLITECNICO NACIONAL Mexico
Artificial neural network, Artificial intelligence, \(p\)-adic numbers, hierarchies, FOS: Physical sciences, Social Sciences, Experimental and Cognitive Psychology, Mathematical analysis, Differential equation, Engineering, FOS: Mathematics, Cauchy distribution, Network Analysis of Psychopathology and Mental Disorders, Psychology, Mathematical Physics, p-adic, Artificial neural networks and deep learning, Cellular neural network, Topology (electrical circuits), Chaos-based Image Encryption Techniques, Cellular Automata and Lattice Gases (nlin.CG), deep learning, \(p\)-adic theory, Applied mathematics, Computer science, FOS: Psychology, Aerospace engineering, Combinatorics, Physical Sciences, Computer Science, Computer Vision and Pattern Recognition, Differential (mechanical device), cellular neural networks, p-adic Models in Mathematical Physics, Nonlinear Sciences - Cellular Automata and Lattice Gases, Mathematics
Artificial neural network, Artificial intelligence, \(p\)-adic numbers, hierarchies, FOS: Physical sciences, Social Sciences, Experimental and Cognitive Psychology, Mathematical analysis, Differential equation, Engineering, FOS: Mathematics, Cauchy distribution, Network Analysis of Psychopathology and Mental Disorders, Psychology, Mathematical Physics, p-adic, Artificial neural networks and deep learning, Cellular neural network, Topology (electrical circuits), Chaos-based Image Encryption Techniques, Cellular Automata and Lattice Gases (nlin.CG), deep learning, \(p\)-adic theory, Applied mathematics, Computer science, FOS: Psychology, Aerospace engineering, Combinatorics, Physical Sciences, Computer Science, Computer Vision and Pattern Recognition, Differential (mechanical device), cellular neural networks, p-adic Models in Mathematical Physics, Nonlinear Sciences - Cellular Automata and Lattice Gases, Mathematics
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