ControlJEPA: Principled Trajectory Regularization via Lyapunov Tube Loss

Overview & Synopsis

Next-token prediction leaves hidden-state trajectories largely unconstrained, while existing geometric regularizers primarily control the direction rather than the magnitude of trajectory deviations. We introduce \emph{ControlJEPA}, a trajectory regularization framework based on a discrete-time Lyapunov contraction condition from practical Input-to-State Stability theory. Its Lyapunov Tube Loss penalizes violations of this condition on a normalized, scale-invariant measure of transversal deviation. When the contraction condition holds at every step, the hidden-state trajectory remains within an explicit tube around the reference secant. In the partial-ISS regime, we bound mean transversal energy, temporal variance, and average tube width using the Lyapunov loss and contraction parameters, with horizon-independent variance bounds under uniformly bounded violations. ControlJEPA requires no architectural modifications. Across six benchmarks and six model families, it consistently improves accuracy and data efficiency over standard fine-tuning and prior trajectory regularizers. The resulting smoother transversal profile also persists empirically during inference, when the regularizer is inactive. The code is publicly available at: \url{https://github.com/t-khanusa/ControlJEPA}