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The delta rule

The delta rule. Learn from your mistakes. If it ain’t broke, don’t fix it. Outline. Supervised learning problem Delta rule Delta rule as gradient descent Hebb rule. Given examples. Find perceptron such that. Supervised learning. Example: handwritten digits.

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The delta rule

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  1. The delta rule

  2. Learn from your mistakes

  3. If it ain’t broke, don’t fix it.

  4. Outline • Supervised learning problem • Delta rule • Delta rule as gradient descent • Hebb rule

  5. Given examples Find perceptron such that Supervised learning

  6. Example: handwritten digits • Find a perceptron that detects “two”s.

  7. Delta rule • Learning from mistakes. • “delta”: difference between desired and actual output. • Also called “perceptron learning rule”

  8. Two types of mistakes • False positive • Make w less like x. • False negative • Make w more like x. • The update is always proportional to x.

  9. Objective function • Gradient update • Stochastic gradient descent on • E=0 means no mistakes.

  10. Perceptron convergence theorem • Cycle through a set of examples. • Suppose a solution with zero error exists. • The perceptron learning rule finds a solution in finite time.

  11. If examples are nonseparable • The delta rule does not converge. • Objective function is not equal to the number of mistakes. • No reason to believe that the delta rule minimizes the number of mistakes.

  12. Memorization & generalization • Prescription: minimize error on the training set of examples • What is the error on a test set of examples? • Vapnik-Chervonenkis theory • assumption: examples are drawn from a probability distribution • conditions for generalization

  13. contrast with Hebb rule • Assume that the teacher can drive the perceptron to produce the desired output. • What are the objective functions?

  14. Is the delta rule biological? • Actual output: anti-Hebbian • Desired output: Hebbian • Contrastive

  15. Objective function • Hebb rule • distance from inputs • Delta rule • error in reproducing the output

  16. Supervised vs. unsupervised • Classification vs. generation • I shall not today attempt further to define the kinds of material [pornography] … but I know it when I see it. • Justice Potter Stewart

  17. Smooth activation function • same except for slope of f • update is small when the argument of f has large magnitude.

  18. Objective function • Gradient update • Stochastic gradient descent on • E=0 means zero error.

  19. Smooth activation functions are important for generalizing the delta rule to multilayer perceptrons.

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