@gheb_dev @gregoirehebert
Binary Step
Gaussian
Hyperbolic Tangent
Parametric Rectified Linear Unit
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@gheb_dev @gregoirehebert
Binary Step
Gaussian
Hyperbolic Tangent
Parametric Rectified Linear Unit
Sigmoid
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@gheb_dev @gregoirehebert
Binary Step
Gaussian
Hyperbolic Tangent
Parametric Rectified Linear Unit
Sigmoid
Thresholded Rectified Linear Unit
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@gheb_dev @gregoirehebert
Binary Step
Gaussian
Hyperbolic Tangent
Parametric Rectified Linear Unit
Sigmoid
Thresholded Rectified Linear Unit
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@gheb_dev @gregoirehebert
Sigmoid
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0 - 10
?
0 - 1 0 - 1
Activation Activation
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@gheb_dev @gregoirehebert
?
Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
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?
Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
@gheb_dev @gregoirehebert
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?
Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
@gheb_dev @gregoirehebert
Bias Bias
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?
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev @gregoirehebert
0.4 0.8
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev @gregoirehebert
0.4 0.8
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0 - 10
?
0 - 1 0 - 1
Activation Activation
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@gheb_dev @gregoirehebert
H = sigmoid (Input x weight + bias)
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x w + b)
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
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@gheb_dev @gregoirehebert
H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
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@gheb_dev @gregoirehebert
H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
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@gheb_dev @gregoirehebert
H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
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H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
@gheb_dev @gregoirehebert
TRAINING
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@gheb_dev @gregoirehebert
H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev @gregoirehebert
0.4 0.8
BACK PROPAGATION
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
The derivative or Slope
For any function f, it’s derivative f’
calculate the direction
S >= 0 then you must increase the value
S <= 0 then you must decrease the value
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
And the LEARNING RATE
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
And the LEARNING RATE
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
And the LEARNING RATE
ΔWeights GRADIENT x H
=
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
LINEAR GRADIENT DESCENT
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
And the LEARNING RATE
ΔWeights GRADIENT x H
=
Weights ΔWeights + weights
=
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@gheb_dev @gregoirehebert
BACK PROPAGATION
LINEAR GRADIENT DESCENT
ERROR EXPECTATION - OUTPUT
=
GRADIENT Sigmoid’ (OUTPUT)
=
Multiplied by the error
And the LEARNING RATE
ΔWeights GRADIENT x H
=
Weights ΔWeights + weights
=
Bias Bias + GRADIENT
=
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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev
0.4 0.8
BACK PROPAGATION
LINEAR GRADIENT DESCENT
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H
Or not
8
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
LINEAR GRADIENT DESCENT
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H
8
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
LINEAR GRADIENT DESCENT
0.97988
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H
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
LINEAR GRADIENT DESCENT
2
0.02295
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H
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
LINEAR GRADIENT DESCENT
2
0.02295
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@gheb_dev @gregoirehebert
CONGRATULATIONS !
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CONGRATULATIONS !
Let’s play together :)
https://github.com/GregoireHebert/sflive-nn/
@gheb_dev @gregoirehebert
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CONGRATULATIONS !
Let’s play together :)
https://github.com/GregoireHebert/sflive-nn/
@gheb_dev @gregoirehebert