How can we reliably optimize on manifolds learned from data? We present an iso-Riemannian optimization framework that overcomes challenges of classical methods, and allows for interpretable clustering and efficient inverse problem solving, even in high dimensions. Lead:@WillemDiepev1. bit.ly/4hG5Seh

How does neural feature geometry evolve during training? Modeling feature spaces as geometric graphs, we show that nonlinear activations drive transformations resembling Ricci flow, revealing how class structure emerges and suggesting geometry-informed training principles.
arxiv.org/abs/2509.22362

Convexity verification is central to optimization in ML and data science. We introduce a framework for testing geodesic convexity in nonlinear programs on geometric domains. Julia implementation available to leverage certificates in applications. Led by Andrew Cheng, Vaibhav Dixit. bit.ly/3HIlkJu

Single-cell data reveals developmental hierarchies, but common embeddings distort them. We present Contrastive Poincaré Maps, a self-supervised hyperbolic encoder that preserves hierarchies, scales efficiently, and uncovers lineage across datasets. Lead: @nithyabhasker.bsky.social 🧬 bit.ly/4211hMY

Community detection is a classical graph learning task. Our new JMLR paper shows how discrete Ricci curvature and geometric flows unveil (mixed) communities and studies relations between the curvature of a graph and its dual.
w\ Yu Tian, Zach Lubberts: www.jmlr.org/papers/v26/2...

Hypergraphs naturally parametrize higher-order relations.Yet GNNs on hypergraph expansions often outperform specialized topological models. We show that adding hypergraph-level encodings yields significant performance and expressivity gains.w/ Raphael Pellegrin, Lukas Fesser arxiv.org/pdf/2502.09570