Learning from few examples with nonlinear feature maps

TL;DR

This paper investigates how nonlinear feature maps influence the ability of models to generalize from very limited data, revealing relationships between data dimensionality, distribution properties, and learning success.

Contribution

It provides new theoretical insights into the role of nonlinear transformations in enabling successful learning from few examples.

Findings

Higher-dimensional feature spaces can improve learning success with few data points.

Data distribution properties significantly affect generalization in nonlinear feature mappings.

Theoretical relationships between data intrinsic dimensions and learning probabilities are established.

Abstract

In this work we consider the problem of data classification in post-classical settings were the number of training examples consists of mere few data points. We explore the phenomenon and reveal key relationships between dimensionality of AI model's feature space, non-degeneracy of data distributions, and the model's generalisation capabilities. The main thrust of our present analysis is on the influence of nonlinear feature transformations mapping original data into higher- and possibly infinite-dimensional spaces on the resulting model's generalisation capabilities. Subject to appropriate assumptions, we establish new relationships between intrinsic dimensions of the transformed data and the probabilities to learn successfully from few presentations.