PAL - A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction

This repo contains the code for PAL, a probabilistic neuro-symbolic layer for algebraic constraint satisfaction. This is a simplified implementation that focuses on the spline-case.

Check out the paper: https://arxiv.org/abs/2503.19466v1

Example Prediction

This is an example prediction of PAL on the Constrained Stanford Drone Dataset (https://github.com/april-tools/constrained-sdd). We predict a probability distribution over the future trajectory while guaranteeing constraint-satisfaction.

Citation

Leander Kurscheidt, Paolo Morettin, Roberto Sebastiani, Andrea Passerini, Antonio Vergari, A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction, arXiv:2503.19466

Installation

Just clone it and run:

./setup.sh

And you're ready to go!

Constrained Stanford Drone Dataset

We provide an example script how to train a simple MLP on the constrained SDD-dataset. A model can be trained like this:

python pal/training/train_mlp_sdd.py --epochs 10 --init_last_layer_positive --seed 1744909132

This should result in a (mean) test log-likelihood of -1.9149.

There is also an unconditional variant of the experiment (fig. 1) in the paper. It can be trained like this:

python pal/training/train_unconditional_sdd.py --init_positive --use_float64 --num_knots 14 --num_mixtures 10 --lr 0.01 --epochs 1500 --seed 1764087361

This should result in a (mean) test log-likelihood of -2.9493.

GASP!

The dependency was added via subtree from https://github.com/april-tools/gasp.git into pal/wmi/gasp! update via:

git subtree pull --prefix pal/wmi/gasp https://github.com/april-tools/gasp.git main --squash

push via:

git subtree push --prefix pal/wmi/gasp https://github.com/april-tools/gasp.git main