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A hitchhiker’s guide to neuroevolution in Erlang

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The document discusses artificial neural networks and how they can be trained using a perceptron learning algorithm. It provides an example of training a perceptron to perform the logical AND operation. Over multiple epochs, the perceptron's weights are adjusted based on its errors to correctly output a 1 only when both the x1 and x2 inputs are 1.

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J e r o e n S o e t e r s NEUROEVOLUTION A hitchhiker’s guide to neuroevolution in Erlang.
MEET GARY 2
WHAT IS MACHINE LEARNING? • Artificial Neural Networks • Genetic Algorithms 3
ARTIFICIAL NEURAL NETWORKS 4
BIOLOGICAL NEURAL NETWORKS 5 Dendrites Soma Axon Synapse
A MODEL FOR A NEURON 6 Y w1 w2 wn x1 x2 xn Dendrites Synapses Axon Soma
A MODEL FOR A NEURON 6 Y w1 w2 wn x1 x2 xn Input signals Weights Output signal Neuron
HOW DOES THE NEURON DETERMINE IT’S OUTPUT? Y =sign ∑xiwi - ⍬ 7 n=1 n
ACTIVATION FUNCTION 8 X Y
MEET FRANK 9
PERCEPTRON LEARNING RULE ℮(p) = Yd(p) - Y(p) wi(p + 1) = wi(p) + α • wi(p) • ℮(p) = 10
PERCEPTRON TRAINING ALGORITHM 11 weight training start stop weights converged? yes no set weights and threshold to random values [-0.5, 0.5] activate the perceptron
LOGIC GATES 12 input values x1 x2 x1 AND x2 x1 OR x2 x1 XOR x2 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 0.3
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 00
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 0.3
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 00
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 0.3
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 10
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= -1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 0.2
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 -0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 01
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.0
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
A LITTLE GEOMETRY… 18 0 1 1 x2 x1 0 1 1 x2 x10 1 1 x2 x1 x1 AND x2 x1 OR x2 x1 XOR x2
WE NEED MORE LAYERS 19 3 4 5 1 2 Input layer Hidden layer Output layer x1 x2 Y
PROBLEMS WITH BACK PROPAGATION •a training set of sufficient size is required •topology of the network needs to be known in advance •no recurrent connections are allowed •activation function must be differentiable Does not emulate the biological world 20
EVOLUTIONARY COMPUTATION 21
MEET JOHN 22
THE CHROMOSOME 23 10 11 101 0
1 1000 11 0 CROSSOVER 24 0 111 0 11 0 1 100 1 10 0 parents
1 1000 11 0 CROSSOVER 24 0 111 0 11 0 1 100 1 10 0 ✂ parents ✂
1 1000 11 0 1 10 00 111 offspring CROSSOVER 24 0 111 1 10 0 ✂ parents ✂
MUTATION 25 A D10 11 101 0
MUTATION 25 A DA D10 11 101 01 0
MUTATION 25 A DA D10 11 101 01 00 1
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •chose the initial population size N, crossover probability (Pc) and mutation probability (Pm) •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome 26
EVOLUTIONARY ALGORITHM 27 start stop generate a population calculate fitness termination criteria satisfied? yes no new population size = N? crossover and mutation select pair for mating add to new population replace population no yes
TRAVELING SALESMAN 28 A B D F G C E H
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 29
THE CHROMOSOME 30 HG FE ABC D
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 31
FITNESS FUNCTION Fitness = 1 / total distance 32
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 33
CROSSOVER 34 G EBC H FA D A FEB H DC G parents
CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F C
H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F C G
MUTATION 35 HG FE ABC D
MUTATION 35 HG FE ABC DA D
MUTATION 35 HG FE ABC DA DAD
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 36
DEMO 37
DEMO 37
NEUROEVOLUTION 38
MEET GENE 39
SIMULATION •inputs (sensors) •outputs (actuators) •fitness function 40
CLEANING ROBOT 41
FOREX TRADING 42
AND LOTS MORE… •data compression •training NPCs in a video game •cyber warfare 43
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 44
THE CHROMOSOME 45
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 46
FITNESS FUNCTION Fitness = performance of network on an actual problem 47
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 48
CROSSOVER Crossover doesn’t work for large neural nets! 49
MUTATE ACTIVATION FUNCTION 50
MUTATE ACTIVATION FUNCTION 50
ADD CONNECTION 51
ADD CONNECTION 51
ADD NEURON 52
ADD NEURON 52
OUTSPLICE 53
OUTSPLICE 53
MUTATION OPERATORS and lots more… 54
EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 55
