  We present a local-to-global and measure-theoretical approach to
understanding datasets. The core idea is to formulate a logifold structure and
to interpret network models with restricted domains as local charts of
datasets. In particular, this provides a mathematical foundation for ensemble
machine learning. Our experiments demonstrate that logifolds can be 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 the importance of restricting to domains of classifiers in an
ensemble.
