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# 🚀 Grounding Continuous Representations in Geometry: Equivariant Neural Fields

[![License: MIT](https://img.shields.io/badge/License-MIT-purple)](https://opensource.org/licenses/MIT)
[![Python](https://img.shields.io/badge/python-3.11+-blue.svg)](https://www.python.org/downloads/release/python-3110/)
[![jax_badge][jax_badge_link]](https://github.com/google/jax)
[![badge](https://img.shields.io/badge/ArXiv-2406.06660-b31b1b?logo=arxiv&logoColor=b31b1b)](https://arxiv.org/abs/2406.05753)

[jax_badge_link]: https://img.shields.io/badge/JAX-Accelerated-9cf.svg?style=flat-square&logo=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC0AAAAaCAYAAAAjZdWPAAAIx0lEQVR42rWWBVQbWxOAkefur%2B7u3les7u7F3ZIQ3N2tbng8aXFC0uAuKf2hmlJ3AapIgobMv7t0w%2Ba50JzzJdlhlvNldubeq%2FY%2BXrTS1z%2B6sttrKfQOOY4ns13ecFImb47pVvIkukNe4y3Junr1kSZ%2Bb3Na248tx7rKiHlPo6Ryse%2F11NKQuk%2FV3tfL52yHtXm8TGYS1wk4J093wrPQPngRJH9HH1x2fAjMhcIeIaXKQCmd2Gn7IqSvG83BueT0CMkTyESUqm3vRRggTdOBIb1HFDaNl8Gdg91AFGkO7QXe8gJInpoDjEXC9gbhtWH3rjZ%2F9yK6t42Y9zyiC1iLhZA8JQe4eqKXklrJF0MqfPv2bc2wzPZjpnEyMEVlEZCKQzYCJhE8QEtIL1RaXEVFEGmEaTn96VuLDzWflLFbgvqUec3BPVBmeBnNwUiakq1I31UcPaTSR8%2B1LnditsscaB2A48K6D9SoZDD2O6bELvA0JGhl4zIYZzcWtD%2BMfdvdHNsDOHciXwBPN18lj7sy79qQCTNK3nxBZXakqbZFO2jHskA7zBs%2BJhmDmr0RhoadIZjYxKIVHpCZngPMZUKoQKrfEoz1PfZZdKAe2CvP4XnYE8k2LLMdMumwrLaNlomyVqK0UdwN%2BD7AAz73dYBpPg6gPiCN8TXFHCI2s7AWYesJgTabD%2FS5uXDTuwVaAvvghncTdk1DYGkL0daAs%2BsLiutLrn0%2BRMNXpunC7mgkCpshfbw4OhrUvMkYo%2F0c4XtHS1waY4mlG6To8oG1TKjs78xV5fAkSgqcZSL0GoszfxEAW0fUludRNWlIhGsljzVjctr8rJOkCpskKaDYIlgkVoCmF0kp%2FbW%2FU%2F%2B8QNdXPztbAc4kFxIEmNGwKuI9y5gnBMH%2BakiZxlfGaLP48kyj4qPFkeIPh0Q6lt861zZF%2BgBpDcAxT3gEOjGxMDLQRSn9XaDzPWdOstkEN7uez6jmgLOYilR7NkFwLh%2B4G0SQMnMwRp8jaCrwEs8eEmFW2VsNd07HQdP4TgWxNTYcFcKHPhRYFOWLfJJBE5FefTQsWiKRaOw6FBr6ob1RP3EoqdbHsWFDwAYvaVI28DaK8AHs51tU%2BA3Z8CUXvZ1jnSR7SRS2SnwKw4O8B1rCjwrjgt1gSrjXnWhBxjD0Hidm4vfj3e3riUP5PcUCYlZxsYFDK41XnLlUANwVeeILFde%2BGKLhk3zgyZNeQjcSHPMEKSyPPQKfIcKfIqCf8yN95MGZZ1bj98WJ%2BOorQzxsPqcYdX9orw8420jBQNfJVVmTOStEUqFz5dq%2F2tHUY3LbjMh0qYxCwCGxRep8%2FK4ZnldzuUkjJLPDhkzrUFBoHYBjk3odtNMYoJVGx9BG2JTNVehksmRaGUwMbYQITk3Xw9gOxbNoGaA8RWjwuQdsXdGvpdty7Su2%2Fqn0qbzWsXYp0nqVpet0O6zzugva1MZHUdwHk9G8aH7raHua9AIxzzjxDaw4w4cpvEQlM84kwdI0hkpsPpcOtUeaVM8hQT2Qtb4ckUbaYw4fXzGAqSVEd8CGpqamj%2F9Q2pPX7miW0NlHlDE81AxLSI2wyK6xf6vfrcgEwb0PAtPaHM1%2BNXzGXAlMRcUIrMpiE6%2Bxv0cyxSrC6FmjzvkWJE3OxpY%2BzmpsANFBxK6RuIJvXe7bUHNd4zfCwvPPh9unSO%2BbIL2JY53QDqvdbsEi2%2BuwEEHPsfFRdOqjHcjTaCLmWdBewtKzHEwKZynSGgtTaSqx7dwMeBLRhR1LETDhu76vgTFfMLi8zc8F7hoRPpAYjAWCp0Jy5dzfSEfltGU6M9oVCIATnPoGKImDUJNfK0JS37QTc9yY7eDKzIX5wR4wN8RTya4jETAvZDCmFeEPwhNXoOlQt5JnRzqhxLZBpY%2BT5mZD3M4MfLnDW6U%2Fy6jkaDXtysDm8vjxY%2FXYnLebkelXaQtSSge2IhBj9kjMLF41duDUNRiDLHEzfaigsoxRzWG6B0kZ2%2BoRA3dD2lRa44ZrM%2FBW5ANziVApGLaKCYucXOCEdhoew5Y%2Btu65VwJqxUC1j4lav6UwpIJfnRswQUIMawPSr2LGp6WwLDYJ2TwoMNbf6Tdni%2FEuNvAdEvuUZAwFERLVXg7pg9xt1djZgqV7DmuHFGQI9Sje2A9dR%2FFDd0osztIRYnln1hdW1dff%2B1gtNLN1u0ViZy9BBlu%2BzBNUK%2BrIaP9Nla2TG%2BETHwq2kXzmS4XxXmSVan9KMYUprrbgFJqCndyIw9fgdh8dMvzIiW0sngbxoGlniN6LffruTEIGE9khBw5T2FDmWlTYqrnEPa7aF%2FYYcPYiUE48Ul5jhP82tj%2FiESyJilCeLdQRpod6No3xJNNHeZBpOBsiAzm5rg2dBZYSyH9Hob0EOFqqh3vWOuHbFR5eXcORp4OzwTUA4rUzVfJ4q%2FIa1GzCrzjOMxQr5uqLAWUOwgaHOphrgF0r2epYh%2FytdjBmUAurfM6CxruT3Ee%2BDv2%2FHAwK4RUIPskqK%2Fw4%2FR1F1bWfHjbNiXcYl6RwGJcMOMdXZaEVxCutSN1SGLMx3JfzCdlU8THZFFC%2BJJuB2964wSGdmq3I2FEcpWYVfHm4jmXd%2BRn7agFn9oFaWGYhBmJs5v5a0LZUjc3Sr4Ep%2FmFYlX8OdLlFYidM%2B731v7Ly4lfu85l3SSMTAcd5Bg2Sl%2FIHBm3RuacVx%2BrHpFcWjxztavOcOBcTnUhwekkGlsfWEt2%2FkHflB7WqKomGvs9F62l7a%2BRKQQQtRBD9VIlZiLEfRBRfQEmDb32cFQcSjznUP3um%2FkcbV%2BjmNEvqhOQuonjoQh7QF%2BbK811rduN5G6ICLD%2BnmPbi0ur2hrDLKhQYiwRdQrvKjcp%2F%2BL%2BnTz%2Fa4FgvmakvluPMMxbL15Dq5MTYAhOxXM%2FmvEpsoWmtfP9RxnkAIAr%2F5pVxqPxH93msKodRSXIct2l0OU0%2FL4eY506L%2B3GyJ6UMEZfjjCDbysNcWWmFweJP0Jz%2FA0g2gk80pGkYAAAAAElFTkSuQmCC