RANDOM IMPACT MUTATION Number of mutations = random(1, network size) 56
MEMETIC ALGORITHM 57 apply to a problem start generate a population local search: Hill Climber calculate effective fitness select fit organisms create offspring
STOCHASTIC HILL CLIMBER (LOCAL SEARCH) 58 start new fitness > old fitness? yes no stopping condition reached? stop apply NN to a problem backup and perturb weights restore backed-up weights
A LANGUAGE FOR NEUROEVOLUTION •The system must be able to handle very large numbers of concurrent activities •Actions must be performed at a certain point in time or within a certain time •Systems may be distributed over several computers •The system is used to control hardware •The software systems are very large 59
A LANGUAGE FOR NEUROEVOLUTION 59 •The system exhibits complex functionality such as, feature interaction. •The systems should be in continuous operation for many years. •Software maintenance (reconfiguration, etc) should be performed without stopping the system. •There are stringent quality, and reliability requirements. •Fault tolerance
A LANGUAGE FOR NEUROEVOLUTION 59 •The system exhibits complex functionality such as, feature interaction. •The systems should be in continuous operation for many years. •Software maintenance (reconfiguration, etc) should be performed without stopping the system. •There are stringent quality, and reliability requirements. •Fault tolerance Bjarne Dacker. Erlang - A New Programming Language. Ericsson Review, no 2, 1993.
MEET JOE 60
1:1 MAPPING 61 neuron neuronneuron neuron process process process process processprocess genotype erlang
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape sync
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape sense
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape percept
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape forward forward
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape forward forward
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape forward forward
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape action
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape {fitness, halt_flag}
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape sync
THE NEURAL NETWORK 62 neuron neuronneuron actuatorsensor neuron cortex scape
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself cortex
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself {evaluation_completed, fitness} cortex
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself cortex fitness > best fitness
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself backup_weights backup_weights backup_weights backup_weights neuron neuron neuronneuron
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself neuron neuron perturb_weights perturb_weights
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself cortex
THE EXOSELF 63 neuron neuronneuron actuatorsensor neuron cortex scape exoself cortex reactivate
THE POPULATION MONITOR 64 population monitor database
THE POPULATION MONITOR 64 population monitor database private private privateprivate private
THE POPULATION MONITOR 64 population monitor database private private privateprivate private start start start start start
THE POPULATION MONITOR 64 population monitor database private private privateprivate private
THE POPULATION MONITOR 64 population monitor database private private privateprivate private terminated terminated terminated terminated terminated
THE POPULATION MONITOR 64 population monitor database private private privateprivate private
THE POPULATION MONITOR 64 population monitor database private privateprivate
THE POPULATION MONITOR 64 population monitor database private privateprivate private private
THE POPULATION MONITOR 64 population monitor database private privateprivate private private start start start start start
THE DEVIL IS IN THE DETAILS •recurrent connections •newer generations get a higher chance for mutation •neural plasticity •public scapes and steady state evolution 65
POLE BALANCING 66 agent cart actions percepts
DEMO 67
DEMO 67
BENCHMARK RESULTS 68 Method Single-Pole/Incomplete state information Double-Pole/Partial Information W/O Damping Double-Pole W/Damping RWG 8557 415209 1232296 SANE 1212 262700 451612 CNE* 724 76906* 87623* ESP 589 7374 26342 NEAT - - 6929 CMA-ES* - 3521* 6061* CoSyNE* 127* 1249* 3416* DXNN not performed 2359 2313 Our System 647 5184 4792
THE HANDBOOK 69
Feel free to reach out at: e. jsoeters@thoughtworks.com t. @JeroenSoeters THANK YOU
DATA SCIENCE AND ENGINEERING 71

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A hitchhiker’s guide to neuroevolution in Erlang

  • 1. J e r o e n S o e t e r s NEUROEVOLUTION A hitchhiker’s guide to neuroevolution in Erlang.
