arXiv:2607.24954cs.GRcs.CV2026-07

让注意力机制适应网格,实现更稳定高效的几何学习。

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

论文配图:Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes
图 1 · 摘自论文原文
  • 用内在不变的网络生成查询、键、值,避免依赖三角剖分。
  • 在多个基准上超越现有方法,尤其在高频信号和形状对应任务中表现突出。
  • 适合从事网格建模、三维几何处理的研究者使用。

本文提出一种适用于三角网格的注意力机制改进方法。核心思想是赋予注意力机制在网格上学习所需的两个关键属性:内在性与三角剖分无关性。通过从几何处理的基本原理出发,将查询、键、值构建为内在且与三角剖分无关的网络输出,并视其为连续函数的离散化表示。在此基础上,设计基于标准有限元法(FEM)离散化积分的注意力机制,直接作用于三角网格。令人惊讶的是,这一看似简单的思路此前尚未被用于网格上的学习任务。实验表明,该方法在多个常见基准和任务中均达到当前最优性能,包括预测高频率标准信号、形变预测、密集对应关系计算(全形与部分形之间)以及特征描述符预测,显著优于现有的网格架构及点云变换器。

原文摘要 · Abstract (English)

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.

网格学习注意力机制几何处理

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