We consider a supervised learning setup in which the goal is to predicts an
outcome from a sample of irregularly sampled time series using Neural
Controlled Differential Equations (Kidger, Morrill, et al. 2020). In our
framework, the time series is a discretization of an unobserved continuous
path, and the outcome depends on this path through a controlled differential
equation with unknown vector field. Learning with discrete data thus induces a
discretization bias, which we precisely quantify. Using theoretical results on
the continuity of the flow of controlled differential equations, we show that
the approximation bias is directly related to the approximation error of a
Lipschitz function defining the generative model by a shallow neural network.
By combining these result with recent work linking the Lipschitz constant of
neural networks to their generalization capacities, we upper bound the
generalization gap between the expected loss attained by the empirical risk
minimizer and the expected loss of the true predictor.

该篇论文处理的是一种监督式学习框架，利用神经控制微分方程预测来自不规则采样时间序列的结果，并通过理论结果与神经网络的 Lipschitz 常数关联，从而上界估计经验风险最小化器得出的期望损失与真实预测器期望损失之间的归纳差距。