Exercises for the course
Machine Learning 1
Winter semester 2021/22
fu ̈r Softwaretechnik und theoretische ̈at IV, ̈at Berlin Prof. Dr. Klaus- ̈ller Email:
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Exercise Sheet 6
Exercise 1: Designing a Neural Network (25 P)
We would like to implement a neural network that classifies data points in R2 according to decision boundary given in the figure below.
We consider as an elementary computation the threshold neuron whose relation between inputs (ai)i and output aj is given by
zj =iaiwij +bj aj =1zj>0.
(a) Design at hand a neural network that takes x1 and x2 as input and produces the output “1” if the input belongs to class A, and “0” if the input belongs to class B. Draw the neural network model and write down the weights wij and bias bj of each neuron.
Exercise 2: Backward Propagation (5 + 20 P)
We consider a neural network that takes two inputs x1 and x2 and produces an output y based on the following set of computations:
z3 =x1·w13+x2·w23 a3 = tanh(z3)
z4 =x1 ·w14 +x2 ·w24 a4 = tanh(z4)
z5 =a3·w35+a4·w45 a5 = tanh(z5)
z6 =a3 ·w36 +a4 ·w46 a6 = tanh(z6)
(a) Draw the neural network graph associated to this set of computations.
(b) Write the set of backward computations that leads to the evaluation of the partial derivative ∂y/∂w13. Your
answer should avoid redundant computations. Hint: tanh′(t) = 1 − (tanh(t))2.
Exercise 3: Programming (50 P)
Download the programming files on ISIS and follow the instructions.
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