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S. Grünbacher, R. Hasani, M. Lechner, J. Cyranka, S. Smolka, R. Grosu:
"On The Verification of Neural ODEs with Stochastic Guarantees";
ArXiv, . (2020), 12 pages.

We show that Neural ODEs, an emerging class of timecontinuous
neural networks, can be verified by solving a
set of global-optimization problems. For this purpose, we
introduce Stochastic Lagrangian Reachability (SLR), an
abstraction-based technique for constructing a tight Reachtube
(an over-approximation of the set of reachable states
over a given time-horizon), and provide stochastic guarantees
in the form of confidence intervals for the Reachtube bounds.
SLR inherently avoids the infamous wrapping effect (accumulation
of over-approximation errors) by performing local
optimization steps to expand safe regions instead of repeatedly
forward-propagating them as is done by deterministic
reachability methods. To enable fast local optimizations, we
introduce a novel forward-mode adjoint sensitivity method
to compute gradients without the need for backpropagation.
Finally, we establish asymptotic and non-asymptotic convergence
rates for SLR.

https://publik.tuwien.ac.at/files/publik_293051.pdf