The Information Limits of Neural Controlled Differential Equations Under Sparse Observations

arXiv:2611.03887v1 Announce Type: new Abstract: Neural controlled differential equations (Neural CDEs) evolve hidden states along continuous paths constructed by interpolating discrete observations. Sparse measurements leave the input between observation times undetermined, and admissible continuous paths consistent with the same data can produce different terminal states. We characterize this ambiguity for planar drivers with bounded speed. The set of compatible terminal states admits a leading-order zonotopic approximation determined by feasible signed areas and transported Lie brackets. Its projection onto a scalar prediction yields a computable, target-specific ambiguity certificate. We also study the number of measurements needed to reduce the remaining uncertainty.