Towards a mathematical understanding of learning from few examples with nonlinear feature maps
This work addresses the challenge of few-shot learning for AI researchers by providing a foundational mathematical understanding, though it appears incremental as it builds on existing concepts of feature maps.
The paper tackles the problem of data classification with few training examples by mathematically analyzing how nonlinear feature transformations into high-dimensional spaces affect a model's generalization capabilities, revealing key relationships between feature space geometry, data distribution structure, and generalization.
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.