The paper extends Neural ODE for considering input observations and incorporating them in a continuous manner. Inputs can then be irregularly sampled and partially observed. Experiments are performed for classification tasks on a number of time series datasets. Continuous functions are built by using interpolation schemes – here splines. All the reviewers agree that this is a strong contribution extending the use of Neural ODE idea to additional settings and possibly overcoming some issues of the original approach, e.g. computational efficiency. The paper is well motivated and the approach theoretically grounded. The reviewers agree that the authors clarified several issues in their response. The authors are encouraged to use the additional page to incorporate the additional information discussed in the response, e.g. regarding the technical proof (section 3, R4) and the role of splines (e.g the baseline spline + RNN as suggested by R3, R1).