1. CSE 573 Introduction to Artificial Intelligence Neural Networks
Henry Kautz
Autumn 2005

4. Perceptron weighted sum of inputs (sigmoid unit) “soft” threshold
constant term
weighted sum of inputs
“soft” threshold

6. Training a Neuron
Idea: adjust weights to reduce sum of squared errors over training set
Error = difference between actual and intended output
Algorithm: gradient descent
Calculate derivative (slope) of error function
Take a small step in the “downward” direction
Step size is the “training rate”

7. Gradient of the Error Function

8. Gradient of the Error Function

9. Single Unit Training Rule
In short: adjust weights on inputs that were “on” in proportion to the error and the size of the output

10. Beyond Perceptrons Single units can learn any linear function
Single layer of units can learn any set of linear inequalities
Adding additional layers of “hidden” units between input and output allows any function to be learned!
Hidden units trained by propagating errors back through the network

14. Character Recognition Demo

15. Beyond Backprop…
Backpropagation is the most common algorithm for supervised learning with feed-forward neural networks
Many other learning rules for these and other cases have been studied

16. Hebbian Learning Alternative to backprop for unsupervised learning
Increase weights on connected neurons whenever both fire simultaneously
Neurologically plausible (Hebbs 1949)

17. Self-organizing maps (SOMs)
Unsupervised learning for clustering inputs
“Winner take all” network
one cell per cluster
Learning rule: update weights near “winning” neuron to make it closer to the input

18. Recurrent Neural Networks
Include time-delay feedback loops
Can handle temporal data tasks, such as sequence prediction