A softmax layer in a neural network takes an input vector x and produces an output vector

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A softmax layer in a neural network takes an input vector x and produces an output vector y, where

a. Obtain the derivatives ∂_yj/∂_xi in terms of x-values for the cases i = j and i ≠ j.

b. Re-express the derivatives in terms of y-values.

c. What can you say about the signs of the derivatives?

d. Using the indicator function 1(i = j), which has value 1 if i = j and 0 otherwise, combine your two expressions from part (b) into a single expression for the derivative ∂_yj/∂_xi.

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Artificial Intelligence A Modern Approach

ISBN: 9780134610993

4th Edition

Authors: Stuart Russell, Peter Norvig

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Question Posted: Mar 13, 2023 04:42 AM

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A softmax layer in a neural network takes an input vector x and produces an output vector

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yj Σ ear; •k = la €*k

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a The derivative of the softmax function with respect to the input x can be calculated ...View the full answer

Artificial Intelligence A Modern Approach

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