Learning from few examples with nonlinear feature maps
This work addresses the challenge of few-shot learning for AI models, but it appears incremental as it builds on existing analysis of feature transformations.
The paper tackles the problem of data classification with very few training examples by analyzing how nonlinear feature maps to higher-dimensional spaces affect generalization, establishing relationships between intrinsic dimensions and success probabilities.
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.