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arXiv · 2012.08863

On The Verification of Neural ODEs with Stochastic Guarantees

Sophie Gruenbacher·Ramin Hasani·Mathias Lechner·Jacek Cyranka·Scott A. Smolka·Radu Grosu
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Abstract

We show that Neural ODEs, an emerging class of time-continuous 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.

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Sophie Gruenbacher, Ramin Hasani, Mathias Lechner, Jacek Cyranka, Scott A. Smolka, Radu Grosu. 2020-12-16. On The Verification of Neural ODEs with Stochastic Guarantees. https://arxiv.org/abs/2012.08863

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