Additional exercises for Fundamentals of Computational Neuroscience as a warm-up for the final

1. Network Construction

a) Visualize a feedforward network and a recurrent network with the following weight matrix

	(	2	4	3	)
w =		1	1	0
		3	0	2

2. Function approximation with multilayer perceptrons

Can a multiplayer feedforward mapping network approximate an exponential function?

3. Boolean function

A certain Boolean function is given by the following table:

x1	x2	x3	y1	y2
1	1	0	1	1
1	0	0	0	1
0	1	0	1	0
0	0	1	1	1

where x₁, x₂, and x₃ represent the input and y₁ and y₂ the outputs.

a) Is this function linear separable?

b) Draw a principle network architecture that can implement this function.

c) Specify the weights and thresholds to represent the above function

4. Supervised learning

Specify a supervised learning rule for feedforward mapping networks that does not use error backpropagation.

5. Hebbian Learning

Given are the pattern x¹ = (1, 1, -2)’ and x² = (-1.5, 2, -0.5)’ , which we want to imprint into an attractor network with Hebbian learning. Give the weight matrix after learning.