---
library_name: pytorch
tags:
  - functional-pca
  - implicit-neural-representations
  - orthonormal-bases
---

# Learning Orthonormal Bases for Function Spaces: pretrained FPCA models

Trained checkpoints for the official implementation of
[*Learning Orthonormal Bases for Function Spaces*](https://arxiv.org/abs/2605.19959) (NeurIPS 2026).
Code: [github.com/HamidrezaKmK/Learning-ONBs](https://github.com/HamidrezaKmK/Learning-ONBs).

Each subfolder is one functional-PCA experiment: a learned mean function, a dictionary with a learned
orthogonal synthesis, and a learned isometry (an Eulerian flow) that turns the dictionary into
principal functions for the data.

| Subfolder | Data | Dictionary |
|---|---|---|
| `1d_fpca` | 1-D tent + sine processes | Fourier |
| `1d_fpca_haar` | 1-D tent + sine processes | Haar wavelets |
| `1d_fpca_voronoi` | 1-D tent + sine processes | Voronoi cells |
| `dwsnets_mnist_eulerian` | MNIST SIRENs (DWSNets) | 2-D Fourier |
| `implicit_zoo_cifar_eulerian` | CIFAR-10 SIRENs | 2-D Fourier, RGB |
| `celeba_eulerian` | CelebA-HQ 64×64 | 2-D Fourier, RGB |

Each holds `config.yaml` (the training config), `model.safetensors` (weights only) and
`metadata.json` (training epoch and captured energy).

## Usage

```python
# pip install from the GitHub repo, then:
from infidictionary.pretrained import load_pretrained
from infidictionary.domain_samplers import SquareSampler

model = load_pretrained("Shengdebao/Learning-ONBs", subfolder="dwsnets_mnist_eulerian")
xy = SquareSampler(stratified=True, add_noise=False).sample(28)   # 28x28 grid on [0, 1]^2
basis = model.basis(xy, num_atoms=64)   # (64, 784, 1) learned principal functions
mean = model.mean(xy)                   # (784, 1)
```

The analysis notebooks in the GitHub repo download these automatically.

## Citation

```bibtex
@inproceedings{kamkari2026learning,
  title={Learning Orthonormal Bases for Function Spaces},
  author={Kamkari, Hamidreza and Nabizadeh, Mohammad Sina and Solomon, Justin},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
  year={2026},
  eprint={2605.19959},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2605.19959}
}
```