Neural Hybrid Automata Supplementary Material 14 A.1 Neural Hybrid Automata: Modules and Hyperparameters 14 A.2 Gradient Pathologies

A.1 Neural Hybrid Automata: Modules and Hyperparameters We provide a notation and summary table for Neural Hybrid Automata (NHA). The table serves as a quick reference for the core concepts introduced in the main text. The only NHA hyperparameter beyond module architectural choices is m, or number of latent modes provided to the model at initialization. Performance effects of changing m have been explored in Section 5.2 and Appendix B.2. Appendix B.2 further provides analyzes potential techniques to prune additional modes. A.2 Gradient Pathologies We provide some theoretical insights on the phenomenon of gradient pathologies with the simple example of a one-dimensional linear hybrid system with two modes and one timed jump, { ax This, in turn, affects the gradients for b, which results different than 0 despite the fact that b, from (A.1) should not be affecting the solution at points t In nonlinear systems with multiple events (including stochasticity) these effects can have a great empirical effect on a training procedure.