# SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data

arXiv: https://arxiv.org/abs/2506.01189 · HTML: https://mlsanity.com/paper/2506.01189/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 19 of 19)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [Lightweight Deep Learning for Resource-Constrained Environments: A Survey](https://mlsanity.com/paper/2404.07236/) (2024)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [Surface Networks](https://mlsanity.com/paper/1705.10819/) (2017)
- [3D Shape Sequence of Human Comparison and Classification using Current and Varifolds](https://mlsanity.com/paper/2207.12485/) (2022)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)
- [A new variational model for shape graph registration with partial matching constraints](https://mlsanity.com/paper/2105.00678/) (2021)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Metrics, quantization and registration in varifold spaces](https://mlsanity.com/paper/1903.11196/) (2019)
- [VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data](https://mlsanity.com/paper/2307.03553/) (2023)
- [Universal approximation theorem for neural networks with inputs from a topological vector space](https://mlsanity.com/paper/2409.12913/) (2024)
- [Neural varifolds: an aggregate representation for quantifying the geometry of point clouds](https://mlsanity.com/paper/2407.04844/) (2024)

## Built on by (most cited first, 1 of 1)

- [Feature-based morphological analysis of shape graph data](https://mlsanity.com/paper/2602.16120/) (2026)

## Abstract (arXiv)

Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the non-Euclidean nature of shape spaces, which are defined as equivalence classes under invariance groups. Building machine learning frameworks that incorporate such invariances, notably to shape parametrization, is often crucial to ensure generalizability of the trained models to new observations. This work proposes textitSVarM to exploit varifold representations of shapes as measures and their duality with test functions h:ℝn × Sn-1 rightarrow ℝ. This method provides a general framework akin to linear support vector machines but operating instead over the infinite-dimensional space of varifolds. We develop classification and regression models on shape datasets by introducing a neural network-based representation of the trainable test function h. This approach demonstrates strong performance and robustness across various shape graph and surface datasets, achieving results comparable to state-of-the-art methods while significantly reducing the number of trainable parameters.