Variational Atlas Autoencoders and Self-Supervised Chart Selection

Arno Coomans, Merlin Nimier-David, Eugene d'Eon, Boris Bonev

Complex, high-dimensional data lie on manifolds that a single global latent coordinate system cannot represent without distortion. We introduce Variational Atlas Autoencoders, a mixture-of-charts framework that learns an atlas of local latent representations, each responsible for one region of the data manifold. The central difficulty in learning an atlas is deciding which chart should be responsible for which data point without labels. We show that this decision need not be a heuristic. By treating the chart index as a latent variable, the evidence lower bound yields the training objective and casts chart assignment as posterior inference, valid for any routing distribution. Within this framework, we propose latent-evidence routing, which assigns a point to a chart in proportion to the evidence of its encoding under that chart's latent prior. This has a simple interpretation: the closer a point lands to the center of a chart's latent space, and the more confidently it is placed there, the more likely it is to belong to that chart. Chart assignment thus emerges as posterior inference, depends on the encoder alone, and is fully self-supervised, so the charts discover structure in…