Shengdebao/Learning-ONBs

Learning Orthonormal Bases for Function Spaces: pretrained FPCA models

Trained checkpoints for the official implementation of Learning Orthonormal Bases for Function Spaces (NeurIPS 2026). Code: 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

# 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

@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}
}