Biologically Inspired Compu4ng: Neural Computa4on. Lecture 2. Patricia A. Vargas

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1 Biologically Inspired Compu4ng: Neural Computa4on Lecture 2 Patricia A. Vargas

2 Lecture 2 I. Lecture 1 Revision II. Ar4ficial Neural Networks (Part I) I. Ar4ficial Neuron II. Neural Network Architectures III. Learning Paradigms F21BC2 BIC Neural Computa4on 2

3 Biological Neural Network How does our brain process all the informa4on it receives/ perceives and what are the main mechanisms involved? h N etwork of neurons N euron B rain S ynapse 3

4 The Synapse A neuron ac4va4on is also called spiking, firing, or triggering of an ac4on poten4al. 4

5 Synap4c Plas4city The synap4c plas4city I defined by the capability of changing or modifying the synapses. Exploring the synap4c plas4city is crucial for the great majority of learning algorithms designed for ar4ficial neural networks. 5

6 (ANN) History 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland 6

7 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Ar4ficial Neural Networks McCulloch and Pi[s (1943) first ar4ficial neuron model x 1 x 2! u ativação f(u) x 1 and x 2 : u: result of the summing junc4on f(u) : ac4va4on func4on y : output f(u) y Saída MCCULLOCH, W.S. & PITTS, W. A logical calculus of the ideas immanent in nervous ac4vity, Bulle4n of Mathema4cal Biophysics, vol. 5, pp , " u 7

8 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Norbert Wiener (1948) WIENER, N. (1948) Cyberne4cs, The MIT Press. 8

9 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Donald Hebb (1949) Hebbian Learning Hebb, D.O. (1949), The organiza4on of behavior, New York, Wiley. 9

10 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Ar4ficial Neural Networks Frank Rosenbla[ (1957) Perceptron Rosenbla[, F. (1958), The perceptron: A probabilis4c model for informa4on storage and organiza4on in the brain, Psychological Review, v65, n6, pp: F21BC2 BIC Neural Computa4on

11 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Widrow Hoff Learning Rule (1958) LMS (Least Mean Square) algorithm Widrow and Hoff (1960), Adap4ve Switching Circuits, IRE WESCON conven4on record, pp: Widrow and Lehr (1990), 30 years of adap4ve neural networks: perceptron, madaline, and backpropaga4on, Proc. Of the Inst. of Electrical and Electronics Engineers, v78, pp:

12 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Marvin Minsky and Seymour Papert (1969) Book: Perceptrons. This book marked the beginning of the dark era in ANN research the field stagnated for more than 10 years. New updated version of the book was published in

13 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Hopfield (1982) Hopfield ANN: a recurrent ar4ficial neural network HOPFIELD, J.J. (1982), Neural networks and physical systems with emergent collec4ve computa4onal abili4es, Proceedings of the Na8onal Academy of Sciences of the U.S.A., vol. 79, pp

14 1943 McCulloch e Pitts 1948 Wiener 1949 Hebb 1957 Rosenblatt 1958 Widrow e Hoff 1969 Minsky e Papert Kohonen, Grossberg, Widrow, Anderson, Caianiello, Fukushima, Aleksander 1974 Werbos 1982 Hopfield 1986 Rumelhart e McClelland Rumelhart and McClelland (1986) Backpropaga4on Algorithm to train Mul4 Layer perceptron ANN. RUMELHART, D.E. & MCCLELLAND, J.L. (1986), Parallel Distributed Processing: Explora4ons in the Microstructure of Cogni4on, vols. 1 & 2, The MIT Press. 14

15 Generic Ar4ficial Neurons Entradas Input Signals x 1 x 2 x m Pesos Synap4c das Weights conexões w k1 w k2 w km b k Limiar(bias) " Summing Junção Junc4on somadora u k Função Ac4va4on de Func4on ativação f(u k ) y k Output Saída Entradas Input Signals +1 x 1 x 2 x m Synap4c Pesos das Weights conexões w k0 = b 0 w k1 w k2 w km! u k Summing Junção Junc4on somadora Ac4va4on Função de Func4on ativação f(u k ) y Output Saída y k ) m & = f ( ) m u = ' $ k ) f * wkj x j + bk ( j= 1 % $ & y ' k = f ( uk ) = f * wkj x j ( j= 0 % 15

16 Ac4va4on func4ons f(u) " u 0 0 1/p 1 1 p= p=3 p=1.5 p= p=1 p=

17 Ac4va4on func4ons: Threshold Func4on f(u) If u Θ then fire If u < Θ then don t fire " u ativação x 1 x 2! u f(u) y Saída

18 Ac4va4on func4ons: Piece wise linear func4on If pu k 1 then f(u k ) = If 0 < pu k < 1 then f(u k ) = pu k If pu k 0 then f(u k ) = /p p is constant and posi4ve

19 Ac4va4on func4ons: Sigmoid func4on p=3 p=1.5 p=0.8 y = f ( ) = pu k k u k pu! pu e e = 1+ e k

20 Ac4va4on func4ons: Hyperbolic tangent func4on 1 p= p=1 p=0.6 y puk! pu u k ) = tanh( pu k = pu! pu = f ( ) e e k! e + e k k

21 Architectures g y j 1 w i0 w ui y g i x ij w ij w

22 Architectures: Single layer Feedforward Networks y i = f(w i.x) = f(! j w ij.x j ), j = 1,,m.!!! " # $ $ $ % & = om o o m w w w w w w! " # " "! W

23 Architectures: Mul4layer Feedforward Networks x 0 x 1 x 2 y 1 y 2 W k is the synap4c weight matrix of layer k y o x m Camada de y = f 3 (W 3 f 2 (W 2 f 1 (W 1 x)))

24 Architectures: Recurrent Neural Networks Z!1 Z!1 Ex: Hopfield Neural Network Z!1

25 Learning Paradigms w(t+1) = w(t) + "w(t) I. Supervised Learning II. Unsupervised Learning III. Reinforcement Learning

26 I. Lecture 1 Revision Lecture 2 II. Ar4ficial Neural Networks (Part I) 26

27 Reading list/homework Lecture 2 Read Chapter 1.3 and 1.6 (inclusive) from the book: Neural Networks and Learning Machines (3rd Edi4on) by Simon O. Haykin (Nov 28, 2008) Answer ques4ons 6 7 from the Tutorial material 27

28 Lecture 2 Related videos: The Human Brain Project (Overview) h[p:// 28

29 Lecture 3 What s next? Ar4ficial Neural Networks (Part II) 29