arXiv:2509. 25778v3 Announce Type: replace Abstract: We presents a method for constructing neural networks intrinsically on statistical manifolds via the lognormal distribution.
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: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.
The paper introduces flow charts, a conditional invertible neural network designed to approximate normal coordinates on Riemannian manifolds, enabling fast Euclidean approximations of exponential and logarithmic maps. It presents a novel nonnegative loss function that is zero exactly when the chart is normal, and demonstrates that flow charts match or surpass specialized neural geodesic interpolators across sixteen synthetic and data‑derived geometries. When pretrained, flow charts achieve a median 60–70× speedup over numerical baselines while maintaining comparable logarithmic map estimation error and improving numerical geodesic solver accuracy.
arXiv:2509. 24627v2 Announce Type: replace Abstract: Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions.
arXiv:2609.30487v1 Announce Type: cross Abstract: We here develop a functional neural network, termed MatFAE, for learning trajectories on the Riemannian manifold of symmetric positive definite (SPD)...
arXiv:2607. 08783v1 Announce Type: cross Abstract: Manifold-valued measurements are prevalent in various machine learning tasks.
arXiv:2608. 00571v1 Announce Type: new Abstract: Learning solution operators for differential equations is a central problem in scientific machine learning.
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:2608. 19688v1 Announce Type: cross Abstract: We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks.
arXiv:2606. 17185v1 Announce Type: new Abstract: Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators.
arXiv:2401. 14381v3 Announce Type: replace Abstract: We propose two graph neural network layers for graphs with features in a Riemannian manifold.
arXiv:2609.16805v1 Announce Type: new Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit a "Ridge of Optimization" characterized by extreme stability and a...