Guaranteed Conformance of Neurosymbolic Models to Natural Constraints (ENFORCER)

arXiv | Video

Our constrained neurosymbolic models outperform the Vanilla and Augmented Lagrangian methods with guarantees on conformance to natural constraints in three case studies

• CARLA – Conformance of a vehicle model to unicycle dynamics with emphasis on no drift at-rest.

Overall conformance to unicycle model: Constrained models obtain similar or slightly worse approximation error (expected in light of Theorem 6) but 3 orders-of-magnitude reduction in constraint loss.
Analysis of model predictions at-rest: Augmented Lagrangian and Vanilla methods predict that a car starting from the origin at rest will drift when given zero control inputs. Constrained models accurately predict little to no movement.

• Artificial Pancreas (AP) – Conformance of AP models to ARMAX model that encodes increasing insulin-decreases glucose constraint.

Overall conformance to ARMAX model: Constrained models obtain slightly higher approximation error (expected in light of Theorem 6) but 2 orders-of-magnitude reduction in constraint loss.
Delta-monotonicity Analysis: Augmented Lagrangian and Vanilla methods, unlike Constrained models, violate “increasing insulin, decreases glucose” constraint.

• PyBullet Drones – Conformance of drone models to quadrotor dynamics with emphasis on hover. See our paper for the complete set of results.

Data and Models

The processed data and trained models can be found inside each case study’s directory at this drive folder.

The raw data is also available inside each case study’s directory at this drive folder.

Alternatively, the instructions to collect all data and train the ARMAX constraint model specifically for AP can be found at README_for_Data_Collection.md.

Training Constrained Neural Network Dynamics Models

Setup conda env:

conda create -n DL_env python=3.8
conda activate DL_env
conda install pytorch torchvision torchaudio pytorch-cuda=11.7 -c pytorch -c nvidia
pip install neupy scipy pybullet

Train vanilla and constrained neural network dynamics models as follows where NAME_OF_ENV can be one of {Carla, Drones, AP, Quadrupeds}

cd scripts
bash run_Vanillas.sh
bash run_{NAME_OF_ENV}.sh

AP delta monotonicity analysis

bash run_delta_monotonicity.sh

Carla prediction drift analysis

bash run_test_at_rest.sh

Some helpful information

• scripts/train.py is the main file. All the bash files above call this file with different arguments. If loading data and models from the drive link above, set –only_eval.
• scripts/dataset.py contains all dataset classes to both load labelled D datasets and create unlabelled \Omega datasets. These classes also create memories (via neupy’s neural gas) in the input space. And compute all lower and upper bounds for each voronoi cell in the input space (where each cell corresponds to one memory).
• scripts/model.py contains the models and trainers. The trainers contain the symbolic wrapper around the neural network. The loss function can be augmented lagrangian or simple MSE.