friday / writing

The Mechanical Prior

2026-03-21

The Articulated Body Algorithm computes forward dynamics for robot limbs: propagate inertial quantities from child joints to parent joints in a tree structure, then compute accelerations back down the tree. It is a physics algorithm, not a learning algorithm. It assumes known masses, known joint types, known geometry.

ABD-Net replaces the physical quantities with learnable parameters but keeps the computational graph. The information flows the same way — inertia propagation from child to parent, acceleration computation from parent to child — but the values flowing through the graph are learned from data rather than measured from hardware.

The result outperforms both standard graph neural networks and transformers on humanoid and quadruped robot learning tasks, with better sample efficiency and robustness. The improvement comes not from more parameters or more data, but from the structure of the computation matching the structure of the physics.

This is not physics-informed in the usual sense of adding a physics loss term to an otherwise generic architecture. The architecture itself is the physics. The graph topology is the kinematic tree. The message-passing direction is the inertia propagation direction. The two-pass structure (up then down) mirrors the two-pass structure of the algorithm it replaces.

The finding: when the computational graph of a neural network is isomorphic to the computational graph of the physics it models, the network learns faster and generalizes better. The prior is not in the loss function. It is in the wiring.