CS1420_Lecture_20.pdf - CS142 Machine Learning Spring 2017 Lecture 20 Instructor Pedro Felzenszwalb Scribes Dan Xiang Tyler Dae Devlin Neural Networks

# CS1420_Lecture_20.pdf - CS142 Machine Learning Spring 2017...

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CS142: Machine Learning Spring 2017 Lecture 20 Instructor: Pedro Felzenszwalb Scribes: Dan Xiang, Tyler Dae Devlin Neural Networks Last time we talked about feed forward neural networks, which just meant we could order the neurons so the inputs of each neuron were neurons that came before in the ordering. Recall the XOR function. The function mapping f : { 0 , 1 } 2 → { 0 , 1 } is defined as follows, (0 , 0) 0 (1 , 0) 1 (0 , 1) 1 (1 , 1) 0 We can represent f as a composition of boolean functions. Indeed, f ( x 1 , x 2 ) = x 1 x 2 = ( x 1 x 2 ) ( ¬ ( x 1 x 2 )) We can write the “or”, “and”, and “not and” operators using the linear threshold function h : → { 0 , 1 } , defined h ( a ) = ( 1 if a 0 0 o.w. Then we can write x 1 x 2 = h ( x 1 + x 2 - 0 . 5) x 1 x 2 = h ( x 1 + x 2 - 1 . 5) ¬ ( x 1 x 2 ) = h ( - x 1 - x 2 + 1 . 5) The boolean circuits drawn to represent these compositions are the same graphical representation we use for neural networks. Overfitting Now consider a neural network represented by a function f mapping the input

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