This code implements the experiments from the NeurIPS 2021 paper:

"Learning Graph Cellular Automata"
Daniele Grattarola, Lorenzo Livi, Cesare Alippi

Paper | Blog

Bibtex:

@article{grattarola2021learning,
  title={Learning graph cellular automata},
  author={Grattarola, Daniele and Livi, Lorenzo and Alippi, Cesare},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={20983--20994},
  year={2021}
}

The dependencies of the project are listed in requirements.txt. You can install them with:

pip install -r requirements.txt

Most scripts have CLI options that you can use to control the behaviour. Run:

python [script_name].py --help

to see a list of options.

The experiments with the Voronoi GCA can be reproduced using the scripts in the voronoi folder.

To train the GNCA:

python run_voronoi.py

To compute the entropy of the GNCA after every training step:

python run_voronoi_entropy.py

To plot the entropies as a function of the rule's threshold:

python run_entropy_v_th.py

The experiments with the Boids GCA can be reproduced using the scripts in the boids folder.

To train the GNCA:

python run_boids.py

To compute the complexity of the GNCA every 10 training steps:

python run_boids.py --test_complexity_every 10

To make all the plots included in the paper, after training the GNCA with run_boids.py:

python evaluate_boids.py

To train the minimal MLP that implements the transition rule:

python run_learn_exact_mlp.py

The experiments to train the GNCA to converge to a fixed target can be reproduced using the scripts in the fixed_target folder.

To train the GNCA:

python run_fixed_target.py  # By default, t=10

To train the GNCA by sampling t randomly in a range:

python run_fixed_target.py --min_steps 10 --max_steps 21  # t \in [10, 20]

To make all plots included in the paper:

python make_plots.py --path results/Grid2d/  # Replace with target folder for each graph