Neural ODEs与并发学习结合实现稳定在线学习
Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees
Neural ODEs首次获得Lyapunov稳定性保证，在动态系统学习中表现优异，尤其在噪声环境下优势明显。
研究人员证明了Neural ODEs的伴随梯度包含正半定轨迹算子作用于参数误差的结构，为在线学习提供了Lyapunov保证。该方法在四个DeepMind Control Suite领域测试，在速度测量噪声下，三个领域达到最低中位预测误差，比基于观察器的并发学习性能提升最多8倍。在清洁测量条件下，在pendulum任务上表现最佳，在cartpole和reacher任务上与最佳基线方法相差不超过1.6倍。
Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees
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.