Deep Sturm-Liouville

Repository with the code of our paper:

David Vigouroux, Joseba Dalmau, Louis Bethune, Victor Boutin (2025). Deep Sturm–Liouville: From Sample-Based to 1D Regularization with Learnable Orthogonal Basis Functions. Proceedings of the 42nd International Conference on Machine Learning, 2025

Run experiments

cd ./experiments
# <experiment> could be dry_bean, adult, bank, cifar10 and mnist
python3.9 train.py --config=<experiment> 

Folder Structure

.
├── dsl                   # The Deep Sturm-Liouville method
    ├── eigenvalues       # Compute the eigenvalues of Strum-Liouville Problem 
    ├── gradients         # Gradients computation methods with the implicit differentiation theorem
    ├── sl                # Sturm-Liouville and Prufer ODEs solvers with a given set of eigenvalues
    ├── vector_fields     # The field lines ODE solvers with stop conditions at the boundaries of the domain
    
    dsl.py                         # The Deep Sturm-Liouville class
    dirichlet_square_linear_dsl.py # DSL with dirichlet conditions for a square domain with linear spline approximator
    
├── experiments           # The setup of experiments, training files and evaluate files
    ├── config            # The parameters to train tabular datasets (adult, bank and dry bean) and Mnist
    ├── datasets_data     # The (adult, bank and dry bean) datasets
    ├── exp_models        # Folder where the models are saved after training
    ├── models            # Generics Neural Networks architectures configured in the config for each dataset
    ├── tests             # Current test
    train.py              # The training file
    evaluate.py           # Evaluate the performance of a model
└── README.md

Citation

@InProceedings{vigouroux_2025_deep_sturm_liouville,
    author    = {David Vigouroux, Joseba Dalmau, Louis Bethune, Victor Boutin},
    title     = {Deep Sturm–Liouville: From Sample-Based to 1D Regularization with
Learnable Orthogonal Basis Functions},
    booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
    month     = {July},
    year      = {2025},
    publisher = {PMLR}
}

Acknowledgments

This work was carried out within the DEEL project which is part of IRT Saint Exupéry and the ANITI AI cluster. The authors acknowledge the financial support from DEEL's Industrial and Academic Members and the France 2030 program – Grant agreements n°ANR-10-AIRT-01 and n°ANR-23-IACL-0002.