  • 3. WHAT IS MACHINE LEARNING? • Artificial Neural Networks • Genetic Algorithms 3
  • 6. A MODEL FOR A NEURON 6 Y w1 w2 wn x1 x2 xn Dendrites Synapses Axon Soma
  • 7. A MODEL FOR A NEURON 6 Y w1 w2 wn x1 x2 xn Input signals Weights Output signal Neuron
  • 8. HOW DOES THE NEURON DETERMINE IT’S OUTPUT? Y =sign ∑xiwi - ⍬ 7 n=1 n
  • 11. PERCEPTRON LEARNING RULE ℮(p) = Yd(p) - Y(p) wi(p + 1) = wi(p) + α • wi(p) • ℮(p) = 10
  • 12. PERCEPTRON TRAINING ALGORITHM 11 weight training start stop weights converged? yes no set weights and threshold to random values [-0.5, 0.5] activate the perceptron
  • 13. LOGIC GATES 12 input values x1 x2 x1 AND x2 x1 OR x2 x1 XOR x2 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0
  • 14. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
  • 15. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
  • 16. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1=
  • 17. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
  • 18. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 0.3
  • 19. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 -0.1
  • 20. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
  • 21. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 00
  • 22. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
  • 23. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
  • 24. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 0.3
  • 25. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 -0.1
  • 26. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
  • 27. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 00
  • 28. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
  • 29. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 -0.1
  • 30. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 0.3
  • 31. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0 -0.1
  • 32. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1
  • 33. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 10
  • 34. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= -1
  • 35. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 -0.1
  • 36. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 0.2
  • 37. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1 -0.1
  • 38. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0
  • 39. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 01
  • 40. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 1
  • 41. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 13 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 1 0 0 0 0.3 -0.1 0 0 0.3 -0.1 0 1 0 0.3 -0.1 0 0 0.3 -0.1 1 0 0 0.3 -0.1 1 -1 0.2 -0.1 1 1 1 0.2 -0.1 0 1 0.3 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
  • 42. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
  • 43. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.3 0.0
  • 44. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
  • 45. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 14 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 2 0 0 0 0.3 0.0 0 0 0.3 0.0 0 1 0 0.3 0.0 0 0 0.3 0.0 1 0 0 0.3 0.0 1 -1 0.2 0.0 1 1 1 0.2 0.0 1 0 0.2 0.0 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
  • 46. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
  • 47. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.0
  • 48. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.0
  • 49. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 15 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 3 0 0 0 0.2 0.0 0 0 0.2 0.0 0 1 0 0.2 0.0 0 0 0.2 0.0 1 0 0 0.2 0.0 1 -1 0.1 0.0 1 1 1 0.1 0.0 0 1 0.2 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
  • 50. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
  • 51. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.2 0.1
  • 52. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 53. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 16 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 4 0 0 0 0.2 0.1 0 0 0.2 0.1 0 1 0 0.2 0.1 0 0 0.2 0.1 1 0 0 0.2 0.1 1 -1 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 54. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 55. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 56. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 57. TRAINING A PERCEPTRON TO PERFORM THE AND OPERATION 17 epoch inputs x1 x2 desired output Yd initial weights w1 w2 actual output Y error ℮ final weights w1 w2 5 0 0 0 0.1 0.1 0 0 0.1 0.1 0 1 0 0.1 0.1 0 0 0.1 0.1 1 0 0 0.1 0.1 0 0 0.1 0.1 1 1 1 0.1 0.1 1 0 0.1 0.1 Threshold: ⍬ = 0.2 ; learning rate: α = 0.1= 0.1 0.1
  • 58. A LITTLE GEOMETRY… 18 0 1 1 x2 x1 0 1 1 x2 x10 1 1 x2 x1 x1 AND x2 x1 OR x2 x1 XOR x2
  • 59. WE NEED MORE LAYERS 19 3 4 5 1 2 Input layer Hidden layer Output layer x1 x2 Y
  • 60. PROBLEMS WITH BACK PROPAGATION •a training set of sufficient size is required •topology of the network needs to be known in advance •no recurrent connections are allowed •activation function must be differentiable Does not emulate the biological world 20
  • 64. 1 1000 11 0 CROSSOVER 24 0 111 0 11 0 1 100 1 10 0 parents
  • 65. 1 1000 11 0 CROSSOVER 24 0 111 0 11 0 1 100 1 10 0 ✂ parents ✂
  • 66. 1 1000 11 0 1 10 00 111 offspring CROSSOVER 24 0 111 1 10 0 ✂ parents ✂
  • 68. MUTATION 25 A DA D10 11 101 01 0
