# Exercise 3.3 - Solution¶

## Checkerboard¶

Open the Tensorflow Playground (www.playground.tensorflow.org) and select on the left the checkerboard pattern as the data basis.

The data is taken from a two-dimensional probability distribution and is represented by the value pairs $x_1$ and $x_2$. The regions $x1$, $x_2 > 0$ and $x_1$, $x_2 < 0$ are shown by one color. For value pairs with $x_1 > 0$, $x_2 < 0$ and $x_1 < 0$, $x_2 > 0$, the regions are indicated by a different color.

In features, select the two independent variables $x_1$ and $x_2$ and start the network training. The network learns that $x_1$ and $x_2$ are for these data not independent variables, but are taken from the probability distribution of the checkerboard pattern.

1. Try various settings for the number of layers and neurons using ReLU as activation function. What is the smallest network that gives a good fit result?
2. What do you observe when training networks with the same settings multiple times? Explain your observations.

## Solutions¶

Hint: click on the images to open the correct playground settings needed to solve the task, respectively.

Try various settings for the number of layers and neurons using ReLU as activation function. What is the smallest network that gives a good fit result?

A network with a single layer holding 3 nodes. However, this configuration is not stable.

A network with a single layer, holding 4 nodes, is way more stable. </em>

Obviously, the $x_1\cdot x_2$ feature is most helpful.