Introduction to Neural Networks

1. Introduction to Neural Networks John Paxton Montana State University Summer 2003

2. Textbook Fundamentals of Neural Networks: Architectures, Algorithms, and Applications Laurene Fausett Prentice-Hall 1994

3. Chapter 1: Introduction • Why Neural Networks? Training techniques exist. High speed digital computers. Specialized hardware. Better capture biological neural systems.

4. Who is interested? • Electrical Engineers – signal processing, control theory • Computer Engineers – robotics • Computer Scientists – artificial intelligence, pattern recognition • Mathematicians – modelling tool when explicit relationships are unknown

5. Characterizations • Architecture – a pattern of connections between neurons • Learning Algorithm – a method of determining the connection weights • Activation Function

6. Problem Domains • Storing and recalling patterns • Classifying patterns • Mapping inputs onto outputs • Grouping similar patterns • Finding solutions to constrained optimization problems

7. A Simple Neural Network w1 x1 y x2 w2 yin = x1w1 + x2w2 Activation is f(yin)

8. Biological Neuron • Dendrites receive electrical signals affected by chemical process • Soma fires at differing frequencies soma dendrite axon

9. Observations • A neuron can receive many inputs • Inputs may be modified by weights at the receiving dendrites • A neuron sums its weighted inputs • A neuron can transmit an output signal • The output can go to many other neurons

10. Features • Information processing is local • Memory is distributed (short term = signals, long term = dendrite weights) • The dendrite weights learn through experience • The weights may be inhibatory or excitatory

11. Features • Neurons can generalize novel input stimuli • Neurons are fault tolerant and can sustain damage

12. Applications • Signal processing, e.g. suppress noise on a phone line. • Control, e.g. backing up a truck with a trailer. • Pattern recognition, e.g. handwritten characters or face sex identification. • Diagnosis, e.g. aryhthmia classification or mapping symptoms to a medical case.

13. Applications • Speech production, e.g. NET Talk. Sejnowski and Rosenberg 1986. • Speech recognition. • Business, e.g. mortgage underwriting. Collins et. Al. 1988. • Unsupervised, e.g. TD-Gammon.

14. Single Layer Feedforward NN w11 x1 y1 w1m wn1 xn ym wnm

15. Multilayer Neural Network • More powerful • Harder to train x1 z1 y1 xn zp ym

16. Setting the Weight • Supervised • Unsupervised • Fixed weight nets

17. Activation Functions • Identity f(x) = x • Binary step f(x) = 1 if x >= q f(x) = 0 otherwise • Binary sigmoid f(x) = 1 / (1 + e-sx)

18. Activation Functions • Bipolar sigmoid f(x) = -1 + 2 / (1 + -sx) • Hyperbolic tangent f(x) = (ex – e-x) / (ex + e-x)

19. History • 1943 McCulloch-Pitts neurons • 1949 Hebb’s law • 1958 Perceptron (Rosenblatt) • 1960 Adaline, better learning rule (Widrow, Huff) • 1969 Limitations (Minsky, Papert) • 1972 Kohonen nets, associative memory

20. History • 1977 Brain State in a Box (Anderson) • 1982 Hopfield net, constraint satisfaction • 1985 ART (Carpenter, Grossfield) • 1986 Backpropagation (Rumelhart, Hinton, McClelland) • 1988 Neocognitron, character recognition (Fukushima)

21. McCulloch-Pitts Neuron x1 f(yin) = 1 if yin >= q y x2 x3

22. Exercises • 2 input AND • 2 input OR • 3 input OR • 2 input XOR