🥼 LaB-GATr 🐊

This repository contains the official implementation of "LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes" (MICCAI 2024) and "Geometric algebra transformers for large 3D meshes via cross-attention" (GRaM workshop @ ICML 2024).

Installation

We recommend creating a new Anaconda environment:

conda create --name lab-gatr python=3.10
conda activate lab-gatr

Next, install PyTorch and xFormers depending on your system. In our case, this was

pip install torch==2.1.0 --index-url https://download.pytorch.org/whl/cu121
pip install xformers==0.0.22.post7 --index-url https://download.pytorch.org/whl/cu121

Additonally, we need Pytorch Geometric (currently only v2.4.0) and some dependencies

pip install torch_geometric==2.4.0
pip install torch_scatter torch_cluster -f https://data.pyg.org/whl/torch-2.1.0+cu121.html

You can now install lab_gatr (which also installs gatr) via

pip install .

from within this repository.

Getting started

LaB-GATr requires two things: a point cloud pooling transform for the tokenisation (patching) and a geometric algebra interface to embed your data in $\mathbf{G}(3, 0, 1)$. In the following we provide a minimal working example.

Let us first create a dummy mesh: n positions and orientations (e.g. surface normal) and an arbitrary scalar feature (e.g. geodesic distance).

import torch

n = 10000

pos, orientation = torch.rand((n, 3)), torch.rand((n, 3))
scalar_feature = torch.rand(n)

We need to compute auxiliary tensors that will be used during tokenisation (patching). We use Pytorch Geometric.

from lab_gatr import PointCloudPoolingScales
import torch_geometric as pyg

transform = PointCloudPoolingScales(rel_sampling_ratios=(0.2,), interp_simplex='triangle')
data = transform(pyg.data.Data(pos=pos, orientation=orientation, scalar_feature=scalar_feature))

Next, we define the embedding of our data in $\mathbf{G}(3, 0, 1)$. This means setting the number of input and output channels plus some logic that wraps around the model. We package this interface as Python class for convenience.

from gatr.interface import embed_oriented_plane, extract_translation

class GeometricAlgebraInterface:
    num_input_channels = num_output_channels = 1
    num_input_scalars = num_output_scalars = 1

    @staticmethod
    @torch.no_grad()
    def embed(data):

        multivectors = embed_oriented_plane(normal=data.orientation, position=data.pos).view(-1, 1, 16)
        scalars = data.scalar_feature.view(-1, 1)

        return multivectors, scalars

    @staticmethod
    def dislodge(multivectors, scalars):
        output = extract_translation(multivectors).squeeze()

        return output

That's it! With the interface class we just defined, we can create the model and run inference.

from lab_gatr import LaBGATr

model = LaBGATr(GeometricAlgebraInterface, d_model=8, num_blocks=10, num_attn_heads=4, use_class_token=False)
output = model(data)

Setting use_class_token=True will result in mesh-level instead of vertex-level output.

New features

Besides tokenisation via message passing, lab_gatr now also supports cross-attention for squence reduction. You can switch between the two by setting pooling_mode='message_passing' or pooling_mode='cross_attention' (default).

Citation

If you use LaB-GATr in your research, please cite either (or both):

@article{Suk2024LaBGATrGA,
  title={LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes},
  author={Julian Suk and Baris Imre and Jelmer M. Wolterink},
  journal={ArXiv},
  year={2024},
  volume={abs/2403.07536},
  url={https://api.semanticscholar.org/CorpusID:268363685}
}

@inproceedings{
  suk2024geometric,
  title={Geometric algebra transformers for large 3D meshes via cross-attention},
  author={Julian Suk and Pim De Haan and Baris Imre and Jelmer M. Wolterink},
  booktitle={ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling},
  year={2024},
  url={https://openreview.net/forum?id=T2bBUlaJTA}
}