For example, consider a "mood forecasting" model that represents temperature in one of the following four buckets:

freezing

chilly

temperate

warm

And represents wind speed in one of the following three buckets:

still

light

windy

Without feature crosses, the linear model trains independently on each of the preceding seven various buckets. So, the model trains on, for example, freezing independently of the training on, for example, windy.

Alternatively, you could create a feature cross of temperature and wind speed. This synthetic feature would have the following 12 possible values:

freezing-still

freezing-light

freezing-windy

chilly-still

chilly-light

chilly-windy

temperate-still

temperate-light

temperate-windy

warm-still

warm-light

warm-windy

Thanks to feature crosses, the model can learn mood differences between a freezing-windy day and a freezing-still day.

If you create a synthetic feature from two features that each have a lot of different buckets, the resulting feature cross will have a huge number of possible combinations. For example, if one feature has 1,000 buckets and the other feature has 2,000 buckets, the resulting feature cross has 2,000,000 buckets.

Formally, a cross is a Cartesian product.

Feature crosses are mostly used with linear models and are rarely used with neural networks.

See Categorical data: Feature crosses in Machine Learning Crash Course for more information.