Schur's Positive-Definite Network

This repository contains our PyTorch implementation of the SpodNet model described in Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure. Can Pouliquen, Mathurin Massias, Titouan Vayer (ICLR 2025)

Preamble

In order to launch the scripts, first run the pip install -e . command from the current location (./).

Data generation

Run the ./exps/data/generate_dataset.py script to generate training and testing sets. The following two commands are generic examples:

python generate_dataset.py -set_type train -n 100 -p 20 -den 0.95 -size 10000 -as_tensor 1 -random_state 0 -same_Theta_true 0 ;

python generate_dataset.py -set_type test -n 100 -p 20 -den 0.95 -size 10000 -as_tensor 1 -random_state 1 -same_Theta_true 0 ;

SpodNet implementation

SpodNet layers are contained in the ./spodnet/ folder.

• ./spodnet/framework.py contains the main SpodNet class, which is the generic layer performing various possible updates to create the UBG, PNP or E2E architectures (specified during initialization of the class).

• ./spodnet/perturbation_layers.py contains the classes implementing the three models' different update rules.

Training

The script for training the different models on various datasets is in ./exps/train_spodnet.py, with the desired setting that can be specified in arguments when launching the script. After running the two above lines to generate train and test datasets, a typical command to do so is for example:

python train_spodnet.py -train_samples 1000 -test_samples 100 -n 100 -p 20 -train_batch_size 10 -test_batch_size 100 -precision_sparsity 0.95 -K 1 -epochs 20 -lr 1e-2 -learning_mode 'UBG'