Assignments week 2 Computational neuroscience

Before you turn this problem in, make sure everything runs as expected. First, restart the
kernel (in the menubar, select Kernel→Restart) and then run all cells (in the menubar,
select Cell→Run All).
Make sure you fill in any place that says YOUR CODE HERE or "YOUR ANSWER HERE", as
well as your name and collaborators below:
NAME = Kiki
COLLABORATORS =

File "<ipython-input-51-dc8f63ce51ce>", line 2
COLLABORATORS =
^
SyntaxError: invalid syntax




Assignments week 2
Complete the assignments below, save the notebook and submit them on canvas.

Assignment 2.1
The sigmoid function from the exercises is not the only activation function that has a
characteristic s shape. Another such function is the hypobolic tangent:

e x −e − x
σ ( x )= x −x
e +e
In contrast to the sigmoid function we used previously, this function is not bounded
between 0 and 1 but between −1 and 1. In order to be able to use this activation function in
neural networks, we need its derivative.
Compute the derivative of the hyperbolic tangent function (show intermediate steps).
Hint 1: split the numerator and denominator into two functions. f ( g )=e x −e − x and
f (x)
g ( x )=e x +e − x such that σ ( x )=
g(x)

Hint 2: the final derivative should be σ ′ ( x )=1 − σ ( x )2

$ \sigma (x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} $
f (x)
f ( x )=e x − e− x and g ( x )=e x +e − x such that σ ( x )=
g(x)

f ′ ( x ) =e x + e −x
x −x
g ′ ( x )=e −e