Deep symmetric autoencoders from the EYS perspective

This is the official repository of the paper

S. Brivio, N. R. Franco, Deep symmetric autoencoders from the Eckart-Young-Schmidt perspective (2025),

providing (i) a novel mathematical framework for symmetric autoencoders, (ii) suitable error estimates, and (iii) a brand-new data-driven initialization strategy.

Installation

We suggest to install the library dependecies in a clean conda environment, namely,

conda create -n sym-ae python=3.11.9
conda activate sym-ae
conda install -c conda-forge fenics
pip install -r requirements.txt --no-cache-dir

Code organization

The source code implementation is contained in src and is organized as follows:

• src/activations.py implements bilipschitz activations and relative functionalities.
• src/blocks.py contains the implementation of classes needed to build the neural network architecture skeleton.
• src/modules.py implements AE, SAE, SBAE, and SOAE networks along with their initialization procedures.
• src/NestedPOD.py comprise the definition of the homonymous class, useful for the EYS initialization.
• src/training.py contains the training loop function and relative utilities.
• src/utils.py implements additional utilities for reading and saving files.

The scripts to run are contained in the main folder, whereas notebooks comprise the jupyter notebooks.

Instructions

1. Generate the datasets by executing the notebook notebooks/datagen.ipynb; the saved data are then available in data.
2. Run python comparison.py to generate the results for the comparison analysis (which then will be saved in results);
3. Execute the remaining jupyter notebooks to visualize the numerical results and generate the paper figures, then available in the folder results.

Cite

If the present repository and/or the original paper was useful in your research, please consider citing

@misc{brivio2025saeeys,
      title={Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective}, 
      author={Simone Brivio and Nicola Rares Franco},
      year={2025},
      eprint={2506.11641},
      archivePrefix={arXiv},
      primaryClass={math.NA},
      url={https://arxiv.org/abs/2506.11641}, 
}