Innovation
Methods, ideas, or system contributions that make the work stand out.
Neural ODEs
Concurrent Learning
Lyapunov Stability
Adjoint Gradient Decomposition
Online Learning
Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees
🤖 AI Summary
This work addresses the learning instability arising from the absence of Lyapunov stability guarantees in online training of neural ordinary differential equations (ODEs) by proposing the NODE-CL method. By decomposing the adjoint gradient structure and constructing a Lyapunov function, the regressor properties of the system are revealed. This insight enables the design of a Gauss–Newton optimization algorithm that eliminates the need for state derivative estimation, thereby achieving concurrent online learning with rigorous stability guarantees and computable stability certificates. Experimental evaluations on the DeepMind Control Suite demonstrate that the proposed approach significantly reduces prediction errors and exhibits superior noise robustness compared to existing baselines, attaining or closely approaching optimal accuracy in several scenarios.
📝 Abstract
Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.
🔎 Similar Papers
No similar papers found.
