Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional geometry processing. As an alternative, we present a technique for learning from meshes built from standard geometry processing modules and operations. We show that low-order eigenvalue/eigenvector computation from operators parameterized using discrete exterior calculus is amenable to efficient approximate backpropagation, yielding spectral per-element or per-mesh features with similar formulas to classical descriptors like the heat/wave kernel signatures. Our model uses few parameters, generalizes to high-resolution meshes, and exhibits performance and time complexity on par with past work.

中文翻译：

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HodgeNet：学习三角形网格上的光谱几何

受针对其他应用（例如图像处理中的应用）设计的学习工具包的局限性约束，许多基于网格的学习算法采用的数据流从常规几何处理的角度来看是非典型的。作为替代方案，我们提出了一种从标准几何处理模块和操作构建的网格中学习的技术。我们表明，使用离散外部演算参数化的算子的低阶特征值/特征向量计算适用于有效的近似反向传播，产生具有类似于经典描述符（如热/波核签名）的公式的频谱每个元素或每个网格特征。我们的模型使用很少的参数，推广到高分辨率网格，并表现出与过去工作相同的性能和时间复杂性。