1. CSE 473 Introduction to Artificial Intelligence Neural Networks
Henry Kautz
Spring 2006

11. Training a Single 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”
Single-layer network: can train each unit separately

12. Gradient Descent

13. Computing Partial Derivatives

14. Single Unit Training Rule
Adjust weight i in proportion to…
Training rate
Error
Derivative of the “squashing function”
Degree to which input i was active

15. Sigmoid Units

16. Sigmoid Unit Training Rule
Adjust weight i in proportion to…
Training rate
Error
Degree to which output is ambiguous
Degree to which input i was active

17. Expressivity of Neural Networks
Single units can learn any linear function
Single layer of units can learn any set of linear inequalities (convex region)
Two layers can learn any continuous function
Three layers can learn any computable function

22. Character Recognition Demo

23. BackProp Demo 1 http://www.neuro.sfc.keio.ac.jp/~masato/jv/sl/BP.html
Local version: BP.html

24. Backprop Demo 2 http://www.williewheeler.com/software/bnn.html
Local version: bnn.html

25. Modeling the Brain
Backpropagation is the most commonly used algorithm for supervised learning with feed-forward neural networks
But most neuroscientists believe that brain does not implement backprop
Many other learning rules have been studied

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

27. Self-Organizing Maps Unsupervised method for clustering data
Learns a “winner take all” network where just one output neuron is on for each cluster

28. Why “Self-Organizing”

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