Does a car’s neural network model conform to Newton’s first laws?
Key Insight
Neural network dynamics models are the workhorse for robotics, personalized medicine, scientific discovery…
But they do not readily conform to natural constraints (physics, medicine, etc.)!
We learn neural networks constrained-by-construction
with a symbolic wrapper.
Motivation
We can leverage readily available black-box physics and medical simulators!
Trajectories generated, starting at rest at the origin, with zero acceleration and steering for 20 timesteps.
Our constrained models conform (have negligible drift). Augmented lagrangian has a large drift.
MLP trained on CARLA simulator data.
Problem Formulation
Overall Approach (key ideas)
Results
Guarantees
Consider:
Given:
Find:
Step 1 . Learn memories (prototypes) that represent the state-action space topology using a Growing Neural Gas.
Step 2 . Build a partition of the state-action space using these memories as center of Voronoi cells.
Step 3 . Build interval abstractions of the black-box model M for each Voronoi cell.
Step 4 . Learn neural network constrained by construction.
,
,
Code
arXiv
Informally, assuming the vanilla model has low approx. loss, the constrained model will have guaranteed conformance to model M with a small increase in approx. loss (that reduces with more memories)
Conformance of an NN model trained on artificial pancreas simulator to “increased insulin decreases glucose” constraints
Conformance of a NN model trained on PyBullet Drones simulator to first principles quadrotor dynamics
Ours
Augmented Lagrangian
Vanilla
Order-of-magnitude lower constraint loss (and similar or slightly higher approximation loss)
Related
and
Future
Work
Performance (approx., constraint, efficiency)
No prior knowledge
Lots of prior knowledge
PINN (white-box M)
Constraint
Layers
(inefficient with black-box M)
Vanilla
Augmented
Lagrangian
Ours (black-box M)
Future Work
Guaranteed Conformance of Neurosymbolic
(Dynamics) Models to Natural Constraints
Kaustubh Sridhar, Souradeep Dutta, James Weimer, Insup Lee