The paper introduces Cartan flow matching, a framework for training flow matching models on Riemannian symmetric spaces such as spheres, hyperbolic space, and Grassmannians. By leveraging the algebraic structure of these manifolds, the authors reformulate flow matching on a subspace of the Lie algebra of the isometry group, thereby linearizing the problem and eliminating the need for geodesic interpolation paths. The framework is demonstrated on real Grassmannians SO(n)/SO(k) × SO(n-k).
By Francesco Ruscelli, Ferdinando Zanchetta, Rita Fioresi
arXiv:2610.01322v1 Announce Type: cross
Abstract: We introduce the Clifford Sheaf Neural Network (CSNN), an equivariant sheaf neural network for geometric graphs that places a Clifford algebra on eac...
By Kotaro Kamiya, Joel Nicholls
arXiv:2609.00521v1 Announce Type: cross
Abstract: From horizon detection to fibre structures in X-ray imaging, many vision tasks recover lines via peak detection in Hough space $H=S^1\times\mathbb{R}...
By Benjamin El-Zein, Dominik Eckert, Paul Zech, Christopher Syben, Bernhard Geiger, Steffen Kappler, Sebastian Stober
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.
By Gergely B\'erczi, Young-Hoon Kiem
arXiv:2607. 06723v2 Announce Type: replace-cross Abstract: Adaptive optimizers carry hidden states that change how visible gradients become parameter motion.
By Zavier Li
arXiv:2606. 20183v1 Announce Type: new Abstract: Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it.
By Jian Xu, Delu Zeng, John Paisley, Qibin Zhao