Transport of Algebraic Structure to Latent Embeddings

This codebase accompanies our paper (project website):

Transport of Algebraic Structure to Latent Embeddings
Samuel Pfrommer, Brendon G. Anderson, Somayeh Sojoudi
2024 International Conference on Machine Learning (ICML, Spotlight).

Setup and execution

To set up the environment, make a virtualenv and run bash setup.sh.

Make sure to log in to a Weights & Biases account (free for academic users).

All scripts to reproduce the results should then be run from within latalg with the virtual environment activated.

bash experiments/gen_data.sh
bash experiments/train_latent_model.sh
bash experiments/train_oeprator_modules.sh
bash experiments/test.sh

Output figures will lie in the test_out directory.

Key implementations

The various combinations of candidate operations are defined in main/algebra.py, as are Algorithms 2 and 3 for generating terms. The parameterization of the induced latent algebra is defined in main/operator_module.py. The computation of metrics is defined in _step_variables in main/operator_module.py. The data directory contains code for generating the dataset of INRs as well as training an inr2vec encoder-decoder architecture over this dataset.