Neural Networks Perceptrons Page Multilayer Perceptron Page MLP

Neural Networks Perceptrons Page

Multi-layer Perceptron Page

MLP Single Perceptron Unit y X 0 = . . . -1 x 1 Page 3 x 2 xn

MLP 2 -Layer Perceptron Network O 3 -1 O 2 -1 -1 x 1 Page 4 Hidden units x 2

Multilayer Layer Perceptron y 2 -Layer Perceptron Network W 02 O 3 -1 W 13 W 23 O 1 O 2 W 01 W 02 -1 -1 W 11 W 21 W 12 W 22 x 1 W 01 = 3/2 W 11 = 1 W 12 = 1 W 02 = 1/2 W 21 = 1 W 22 = 1 Page 5 Hidden units

Multilayer Layer Perceptron y 2 -Layer Perceptron Network W 02 O 3 -1 W 13 W 23 O 1 O 2 W 01 W 02 -1 -1 W 11 W 21 W 12 X 2 W 22 x 1 1 W 01 = 3/2 W 11 = 1 W 12 = 1 W 02 = 1/2 W 21 = 1 W 22 = 1 Page 6 XOR PROBLEM 0 0 1 X 1

Multilayer Layer Perceptron y HIDDEN UNIT (O 1) DECISION BOUNDARY W 02 O 3 -1 W 13 W 23 O 1 O 2 W 01 W 02 X 2 -1 -1 W 11 W 21 W 12 W 22 O 1 X 2 O 1 0 0 1 1 1 x 2 x 1 1 W 01 = 3/2 W 11 = 1 W 12 = 1 W 02 = 1/2 W 21 = 1 W 22 = 1 Page 7 X 1 0 0 1 X 1

Multilayer Layer Perceptron HIDDEN UNIT (O 2) DECISION BOUNDARY y W 02 O 3 -1 W 13 W 23 O 1 O 2 W 01 W 02 W 11 W 21 W 12 HIDDEN UNIT (O 2) DECISION BOUNDARY W 01 = 3/2 W 11 = 1 W 12 = 1 W 02 = 1/2 W 21 = 1 W 22 = 1 Page 8 O 2 0 0 1 1 1 0 1 1 W 22 x 1 X 2 -1 -1 X 1 O 2 1 0 0 1 X 1

Multilayer Layer Perceptron XOR PROBLEM y X 1 X 2 O 1 O 2 Y -1 0 0 0 W 23 0 1 1 1 0 W 02 O 3 W 13 O 1 O 2 W 01 W 02 -1 -1 W 11 W 21 W 12 O 2 W 22 x 1 1 W 01 = 3/2 W 11 = 1 W 12 = 1 W 02 = 1/2 W 21 = 1 W 22 = 1 Page 9 0 0 O 1