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

arXiv: https://arxiv.org/abs/2211.03607 · HTML: https://mlsanity.com/paper/2211.03607/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting](https://mlsanity.com/paper/2207.06569/) (2022)
- [High-dimensional separability for one- and few-shot learning](https://mlsanity.com/paper/2106.15416/) (2021)
- [Stochastic Separation Theorems](https://mlsanity.com/paper/1703.01203/) (2017)
- [Demystification of Few-shot and One-shot Learning](https://mlsanity.com/paper/2104.12174/) (2021)
- [Augmented Artificial Intelligence: a Conceptual Framework](https://mlsanity.com/paper/1802.02172/) (2018)

## Built on by (most cited first, 2 of 2)

- [Relative intrinsic dimensionality is intrinsic to learning](https://mlsanity.com/paper/2311.07579/) (2023)
- [Agile gesture recognition for low-power applications: customisation for generalisation](https://mlsanity.com/paper/2403.15421/) (2024)

## Abstract (arXiv)

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.