The rectifier function 0 if x < 0 r(x) = X if x 0 is used...

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The rectifier function 0 if x < 0 r(x) = X if x 0 is used in artificial neural networks to model the firing of neurons. However, r(x) is not differentiable at 0. Differentiability can improve the stability and performance of neural networks. Two common differentiable approximations to r(x) are the softplus function and the swish function p(x) = log (1+ e) s(x) = 1+e-** In this assignment, you may use without proof the facts that p(x) > r(x) and s(x) r(x) for all x, and p(x) and r(x) are both continuous. Where is p(x) the worst approximation to r(x)? In other words, where is the vertical distance between the two functions maximized? The rectifier function 0 if x < 0 r(x) = X if x 0 is used in artificial neural networks to model the firing of neurons. However, r(x) is not differentiable at 0. Differentiability can improve the stability and performance of neural networks. Two common differentiable approximations to r(x) are the softplus function and the swish function p(x) = log (1+ e) s(x) = 1+e-** In this assignment, you may use without proof the facts that p(x) > r(x) and s(x) r(x) for all x, and p(x) and r(x) are both continuous. Where is p(x) the worst approximation to r(x)? In other words, where is the vertical distance between the two functions maximized?

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In order to find where the vertical distance between the softplus function px and the rectifier func... View the full answer