Perceptrons

• Two-layer directed, weighted graph
  • First layer: input nodes
    • Includes a special "threshold" input; value is fixed at -1.0
  • Second layer: output nodes
• Computing an output
  • For each output
    • For each input with an edge to that output
      • Multiply edge weight by input value
    • Add up all the weights for the output
    • Threshold the output (sigmoid(x) = 1 / (1 + e^-x))
• Supervised learning:
  • Training set:
    • Designed by a "teacher"
    • Sets of matched inputs/outputs ("examples")
  • Training procedure
    • For each input/output pair:
      • Apply the network to the input
      • For each output
        • Compute the "error" (target output - perceptron output)
        • Multiply the error by the learning rate and the gradient of the input (calculated using the output value)
      • For each weight
        • Multiply the input value by the delta
        • Add this result to the weight