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.
Related stories
arXiv Computer Vision
4d ago
Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations
arXiv:2609.37817v1 Announce Type: new Abstract: Geometric representation learning predominantly scaffolds representations onto flat Euclidean subspaces or compact product tori ($\mathbb{T}^K$). Howev...
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
Aug 21
K\"ahler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold
arXiv:2608. 19584v1 Announce Type: new Abstract: We study landscapes for complex-parameterized networks.
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 AI
4d ago
Building Transformation Layers for Riemannian Neural Networks
arXiv:2609.35436v2 Announce Type: replace Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....
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.
arXiv Machine Learning
Sep 4
A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.