# HodgeNet: Learning Spectral Geometry on Triangle Meshes

arXiv: https://arxiv.org/abs/2104.12826 · HTML: https://mlsanity.com/paper/2104.12826/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2021.

## Built on by (most cited first, 13 of 13)

- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [M"obius Convolutions for Spherical CNNs](https://mlsanity.com/paper/2201.12212/) (2022)
- [Laplacian2Mesh: Laplacian-Based Mesh Understanding](https://mlsanity.com/paper/2202.00307/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Representation-Agnostic Shape Fields](https://mlsanity.com/paper/2203.10259/) (2022)
- [HodgeFormer: Transformers for Learnable Operators on Triangular Meshes through Data-Driven Hodge Matrices](https://mlsanity.com/paper/2509.01839/) (2025)
- [NASM: Neural Anisotropic Surface Meshing](https://mlsanity.com/paper/2410.23109/) (2024)
- [CageNet: A Meta-Framework for Learning on Wild Meshes](https://mlsanity.com/paper/2505.18772/) (2025)
- [Iskra: A System for Inverse Geometry Processing](https://mlsanity.com/paper/2602.12105/) (2026)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)
- [Learning Laplacian Eigenspace with Mass-Aware Neural Operators on Point Clouds](https://mlsanity.com/paper/2605.24390/) (2026)
- [Recent Advances and Trends in Learning-based 3D Representations](https://mlsanity.com/paper/2606.04871/) (2026)

## Abstract (arXiv)

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.