Attention on the Sphere

• URL: http://arxiv.org/abs/2505.11157v1
• Date: Fri, 16 May 2025 11:59:30 GMT
• Title: Attention on the Sphere
• Authors: Boris Bonev, Max Rietmann, Andrea Paris, Alberto Carpentieri, Thorsten Kurth,
• Abstract summary: We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to process data defined on the two-dimensional sphere.<n>By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant.<n>To further enhance both scalability and model performance, we propose simulating neighborhood attention on the sphere.
• Score: 0.5431339024941462
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Related papers

• Geometric Operator Learning with Optimal Transport [77.16909146519227]
  We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries.<n>For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space.<n> Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses.
  arXiv  Detail & Related papers  (2025-07-26T21:28:25Z)
• Adaptive Particle-Based Shape Modeling for Anatomical Surface Correspondence [3.743399165184124]
  Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts.<n>Recent advances incorporate implicit radial basis function representations as self-supervised signals to better capture the complex geometric properties of anatomical structures.<n>This paper introduces two mechanisms to increase surface adaptivity while maintaining consistent particle configurations.
  arXiv  Detail & Related papers  (2025-07-10T02:19:10Z)
• Representing spherical tensors with scalar-based machine-learning models [0.0]
  equivariant models of 3D point clouds are able to approximate structure-property relations in a way that is fully consistent with the structure of the rotation group.<n>The symmetry constraints make this approach computationally demanding and cumbersome to implement.<n>We propose approximations of the general expressions that, while lacking universal approximation properties, are fast, simple to implement, and accurate in practical settings.
  arXiv  Detail & Related papers  (2025-05-08T16:45:28Z)
• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations [0.0]
  We introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations.<n>Our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes.
  arXiv  Detail & Related papers  (2025-04-24T08:30:32Z)
• Learning Shape-Independent Transformation via Spherical Representations for Category-Level Object Pose Estimation [42.48001557547222]
  Category-level object pose estimation aims to determine the pose and size of novel objects in specific categories.<n>Existing correspondence-based approaches typically adopt point-based representations to establish the correspondences between primitive observed points and normalized object coordinates.<n>We introduce a novel architecture called SpherePose, which yields precise correspondence prediction through three core designs.
  arXiv  Detail & Related papers  (2025-03-18T05:43:42Z)
• EDM: Equirectangular Projection-Oriented Dense Kernelized Feature Matching [49.15373858190824]
  We introduce the first learning-based dense matching algorithm, termed Equirectangular Projection-Oriented Kernelized Feature Matching (EDM)<n>Our proposed method achieves notable performance enhancements, with improvements of +26.72 and +42.62 in AUC@5deg on the Matterport3D and Stanford2D3D datasets.
  arXiv  Detail & Related papers  (2025-02-28T03:37:01Z)
• 3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction [50.07071392673984]
  Existing methods learn 3D rotations parametrized in the spatial domain using angles or quaternions. We propose a frequency-domain approach that directly predicts Wigner-D coefficients for 3D rotation regression. Our method achieves state-of-the-art results on benchmarks such as ModelNet10-SO(3) and PASCAL3D+.
  arXiv  Detail & Related papers  (2024-11-01T12:50:38Z)
• GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation [60.33467489955188]
  This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework. We propose a new dynamic 3D Gaussian framework based on motion factorization to recover the object as 3D Gaussian point sets. In addition to the extracted object surfaces, the Gaussian-informed continuum also enables the rendering of object masks during simulations.
  arXiv  Detail & Related papers  (2024-06-21T07:37:17Z)
• SphereDiffusion: Spherical Geometry-Aware Distortion Resilient Diffusion Model [63.685132323224124]
  Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains. In this paper, we introduce a novel framework of SphereDiffusion to address these unique challenges. Experiments on Structured3D dataset show that SphereDiffusion significantly improves the quality of controllable spherical image generation and relatively reduces around 35% FID on average.
  arXiv  Detail & Related papers  (2024-03-15T06:26:46Z)
• Concentric Spherical GNN for 3D Representation Learning [53.45704095146161]
  We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.
  arXiv  Detail & Related papers  (2021-03-18T19:05:04Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.