Question

Once again, consider the use of DNN for classification task with the specific architecture below that we have encountered in the class as well as in assignment 1. This question will investigate deeper into this network to provide it with further flexiblity. sottmax Output layer h(x) Hidden layer hx) w-1, bi-i 2,ha Hidden layer Wih1 Input layer h° (x)x Since the last layer has lwa hidden units followed by a softmax functio, this DNN is a binary classifier. Binary classifier is a special type of classiier where we can further simplify to provide flexiblity and theoretical analysis. For notation simplicity, at the last layer, let (x)h1 a) Show that the aulput vector can be written as y o-yi where and verily that 0 s yoy and yoy1 [1.5 points] (b) Since yo y1, one can simply use the quantity yi- to represent the output y of the whole DNN, which represents the probablity of outputing class l. Let h-hi-ho, show that one can simply now write: y-σ(h) where σΘ is the usual sigmoid (logistic) function. [1.5 points]

Answer 1

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