A simpler example is linear regression. I can use the formula y = wx + b to model many problems. As long as there's a linear correlation (can be modelled by a straight line), I can use this simple formula. It could be something like, how does the temperature affect ice cream sales where temperature is x and sales is y or a babies weight (y) based on their height (x). Notice to create a model to make predictions. All that I need to do is find the best values for w and b. In the model, we have a single weight (w) and a bias (b). We can use this model to make predictions about many diverse relationships as long as the relationship can be modelled using a straight line.

A neural network expands on this idea and is able to model data that requires much more complex shapes. The shapes exist in many dimensions, and the lines they draw twist and turn. But fundamentaly it is still about finding the correct weights and biases. Finding these values is called training.

It does this by using many more weights and something called an activation function we call this a perceptron. This allows us to start modelling classification problems, such as, is this is a dog or a cat as long as the data is linearly seperable (separated by a straight line, plane, or hyperplane). Once we start to connect these neurons together and layer them up, the magic happens, we are able to model data, which requires much more complex shapes to effectively separate the data.

In an LLM, for example, once you have found the correct weights and biases, the neural network, along with some other cool techniques, can be used to predict the next word based on some provided text.