This is not a programming assignment. It’s hand writing assignment. Please read my uploaded file.
CSE 5160 Machine Learning (Spring 2021) Assignment #4 (Due on April 23, 2021)
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Given a neural network, the structure is shown below. Each neuron in the neural network uses the logistic or sigmoid function 𝑔(𝑧) = !
!” $!” as activation function. 𝑧%
[‘] is the output of the
linear part of 𝑗)* neuron in layer 𝑙; 𝑎% [‘] is the output of the activation part of 𝑗)* neuron in layer 𝑙.
1. [20 points] (Forward propagation) Given a training example (�⃗�, 𝑦), 𝑥 ∈ ℝ+, what is the
output of the neural network 𝑦.?
2. [50 points] (Backpropagation) The loss function is defined by logistic loss function 𝐿(𝑦.,𝑦) =
−[𝑦𝑙𝑜𝑔𝑦. + (1 − 𝑦)𝑙𝑜𝑔(1 − 𝑦.)] . Please derive the partial derivatives of loss function with
respect to parameters in the stochastic gradient descent update rules, that is, derive ,- ,.[$]
, 𝑙 = 1,2,3.
𝑧! [!] 𝑎!
𝑧0 [!] 𝑎0
𝑧1 [!] 𝑎1
𝑧!  𝑎!
𝑧0  𝑎0
𝑧!  𝑎!