The Geometry of Statistical Feature Learning in Mean-Field Langevin Dynamics

Excerpt

arXiv:2606.31429v2 Announce Type: cross Abstract: We introduce a geometric formulation of statistical feature learning for supervised regression. Feature learning is defined through a base--fiber decomposition: the base is the feature-side geometry produced by training, and the fiber is the learned feature space where estimation is performed. We prove this property for spherical mean-field Langevin dynamics, viewed as the Wasserstein gradient flow of a negative entropy-regularized empirical risk