The Atlas-Learn Approach to the Manifold Hypothesis

The manifold hypothesis , the idea that real-world high-dimensional data concentrates near a low-dimensional curved subspace, is foundational to modern machine learning. Many popular manifold learning methods such as UMAP, t-SNE, Isomap, and diffusion maps do achieve dimensionality reduction by embedding data into a flat Euclidean space , but they do not attempt to directly learn the underlying…