**Authors**: David R. Wessels*, David M. Knigge*,  Riccardo Valperga, Samuele Papa, Sharvaree Vadgama, Efstratios Gavves, Erik J. Bekkers

**equal contribution *

___
## Overview
This is the reproducibility repo for the paper  "Grounding Continuous Representations in Geometry: Equivariant Neural Fields". All experiments
in the paper should be reproducible using the code in this repository. Data for the experiments is mostly downloadable via torch-dataloaders. However, the celeb-A dataset should be downloaded via the following [https://mmlab.ie.cuhk.edu.hk/projects/CelebA.html](link). Shapenet data is downloaded via the [https://www.shapenet.org/](shapenet) website.

___
## Requirements

To install the requirements, we use conda. We recommend creating a new environment for the project.
```
conda create -n enf-jax python=3.11
conda activate enf-jax
```

Install the relevant dependencies.
```
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu
pip install --upgrade "jax[cuda12]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
pip install optax flax orbax wandb matplotlib trimesh hydra-core tqdm netCDF4 py-pde
conda install -c conda-forge dedalus
```

With pyenv, you can install python 3.11 as follows:
```
pyenv install 3.11.1
pyenv virtualenv 3.11.1 enf-jax
pyenv activate enf-jax

pip install -r requirements.txt
pip install -e .
```

## Repo structure
We list relevant components of the repository here:
- `enf/` contains the code for the Equivariant Neural Field.
- `enf/steerable_attention/invariant/` contains the code for the bi-invariants used in the experiments.
- `experiments/` contains the code for all experiments in the paper.

## Experiments

We specify commands per experiment in the [experiments readme](experiments.md).

## Citation
If you find this code useful, please consider citing our paper:
```
@article{wessels2024grounding,
  title={Grounding Continuous Representations in Geometry: Equivariant Neural Fields},
  author={Wessels, David R and Knigge, David M and Papa, Samuele and Valperga, Riccardo and Vadgama, Sharvaree and Gavves, Efstratios and Bekkers, Erik J},
  journal={arXiv preprint arXiv:2406.05753},
  year={2024}
}
```

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