发表机构
Université de Montréal; Mila; Kiel University（蒙特利尔大学; 米拉研究所; 基尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究为三角形网格学习提出内在与三角剖分无关的注意力机制，通过基于几何处理原理修改注意力机制，用内在网络创建相关量并经有限元离散化设计运行机制，实验表明该方法在多个任务上超当前最优水平。
AI 中文摘要
本文提出了一种适用于三角形网格的注意力机制。核心观察是赋予注意力机制在网格上学习的关键属性——内在性和三角剖分无关性，使其在几何处理中的多个基于学习的任务中取得了最优结果。通过基于几何处理的简单原理自下而上修改注意力机制来实现这一点。具体而言，注意力中使用的量——查询、键和值——由一个内在的、三角剖分无关的网络创建，并被视为连续函数的离散化。由此，我们设计了一种合适的注意力机制，通过对上述函数的积分进行标准有限元离散化来在三角形网格上运行。令人惊讶的是，据我们所知，这种直接的方法尚未用于网格学习。实验表明，我们的方法超过了当前的最优水平，包括基于网格的架构以及点云变压器。具体来说，我们在几个常见的基准测试和任务上有显著改进，如预测规范高频信号、预测变形、计算完整形状和部分形状之间的密集对应关系以及预测特征描述符。
英文摘要
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.
