Perceptron

Perceptron preview image

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Uri_dolphin3 Uri Wilensky (Author)

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Model group CCL | Visible to everyone | Changeable by group members (CCL)
Model was written in NetLogo 5.0.3 • Viewed 355 times • Downloaded 26 times • Run 1 time
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globals [
  epoch-error   ;; average error in this epoch
  perceptron    ;; a single output-node
  input-node-1  ;; keep the input nodes in globals so we can refer
  input-node-2  ;; to them directly and distinctly
]

;; A perceptron is modeled by input-node and bias-node agents
;; connected to an output-node agent.

;; Connections from input nodes to output nodes
;; in a perceptron.
links-own [ weight ]

;; all nodes have an activation 
;; input nodes have a value of 1 or -1
;; bias-nodes are always 1
turtles-own [activation]

breed [ input-nodes input-node ]

;; bias nodes are input-nodes whose activation
;; is always 1.
breed [ bias-nodes bias-node ]

;; output nodes compute the weighted sum of their
;; inputs and then set their activation to 1 if
;; the sum is greater than their threshold.  An
;; output node can also be the input-node for another
;; perceptron.
breed [ output-nodes output-node ]
output-nodes-own [threshold]

;;
;; Setup Procedures
;;

to setup
  clear-all

  ;; set our background to something more viewable than black
  ask patches [ set pcolor white - 3 ]

  set-default-shape input-nodes "circle"
  set-default-shape bias-nodes "bias-node"
  set-default-shape output-nodes "output-node"

  create-output-nodes 1 [
    set activation random-activation
    set xcor 6
    set size 2
    set threshold 0
    set perceptron self
  ]

  create-bias-nodes 1 [
    set activation 1
    setxy 3 7
    set size 1.5
    my-create-link-to perceptron
  ]

  create-input-nodes 1 [
    setup-input-node
    set label "Node 1"
    setxy -6 5
    set input-node-1 self
  ]

  create-input-nodes 1 [
    setup-input-node
    set label "Node 2"
    setxy -6 0
    set input-node-2 self
  ]

  ask perceptron [ compute-activation ]
  reset-ticks
end 

to setup-input-node
    set activation random-activation
    set size 1.5
    my-create-link-to perceptron
    set label-color magenta
end 

;; links an input or bias node to an output node

to my-create-link-to [ anode ] ;; input or bias node procedure
  create-link-to anode [
    set color red + 1
    ;; links start with a random weight
    set weight random-float 0.1 - 0.05
  ]
end 

;;
;; Runtime Procedures
;;

;; train sets the input nodes to a random input
;; it then computes the output
;; it determines the correct answer and back propagates the weight changes

to train ;; observer procedure
  set epoch-error 0
  repeat examples-per-epoch
  [
    ;; set the input nodes randomly
    ask input-nodes
      [ set activation random-activation ]

    ;; distribute error
    ask perceptron [
      compute-activation
      update-weights target-answer
      recolor
    ]
  ]

  ;; plot stats
  set epoch-error epoch-error / examples-per-epoch
  set epoch-error epoch-error * 0.5
  tick
end 

;; compute activation by summing the inputs * weights 
;; and run through sign function which determines whether
;; the computed value is above or below the threshold

to compute-activation ;; output-node procedure
  set activation sign sum [ [activation] of end1 * weight ] of my-in-links
  recolor
end 

to update-weights [ answer ] ;; output-node procedure
  let output-answer activation

  ;; calculate error for output nodes
  let output-error answer - output-answer

  ;; update the epoch-error
  set epoch-error epoch-error + (answer - sign output-answer) ^ 2

  ;; examine input output edges and set their new weight
  ;; increasing or decreasing it by a value determined by the learning-rate
  ask my-in-links [
    set weight weight + learning-rate * output-error * [activation] of end1
  ]
end 

;; computes the sign function given an input value

to-report sign [input]  ;; output-node procedure
  ifelse input > threshold
  [ report 1 ]
  [ report -1 ]
end 

to-report random-activation ;; observer procedure
  ifelse random 2 = 0
  [ report 1 ]
  [ report -1 ]
end 

to-report target-answer ;; observer procedure
  let a [activation] of input-node-1 = 1
  let b [activation] of input-node-2 = 1
  report ifelse-value (run-result (word "my-" target-function " a b")) [1][-1]
end 

to-report my-or [a b];; output-node procedure
  report (a or b)
end 

to-report my-xor [a b] ;; output-node procedure
  report (a xor b)
end 

to-report my-and [a b] ;; output-node procedure
  report (a and b)
end 

to-report my-nor [a b] ;; output-node procedure
  report not (a or b)
end 

to-report my-nand [a b] ;; output-node procedure
  report not (a and b)
end 

;; test runs one instance and computes the output

to test ;; observer procedure
  ask input-node-1 [ set activation test-input-node-1-value ]
  ask input-node-2 [ set activation test-input-node-2-value ]

  ;; compute the correct answer
  let correct-answer target-answer

  ;; color the nodes
  ask perceptron [ compute-activation ]

  ;; compute the answer

  let output-answer [activation] of perceptron

  ;; output the result
  ifelse output-answer = correct-answer
  [
    user-message (word "Output: " output-answer "\\nTarget: " correct-answer "\\nCorrect Answer!")
  ]
  [
    user-message (word "Output: " output-answer "\\nTarget: " correct-answer "\\nIncorrect Answer!")
  ]
end 


;; Sets the color of the perceptron's nodes appropriately
;; based on activation

to recolor ;; output, input, or bias node procedure
  ifelse activation = 1
    [ set color white ]
    [ set color black ]
  ask in-link-neighbors [ recolor ]

  ifelse show-weights?
  [ resize-recolor-links ]
  [
    ask my-in-links [
      set thickness 0
      set label ""
      set color red + 1
    ]
  ]
end 

;; resize and recolor the edges
;; resize to indicate weight
;; recolor to indicate positive or negative

to resize-recolor-links
  ask links [
    set label precision weight 4
    set thickness 0.1 + 4 * abs weight
    ifelse weight > 0
    [ set color red + 1 ]
    [ set color blue ]
  ]
end 

There are 9 versions of this model.

Uploaded by When Description Download
Uri Wilensky almost 10 years ago Updated version tag Download this version
Uri Wilensky almost 10 years ago Updated to version from NetLogo 5.0.3 distribution Download this version
Uri Wilensky over 10 years ago Updated to NetLogo 5.0 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Model from NetLogo distribution Download this version
Uri Wilensky over 12 years ago Perceptron Download this version

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