Abstract--We present a local-to-global and measure-theoretical approach to understanding datasets. The core idea is to form ulate a logifold structure and to interpret network models with restricted domains as local charts of datasets. In particul ar, this provides a mathematical foundation for ensemble machi ne learning. Our experiments demonstrate that logifolds can b e implemented to identify fuzzy domains and improve accuracy compared to taking average of model outputs. Additionally, we provide a theoretical example of a logifold, highlighting t he importance of restricting to domains of classifiers in an ens emble.

In this paper, we develop a local-to-global and measure-theoretical approach to understand datasets. The idea is to take network models with restricted domains as local charts of datasets. We develop the mathematical foundations for these structures, and show in experiments how it can be used to find fuzzy domains and to improve accuracy in data classification problems.