A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper develops optimal transport methods on the roto-translation group SE2.
A new metric mav offers a practical alternative to costly Riemannian distance.
We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.
We investigate solutions to the minimal surface problem with Dirichlet boundary conditions in the roto-translation group equipped with a subRiemannian metric. By work of G. Citti and A. Sarti, such solutions are amodal completions of occluded visual data when using a model of the first layer of the visual cortex. Using…
SE(3)-Transformers maintain equivariance for 3D data under rotations and translations.
Model explains optical illusions using geometric sub-Riemannian geodesics.
Proposes local coordinate frames for improving model performance in complex dynamical systems.
The affine-additive group is hyperbolic with a non-vanishing 4-capacity.
Convolutional Neural Networks (CNNs) require a large amount of annotated data to learn from, which is often difficult to obtain in the medical domain. In this paper we show that the sample complexity of CNNs can be significantly improved by using 3D roto-translation group convolutions (G-Convs) instead of the more conv…
Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter…
We study minimal surfaces in generic sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called {\it horizontal} area functional associated to the canonical {\it horizontal} area form. We derive the intrinsic equation in the general case…
Extended RDS filtering for positions and orientations, improving crossing structure enhancement and inpainting.
Improved tracking of tangled point sources using Riemannian metrics.
Paper introduces a method to generate physically feasible dynamics with physical priors.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space of positions and orientations as a Lie group…
Study of motion control systems on Lie groups with specific geometric constraints.
In the present paper we consider generic Sub-Riemannian structures on the co-rank 1 non-holonomic vector distributions and introduce the associated canonical volume and ''horizontal'' area forms. As in the classical case, the Sub-Riemannian minimal surfaces can be defined as the critical points of the '`horizontal'' ar…
Extends RDS filtering to position-orientation space for better image processing.
Algorithm finds connected components on Lie groups for multi-orientation image analysis.
PDE-based G-CNNs add geometric symmetries to CNNs without augmentation.