In this page we briefly describe the datasets and the code for the numerical experiments presented in "A singular Riemannian geometry approach to Deep Neural Networks II. Reconstruction of 1-D equivalence classes". In all the numerical experiments the neural network is learning a function from \( \mathbb{R}^2 \) to \( \mathbb{R} \), restricted to a suitable subset: The region in which we generate the features employed for the training.

The scripts to generate the dataset can be found in the "datasets" folder, containing the following subfolders:

"surface_1": Contains the Python script to generate the dataset and to train the neural network for the first and fourth numerical experiments ("Learning compact equivalence classes" and "Learning preimages of compact equivalence classes").
"surface_2" : Contains the Python script to generate the dataset and to train the neural network for the second numerical experiment ("Learning non compact equivalence classes").
"thermodynamics" : The script "thermodynamics.py" generates the dataset and trains the neural network for the third and fifth numerical experiments ("A thermodynamics problem" and "Thermodynamics: learning a family of isothermal curves"). "true_isothermal.py" plots the true isothermal curve corresponding to the temperature chosen in the paper.
"classification" : Contains the Python script to generate the dataset and to train the neural network for the sixth numerical experiment ("A classification problem").

Every script saves the structure and the weights/biases of the neural network in "weights.csv" and writes the dataset in another csv file, both in the same folder as the script. In addition some plots of the datasets or of the output of the neural network are created.

To train the neural networks employed in the numerical experiments, we use Keras with TensorFlow as backend.