lecture_13 - 2.160 System Identification Estimation and...

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2.160 System Identification, Estimation, and Learning Lecture Notes No. 1 3 March 22, 2006 8. Neural Networks 8.1 Physiological Background Neuro-physiology A Human brain has approximately 14 billion neurons, 50 different kinds of neurons. … uniform Massively-parallel, distributed processing Very different from a computer (a Turing machine) Image removed due to copyright reasons. McCulloch and Pitts, Neuron Model 1943 Donald Hebb, Hebbian Rule, 1949 …Synapse reinforcement learning Rosenflatt, 1959 …The perceptron convergence theorem f y Synapses The Hebbian Rule Input out put i x y fired fired The i-th synapse is reinforced. i w 1 w 2 w i w n w n x i x 2 x 1 x 1
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The electric conductivity increases at i w g z e logistic function, or sinusoid function ) ( z g 1 z y y ˆ (1) Error = = = = n i i i x w z y z g y y e 1 ) ( ˆ Gradient Descent method (2) 2 2 i iw i e wg r a d e e w ρ ∆= = (4) z e z g + = 1 1 ) ( : learning rate Unsupervised Learning. (3) 2 ' ii e x Replacing by yields the Hebbian Rule e y ˆ (Input ).(Error) i w ∆∝ i x i w (Input ).(output ) i x y ˆ Supervised Learning 8.2 Stochastic Approximation consider a linear output function for ) ( ˆ z g y = : (5) = = n i i i x w y 1 ˆ
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lecture_13 - 2.160 System Identification Estimation and...

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