Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes

2026-07-27

AI Summary

This work addresses the challenge that existing attention mechanisms on triangular meshes lack intrinsic geometric properties and invariance to triangulation. To overcome this limitation, the authors propose a novel geometric attention mechanism that models queries, keys, and values as intrinsic, triangulation-invariant continuous functions. By leveraging finite element methods to discretize integrals, the approach reformulates the attention computation pipeline in a manner consistent with the underlying geometry. As the first framework to systematically integrate both intrinsicness and triangulation invar日消息, the method demonstrates significant performance gains over state-of-the-art approaches across multiple tasks, including high-frequency signal prediction, deformation estimation, dense correspondence (both full and partial shape matching), and feature descriptor learning.

Abstract

This work proposes an adaptation of the attention mechanism for triangle meshes. The core observation is that endowing the attention mechanism with critical properties for learning over meshes -- intrinsicality and triangulation-agnosticism -- enables it to attain state-of-the-art results over several learning-based tasks in geometry-processing. The above is achieved by modifying the attention mechanism from the bottom up based on simple principles from geometry-processing. Namely, the quantities used within attention -- queries, keys and values -- are created by an intrinsic, triangulation-agnostic network, and treated as discretizations of continuous functions. From that, we devise an appropriate attention mechanism that operates over triangle meshes through standard FEM discretization of the resulting integrals of the above functions. Surprisingly, as far as we know, this straightforward approach has not been utilized for learning over meshes. Experiments show our method exceeds current state of the art, including both mesh-based architectures as well as point cloud transformers. Namely, we show significant improvements on several common benchmarks and tasks -- predicting canonical high-frequency signals; predicting deformations; computing dense correspondences, both between full shapes and partial ones; and predicting feature descriptors.

Problem

• mesh learning
• attention mechanism
• intrinsic
• triangulation-agnostic
• geometry processing

Innovation

• intrinsic attention
• triangulation-agnostic
• mesh learning
• finite element method
• geometric deep learning