# LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes

arXiv: https://arxiv.org/abs/2403.07536 · HTML: https://mlsanity.com/paper/2403.07536/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [Self-attention Does Not Need O(n2) Memory](https://mlsanity.com/paper/2112.05682/) (2021)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Expander Graph Propagation](https://mlsanity.com/paper/2210.02997/) (2022)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [Multi-Compound Transformer for Accurate Biomedical Image Segmentation](https://mlsanity.com/paper/2106.14385/) (2021)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Surface Vision Transformers: Attention-Based Modelling applied to Cortical Analysis](https://mlsanity.com/paper/2203.16414/) (2022)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [Mesh convolutional neural networks for wall shear stress estimation in 3D artery models](https://mlsanity.com/paper/2109.04797/) (2021)
- [TransforMesh: A Transformer Network for Longitudinal modeling of Anatomical Meshes](https://mlsanity.com/paper/2109.00532/) (2021)
- [Geometric Deep Learning for Post-Menstrual Age Prediction based on the Neonatal White Matter Cortical Surface](https://mlsanity.com/paper/2008.06098/) (2020)
- [The Multiscale Surface Vision Transformer](https://mlsanity.com/paper/2303.11909/) (2023)
- [Neurodevelopmental Phenotype Prediction: A State-of-the-Art Deep Learning Model](https://mlsanity.com/paper/2211.08831/) (2022)

## Built on by (most cited first, 12 of 12)

- [Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior](https://mlsanity.com/paper/2410.11920/) (2024)
- [Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning](https://mlsanity.com/paper/2507.05695/) (2025)
- [Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models](https://mlsanity.com/paper/2501.09046/) (2025)
- [Active Learning for Deep Learning-Based Hemodynamic Parameter Estimation](https://mlsanity.com/paper/2503.03453/) (2025)
- [Universal Collection of Euclidean Invariants between Pairs of Position-Orientations](https://mlsanity.com/paper/2504.03299/) (2025)
- [Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models](https://mlsanity.com/paper/2507.22817/) (2025)
- [GReAT: leveraging geometric artery data to improve wall shear stress assessment](https://mlsanity.com/paper/2508.19030/) (2025)
- [Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems](https://mlsanity.com/paper/2602.11208/) (2026)
- [Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domains](https://mlsanity.com/paper/2601.02157/) (2026)
- [Real-Time Pulsatile Flow Prediction for Realistic, Diverse Intracranial Aneurysm Morphologies using a Graph Transformer and Steady-Flow Data Augmentation](https://mlsanity.com/paper/2601.19876/) (2026)
- [Inpainting physics: self-supervised learning for context-driven fluid simulation](https://mlsanity.com/paper/2605.08832/) (2026)
- [When Does Equivariance Help? Canonical Alignment in Neural Fluid Surrogates](https://mlsanity.com/paper/2605.18816/) (2026)

## Abstract (arXiv)

Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which creates unique challenges in building deep neural network architectures. Furthermore, patient-specific meshes may not be canonically aligned which limits the generalisation of machine learning algorithms. We propose LaB-GATr, a transfomer neural network with geometric tokenisation that can effectively learn with large-scale (bio-)medical surface and volume meshes through sequence compression and interpolation. Our method extends the recently proposed geometric algebra transformer (GATr) and thus respects all Euclidean symmetries, i.e. rotation, translation and reflection, effectively mitigating the problem of canonical alignment between patients. LaB-GATr achieves state-of-the-art results on three tasks in cardiovascular hemodynamics modelling and neurodevelopmental phenotype prediction, featuring meshes of up to 200,000 vertices. Our results demonstrate that LaB-GATr is a powerful architecture for learning with high-fidelity meshes which has the potential to enable interesting downstream applications. Our implementation is publicly available.