# Neural networks

You may recall from the Feature cross exercises in the Categorical data module, that the following classification problem is nonlinear:

"Nonlinear" means that you can't accurately predict a label with a model of the form $$b + w_1x_1 + w_2x_2$$. In other words, the "decision surface" is not a line.

However, if we perform a feature cross on our features $x_1$ and $x_2$, we can then represent the nonlinear relationship between the two features using a linear model: $b + w_1x_1 + w_2x_2 + w_3x_3$ where $x_3$ is the feature cross between $x_1$ and $x_2$:

Now consider the following dataset:

You may also recall from the Feature cross exercises that determining the correct feature crosses to fit a linear model to this data took a bit more effort and experimentation.

But what if you didn't have to do all that experimentation yourself? Neural networks are a family of model architectures designed to find nonlinear patterns in data. During training of a neural network, the model automatically learns the optimal feature crosses to perform on the input data to minimize loss.

In the following sections, we'll take a closer look at how neural networks work.

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{"lastModified": "Last updated 2024-08-13 UTC."}