  • 69. MUTATION 25 A DA D10 11 101 01 00 1
  • 70. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •chose the initial population size N, crossover probability (Pc) and mutation probability (Pm) •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome 26
  • 71. EVOLUTIONARY ALGORITHM 27 start stop generate a population calculate fitness termination criteria satisfied? yes no new population size = N? crossover and mutation select pair for mating add to new population replace population no yes
  • 73. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 29
  • 75. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 31
  • 76. FITNESS FUNCTION Fitness = 1 / total distance 32
  • 77. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 33
  • 78. CROSSOVER 34 G EBC H FA D A FEB H DC G parents
  • 79. CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents
  • 80. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents
  • 81. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B
  • 82. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E
  • 83. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F
  • 84. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F C
  • 85. H A D offspring CROSSOVER 34 G EBC H FA D A FEB H DC G ✂ ✂ parents B E F C G
  • 89. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 36
  • 97. AND LOTS MORE… •data compression •training NPCs in a video game •cyber warfare 43
  • 98. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 44
  • 100. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 46
  • 101. FITNESS FUNCTION Fitness = performance of network on an actual problem 47
  • 102. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 48
  • 103. CROSSOVER Crossover doesn’t work for large neural nets! 49
  • 113. EVOLUTIONARY ALGORITHM •represent the candidate solution as a chromosome •define a fitness function to measure the performance of the chromosome •define the genetic operators for the chromosome •chose the initial population size N, crossover probability Pc and mutation probability Pm 55
  • 114. RANDOM IMPACT MUTATION Number of mutations = random(1, network size) 56
  • 115. MEMETIC ALGORITHM 57 apply to a problem start generate a population local search: Hill Climber calculate effective fitness select fit organisms create offspring
  • 116. STOCHASTIC HILL CLIMBER (LOCAL SEARCH) 58 start new fitness > old fitness? yes no stopping condition reached? stop apply NN to a problem backup and perturb weights restore backed-up weights
  • 117. A LANGUAGE FOR NEUROEVOLUTION •The system must be able to handle very large numbers of concurrent activities •Actions must be performed at a certain point in time or within a certain time •Systems may be distributed over several computers •The system is used to control hardware •The software systems are very large 59
  • 118. A LANGUAGE FOR NEUROEVOLUTION 59 •The system exhibits complex functionality such as, feature interaction. •The systems should be in continuous operation for many years. •Software maintenance (reconfiguration, etc) should be performed without stopping the system. •There are stringent quality, and reliability requirements. •Fault tolerance
  • 119. A LANGUAGE FOR NEUROEVOLUTION 59 •The system exhibits complex functionality such as, feature interaction. •The systems should be in continuous operation for many years. •Software maintenance (reconfiguration, etc) should be performed without stopping the system. •There are stringent quality, and reliability requirements. •Fault tolerance Bjarne Dacker. Erlang - A New Programming Language. Ericsson Review, no 2, 1993.
  • 121. 1:1 MAPPING 61 neuron neuronneuron neuron process process process process processprocess genotype erlang
  • 141. THE POPULATION MONITOR 64 population monitor database private private privateprivate private
  • 142. THE POPULATION MONITOR 64 population monitor database private private privateprivate private start start start start start
  • 143. THE POPULATION MONITOR 64 population monitor database private private privateprivate private
  • 144. THE POPULATION MONITOR 64 population monitor database private private privateprivate private terminated terminated terminated terminated terminated
  • 145. THE POPULATION MONITOR 64 population monitor database private private privateprivate private
  • 146. THE POPULATION MONITOR 64 population monitor database private privateprivate
  • 147. THE POPULATION MONITOR 64 population monitor database private privateprivate private private
  • 148. THE POPULATION MONITOR 64 population monitor database private privateprivate private private start start start start start
  • 149. THE DEVIL IS IN THE DETAILS •recurrent connections •newer generations get a higher chance for mutation •neural plasticity •public scapes and steady state evolution 65
  • 153. BENCHMARK RESULTS 68 Method Single-Pole/Incomplete state information Double-Pole/Partial Information W/O Damping Double-Pole W/Damping RWG 8557 415209 1232296 SANE 1212 262700 451612 CNE* 724 76906* 87623* ESP 589 7374 26342 NEAT - - 6929 CMA-ES* - 3521* 6061* CoSyNE* 127* 1249* 3416* DXNN not performed 2359 2313 Our System 647 5184 4792
  • 155. Feel free to reach out at: e. jsoeters@thoughtworks.com t. @JeroenSoeters THANK YOU
  • 156. DATA SCIENCE AND ENGINEERING 71