Function approximation using Neural Networks.

Aydin Ahmadli

2018 11 30

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I have a task like this :

Manual design of a neural network for computing a function - Suggest weights of a multi-layered neural network computing the function f(x1, x2) = 3 − x1 − x2, where x1, x2 are input bits (of value 0 or 1 each). The neurons of the network should use the sigmoidal transfer function with the slope 1 and they have biases. The topology of the network must be the following:

(a) two input neurons – inputs are bits (with value 0 or 1),

(b) two neurons in a single hidden layer, and

Outputs of the network will be interpreted as two-bit binary number in the following way:

• output greater or equal to 0.5 will be considered as logical 1,

• output greater less than 0.5 will be considered as logical 0.

List weights and biases of all neurons and also a table with the actual outputs of the network (before rounding) for all four combinations of the input bits.

MY QUESTION: at the end, I will have single weight for each neuron that satisfies all four combaniations? or what? As far as I understood, I need to train and get weight for each neuron that satisfies all four combinations right?