# VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data

arXiv: https://arxiv.org/abs/2307.03553 · HTML: https://mlsanity.com/paper/2307.03553/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [A Neural Representation of Sketch Drawings](https://mlsanity.com/paper/1704.03477/) (2017)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Multi-Graph Transformer for Free-Hand Sketch Recognition](https://mlsanity.com/paper/1912.11258/) (2019)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [Field Convolutions for Surface CNNs](https://mlsanity.com/paper/2104.03916/) (2021)
- [SHREC'22 Track: Sketch-Based 3D Shape Retrieval in the Wild](https://mlsanity.com/paper/2207.04945/) (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)
- [Supervised deep learning of elastic SRV distances on the shape space of curves](https://mlsanity.com/paper/2101.04929/) (2021)
- [Reconstruction of convex bodies from moments](https://mlsanity.com/paper/1605.06362/) (2016)
- [An inexact matching approach for the comparison of plane curves with general elastic metrics](https://mlsanity.com/paper/2001.02858/) (2020)
- [SketchCleanNet -- A deep learning approach to the enhancement and correction of query sketches for a 3D CAD model retrieval system](https://mlsanity.com/paper/2207.00732/) (2022)

## Built on by (most cited first, 4 of 4)

- [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024)
- [Explainable Binary Classification of Separable Shape Ensembles](https://mlsanity.com/paper/2410.12994/) (2024)
- [SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data](https://mlsanity.com/paper/2506.01189/) (2025)
- [Feature-based morphological analysis of shape graph data](https://mlsanity.com/paper/2602.16120/) (2026)

## Abstract (arXiv)

We present a novel geometric deep learning layer that leverages the varifold gradient (VariGrad) to compute feature vector representations of 3D geometric data. These feature vectors can be used in a variety of downstream learning tasks such as classification, registration, and shape reconstruction. Our model's use of parameterization independent varifold representations of geometric data allows our model to be both trained and tested on data independent of the given sampling or parameterization. We demonstrate the efficiency, generalizability, and robustness to resampling demonstrated by the proposed VariGrad layer.