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ST 311 Assignment 1 (theory part)

Due by 5pm, 10 Feb, 2023

Instruction: Attempt all questions. The total marks is 30.

1. Based on the multi-layer perceptrons in Figure 1, express the corresponding Boolean function for the four binary (Boolean) inputs, X,Y,Z and A. Show the intermediate steps.                                                                                                                [15 marks]

Figure 1: Question 1.

2. For the binary classification task, show that the computations by activation function and sigmoid activation function are equivalent. output softmax function computes P(Y = 1|x) = , with bi  for i =  1, 2, while the sigmoid function computes P(Y  =  1|x) =对 j xj  + .

2- output softmax Note that the 2-

zi  =对 wij xj + = 1+exp(1)( −) , with [15 marks]