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We propose a new method to ensure neural ordinary differential equations(ODEs) satisfy output specifications by using invariance set propagation. Ourapproach uses a class of control barrier functions to transform outputspecifications into constraints on the parameters and inputs of the learningsystem. This setup allows us to achieve output specification guarantees simplyby changing the constrained parameters/inputs both during training andinference. Moreover, we demonstrate that our invariance set propagation throughdata-controlled neural ODEs not only maintains generalization performance butalso creates an additional degree of robustness by enabling causal manipulationof the system's parameters/inputs. We test our method on a series ofrepresentation learning tasks, including modeling physical dynamics andconvexity portraits, as well as safe collision avoidance for autonomousvehicles.

On the Forward Invariance of Neural ODEs