I searched on the youtube to find the reasonings to the learning machines because I wanted to understand the theoretical background. I found this biological explanation which shows where the summation Σ function and Sigmoid function came from.

Equation of Sigmoid: 

Screen Shot 2016-10-27 at 17.25.42.png

Derivative of Sigmoid:


In Code:

def sigmoid_fn(x):
return 1.0 / ( 1.0 + np.exp( -x ) )

def sigmoid_dfn(x):
y = sigmoid_fn( x )
return y * ( 1.0 – y )


Derivative of the Hyperbolic Tangent Function. 




[Matrix 1 X 4 ]  * [Matrix 1 X 4]


[Matrix 1 X 4 ]  * [Matrix 4 X 1]




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