arXiv AI
Aug 11
The Field Knows: Cross-Dimensional Geometry from Navigation to Black Holes
arXiv:2608. 07566v1 Announce Type: new Abstract: We introduce a continuous metric field framework trained by a single causal contrastive loss.
Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks
arXiv:2607. 05489v1 Announce Type: cross Abstract: The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds.
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arXiv AI
Jul 24
Riemannian Deep Learning: Modules, Networks, and Geometries
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv AI
Aug 5
Sphere Retraction Normalizations
arXiv:2608. 02668v1 Announce Type: cross Abstract: Residual connections are the de facto mechanism for training deep neural networks stably.
arXiv AI
Jul 22
Riemannian Deep Learning:Modules, Networks, and Geometries
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv Machine Learning
Jul 30
Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces
arXiv:2505. 16035v3 Announce Type: replace Abstract: We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers.
arXiv Machine Learning
Jul 27
Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers
arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
arXiv AI
Jul 13
LieBN: Batch Normalization over Lie Groups
arXiv:2607. 08783v1 Announce Type: cross Abstract: Manifold-valued measurements are prevalent in various machine learning tasks.
arXiv Machine Learning
Jun 11
A Riemannian Approach to Low-Rank Optimal Transport
arXiv:2606. 12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature.
Hugging Face Trending Papers
Jul 21
Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models
Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support.
arXiv Machine Learning
1d ago
Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianc
arXiv:2608. 14556v1 Announce Type: new Abstract: Physical fields on meshes require a separation between topology and geometry: conservation laws are topological and should be exact, while geometry, material response, and anisotropic coupling must be learned from data.
arXiv AI
Jun 18
Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation
arXiv:2606. 18828v1 Announce Type: cross Abstract: Traditional approaches place intelligence in the agent, whether as a learned policy or a search procedure.
arXiv Machine Learning
Aug 11
Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles
arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.