论文标题
迈向从具有非线性特征图的几个示例中学习的数学理解
Towards a mathematical understanding of learning from few examples with nonlinear feature maps
论文作者
论文摘要
我们考虑训练集仅包含几个数据点的数据分类问题。我们从数学上探索了这一现象，并揭示了AI模型特征空间的几何形状，基础数据分布的结构与模型的概括能力之间的关键关系。我们的分析的主要目的是揭示对模型的非线性特征转换的概括能力的影响，将原始数据映射到高且可能是无限的维空间。
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.
