| --- |
| 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} |
| } |
| ``` |
|
|
