  We propose a new method to ensure neural ordinary differential equations
(ODEs) satisfy output specifications by using invariance set propagation. Our
approach uses a class of control barrier functions to transform output
specifications into constraints on the parameters and inputs of the learning
system. This setup allows us to achieve output specification guarantees simply
by changing the constrained parameters/inputs both during training and
inference. Moreover, we demonstrate that our invariance set propagation through
data-controlled neural ODEs not only maintains generalization performance but
also creates an additional degree of robustness by enabling causal manipulation
of the system's parameters/inputs. We test our method on a series of
representation learning tasks, including modeling physical dynamics and
convexity portraits, as well as safe collision avoidance for autonomous
vehicles.
