Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks.

Appendix B proves universal approximation of the Neural CDE model, and is substantially more technical than the rest of this paper. To evaluate the model as discussed in Section 3.2, X must be at least continuous and piecewise differentiable. For example this would be accomplished by taking X to be a quadraticsplineinterpolation. Cubic splines give essentially the minimum regularity for the techniques discussed in thispapertowork'outofthebox'inallcases. The behaviour of controlled differential equations are typically described through the signature transform (also known as path signature or simply signature) [20] of the driving process X.