hypothesis spaces knowing a neural network? -

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so i'm studying artificial intelligence exam, , see question :

knowing e) neural network, corresponding hypothesis spaces?

i know answer b), don't have explanation why b). i'm bit clueless have here...

figure

thank you

the question in artificial intelligence exam consists in finding values x , y output "true" or "false".

the figure (e) shows small feedforward neural network. output of neuron function of weighted sum of every inputs (and bias, represented in figure vertical arrows). example, top-left neuron output function of 10*x + 10*y -10. means output of neuron output1 = f(10*x + 10*y - 10). function f called activation function. here neurons may considered perceptrons. perceptrons simplest models of neurons : activation function step function : f(u) = 1 if u > 0 , f(u) = 0 otherwise.

the aim of question find values of x , y output of network 1/true/positive.

to so, compute outputs of network's neurons , find characteristic of network. top-left neuron : output 1 if 10*x + 10*y -10 > 0 <=> x + y - 1 > 0, 0 otherwise. bottom-left neuron : output 1 if -10*x -10*y +30 > 0 <=> x + y < 3, 0 otherwise.

the last neuron basic neuron works logical and. if both values true/1, output 1 because 1+1-1.5 = 0.5 > 0, output 0 otherwise. therefore, hypothesis space of network intersection of 2 previous spaces, ie. the intersection of x + y - 1 > 0 , x + y < 3, (b).


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