Here are my solutions to exercise 4.

## Implementing Our Network to Classify Digits

### Part 1

#### Question

Write out $a_{′}=σ(wa+b)$ in component form, and verify that it gives the same result as the rule, $1+exp(−∑_{j}w_{j}x_{j}−b)1 $, for computing the output of a sigmoid neuron.

#### Solution

Let it be stated that I have not yet taken linear algebra at college, so I have very limited experience with it.

Let us say that layer 2 has $2$ nodes and layer 1 has $3$ nodes.

The weights from layer 1 to layer 2 can be expressed as the following ($w_{ji}$, where $j$ is the neuron in the second layer and $i$ is the neuron in the first layer):

This is exactly the same as $1+exp(−∑_{j}w_{j}x_{j}−b)1 $ but computed for both neurons at once with matrices!

Say we wanted to compute the output of the first sigmoid neuron in layer 2.

Also, I wanted to note that I found this website called the ml cheatsheet and it has been really useful in describing the mathematic concepts.

The header image was taken from Khan Academy.