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Slovak University of Technology Faculty of Material Science and Technology in Trnava Intelligent Control Methods Lecture 13: Neuronal Nets (Part 1) History: 1921: First attempt of McCulloch to model a brain 1943: First McCulloch’s publication of model of neuron 1947: McCulloch and Pitt described a behaviour of connected neurons 1949: Hebb designed a net with memory 1958: Rosenblatt described learning (“back propagation”) 1962: first neurocomputer 2 Charakteristics: inspired by brain = 40 – 100 mld. neurons, in artificial nets only tens till hundreds, it is enough for simulating of some functions brain distributed parallel information processing (the whole net in the same time) resistant to mistakes (failure of 1 element influences the whole system only slightly) knowledge is represented by connections between neurons they are able to learn they solve no-algorithmic tasks – they need training set instead of algorithm 3 Biological neuron: Dendrits (Input channels) Body (soma) Axón (output channel) synapsis (connection with next dendrit) 4 Formal (artificial) neuron (McCulloch 1943) Inputs Weights x1 w1 Local memory x2 w2 Summer f (xiwi) potential xn y transfer function y = f((xiwi)) wn 5 Transfer functions: y physical restriction n y k * ( xiwi ) Linear: i 1 0 xiwi y Linear with threshold: physical restriction n y k * ( ( xiwi) ) i 1 0 xiwi 6 Nonlinear transfer functions: Unit jump (Unit jump with threshold) n y f ( ( xiwi ), { }) y 1 i 1 = 1 if xiwi 0 = 0 if xiwi 0 0 {} xiwi 7 Nonlinear transfer functions: 1 y Signoidal function 0,5 (S. f. with threshold) n y f ( ( xiwi ),{ }, T ) i 1 0 {} 1 { } 1 e 0 wixi T xiwi T gives output steepness. Wide scope, sharp sensitivity around 0 {}. 8 Nonlinear transfer functions: 1 y Hyperbolic tangent (H. t. with threshold) xiwi 1 e y K xiwi 1 e K 0 -1 0 {} xiwi Wide scope, sharp sensitivity around 0 {}. 9 Neuronal net: Net of neurons Represented by graph – neurons arcs – synaptic connections rates of arcs – synaptic weights nodes 10 Neuronal net: x1 x2 y1 x3 y2 x4 y3 . . . ym xn inputs input layer hidden layer(s) output layer outputs 11 Neuronal net: Inputs: qualitative (binary) – they express the existence of property quantitative (they evaluate the property) numeric values of variables fuzzy values of linguistic variables Outputs: usually of the same type as inputs 12 Neuronal nets topologies: according to number of layers: single-layer (input layer = output layer) multi-layer (without and with hidden layers; commercial software usually estimates the number of hidden layers automatically according to feed-back: direct (outputs lead only to inputs of next layer) with feed-back (outputs lead to inputs of previous layers, too) 13 Neuronal net modes: decision (solution, active dynamics) learning (adaptive dynamics) 14