Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases 事件

Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases arXiv:2602.22873v2 Announce Type: replace-cross Abstract: We introduce a theoretical framework that connects multi-chart autoencoders in manifold learning with the classical theory of vector bundles and characteristic classes. Rather than viewing autoencoders as producing a single global Euclidean embedding, we treat a collection of locally trained encoder-decoder pairs as a learned atlas on a manifold. We show that an