Towards a mathematical understanding of learning from few examples with nonlinear feature maps

Oliver J. Sutton, Alexander N. Gorban, Ivan Yu. Tyukin

Abstract: We consider the problem of data classification where the training set consists of just a few data points. We explore this phenomenon mathematically and reveal key relationships between the geometry of an AI model's feature space, the structure of the underlying data distributions, and the model's generalisation capabilities. The main thrust of our analysis is to reveal the influence on the model's generalisation capabilities of nonlinear feature transformations mapping the original data into high, and possibly infinite, dimensional spaces.