In this problem, we use the squared loss ( y,y ) ( y y ) 2 to evaluate the performance of a neural network Consider the following perceptron parameterized by w f ( x 1 ,x 2 ) ( w 1 x 1 w 2 x 2 ) , where ( x ) (1 e x ) 1 represents the logistic function Compute the partial gradient of with respect to w 1 at ( w 1 ,w 2 ) (0 , 0)for the given training sample( x 1 ,x 2 ,y ) ( Hint the derivative of ( x ) is ( x ) (1 ( x )) )

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Question: In this problem, we use the squared loss ( y,y ) := ( y y ) 2 to evaluate the performance of a neural network.

In this problem, we use the squared loss

(y,y ) := (y y)²

to evaluate the performance of a neural network. Consider the following perceptron parameterized byw:

f(x₁,x₂) = (w₁x₁+ w₂x₂),

where(x) := (1 + e^x)¹represents the logistic function. Compute the partial gradient ofwith respect tow₁at (w₁,w₂) = (0,0)for the given training sample(x₁,x₂,y). (Hint: the derivative of(x)is(x) (1 (x)).)

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