String Stability of Learned Car-Following Models: Audit, Differentiable Penalties, a Certified Hybrid and Corridor-Level Validation

Trajectory accuracy does not establish whether learned car-following laws remain stable in a closed loop. We evaluate six neural or hybrid architectures and a nearest-neighbour baseline trained on 12,512 highway events, combining a pre-specified core protocol with exploratory extensions: anchored equilibrium audits, platoon tests and 1445 corridor simulations of two NGSIM sites against macroscopic ground truth. Five unconstrained networks beat the Intelligent Driver Model by 8–33% in trajectory error yet have 84–95% string-unstable equilibria. Jacobian regularisation stabilises the memoryless models with little accuracy loss; standard rollout-based penalties leave the recurrent models unstable, and a longer-window pilot helps but leaves the hypothesis open. For a hybrid with a margin-constrained core and a Lipschitz-bounded residual, a sufficient condition for local linear string stability is verified over gaps at grid speeds and rechecked after fine-tuning. In the baseline corridor configuration, this hybrid has the lowest macro error of the thirteen protocol laws, with no or rare contacts, while the networks that win on trajectory error collide on the unseen site; the certificate is a local linear statement at the verified speeds, and the corridor claims concern the two reconstructed sites, one of them in sample for the fine-tuned laws. A controlled component ablation finds a lower macro error with the derivative budget than without it, although both pass the equilibrium audit. Trajectory accuracy, equilibrium stability, collision behaviour and corridor fidelity require separate assessment.