Bielecki A. Models of Neurons and Perceptrons: Selected Problems and Challenges

New York: Springer, 2019. — 150 p.This book describes models of the neuron and multilayer neural structures, with a particular focus on mathematical models. It also discusses electronic circuits used as models of the neuron and the synapse, and analyses the relations between the circuits and mathematical models in detail. The first part describes the biological foundations and provides a comprehensive overview of the artificial neural networks. The second part then presents mathematical foundations, reviewing elementary topics, as well as lesser-known problems such as topological conjugacy of dynamical systems and the shadowing property. The final two parts describe the models of the neuron, and the mathematical analysis of the properties of artificial multilayer neural networks. Combining biological, mathematical and electronic approaches, this multidisciplinary book it useful for the mathematicians interested in artificial neural networks and models of the neuron, for computer scientists interested in formal foundations of artificial neural networks, and for the biologists interested in mathematical and electronic models of neural structures and processes.Biological Foundations
Foundations of Artificial Neural NetworksGeneral Foundations
Foundations of Dynamical Systems TheoryModels of the Whole Neuron
Models of Parts of the NeuronGeneral Model of the Perceptron
Linear Perceptrons
Weakly Nonlinear Perceptrons
Nonlinear Perceptrons
Concluding Remarks and CommentsApproximation Properties of Perceptrons
Proofs