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
arXiv:2608.30417v1 Announce Type: new
Abstract: We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$...
By T\=ikun \^Ong
arXiv:2608. 10566v1 Announce Type: cross Abstract: How many directions does a neural representation use to encode a concept?
By Tingan Jin, Shuhang Dong, Haosong Li, Chung-Hsien Chou
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
By Rahul Khorana, Marcus Noack, Jin Qian
How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank.
arXiv:2606. 07627v1 Announce Type: new Abstract: Transfer learning presumes that a representation learned on source tasks carries structure that remains usable on related target tasks.
By Luciano Melodia
The paper investigates the polynomial coefficients of lightning self‑attention, treating them as coordinates of an algebraic variety. In the single‑token case it identifies the coefficient variety as a rank‑constrained Chow‑type variety and derives algebraic equations; for multiple tokens it shows that linear relations reduce the geometry to coefficients involving interactions between distinct tokens, characterized by a common linear factor and a low‑rank condition. The authors provide explicit families of determinantal, Veronese‑type, and Sylvester resultant‑based invariants, and in the rank‑one case give pencil and flattening equations that define the variety set‑theoretically, with small‑dimension computations confirming the theoretical generators.
By Yulia Alexandr, Hao Duan, Guido Mont\'ufar