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ControlJEPA introduces a novel trajectory regularization method using Lyapunov contraction conditions to constrain hidden-state deviations in large language models, directly addressing limitations in current geometric regularizers that only control direction. By enforcing these stability conditions via a specific loss function, the framework improves model accuracy and data efficiency across multiple benchmarks without requiring architectural changes. This work represents a significant advancement in the theoretical foundations of machine learning model stabilization and fine-tuning techniques.
ControlJEPA: Principled Trajectory Regularization via Lyapunov Tube Loss
arXiv:2610.24951v1 Announce Type: new Abstract: 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}
Abstract: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{this https URL}
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.24951 [cs.LG]
(or arXiv:2610.24951v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.24951 Focus to learn more arXiv-issued DOI via DataCite
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