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# Simple Perceptrons - PowerPoint PPT Presentation

Simple Perceptrons. Or one-layer feed-forward networks. Perceptrons or Layered Feed-Forward Networks. Equation governing comp of simple perceptron. activation function, usually nonlinear, e.g. step function or sigmoid. ksi. Threshold or no threshold?. with threshold.

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## PowerPoint Slideshow about 'Simple Perceptrons' - gretel

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Presentation Transcript

### Simple Perceptrons

Or one-layer feed-forward networks

activation function, usually nonlinear, e.g. step function or sigmoid

ksi

with threshold

without threshold; threshold simulated with connections to an input terminal permanently tied to -1

Is to ask for: actual output pattern = target pattern

• Also assume the targets have plus/minus 1 values and no values in between those extremes, that is,

• Then all that matter is that for each input pattern, the net input (weighted sum) h to each output unit has the same sign as the target zeta

• To simplify notation, note that the output units are independent

• [In a multilayer nn, however, the hidden (non-output) layers aren’t independent]

• So let’s consider only one output at a time

• Drop the i subscripts

Weights and each input pattern live in the same space.

Advantage: can geometrically represent these two vectors together.

A simple learning algorithm interpretation

• Also called the Perceptron Rule

• Go through the input patterns one by one

• For each pattern go through the output units one by one, asking whether output is the desired one.

• If so, leave the weight into that unit alone

• Else in the spirit of Hebb add to each connection something proportional to product of the input and desired output

Simplified Simple Learning Algorithm interpretation(for one neuron case)

• Cycle through the learning patterns

• For each pattern ksi

• If the output (O) != desired output (zeta), add product of the desired output and the input to w. (i.e., w = w + z*x)

• Keep cycling through the patterns until done.

• Convergence is guaranteed provided the two classes of input points are linearly separable.

• Perceptron convergence theorem guarantees this

Weight Update Formula, interpretation“Hebbian” from blue book, too complicated