On The Verification of Neural ODEs with Stochastic Guarantees

• URL: http://arxiv.org/abs/2012.08863v1
• Date: Wed, 16 Dec 2020 11:04:34 GMT
• Title: On The Verification of Neural ODEs with Stochastic Guarantees
• Authors: Sophie Gruenbacher, Ramin Hasani, Mathias Lechner, Jacek Cyranka, Scott A. Smolka, Radu Grosu
• Abstract summary: We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. We introduce Lagran Reachability ( SLR), an abstraction-based technique for constructing a tight Reachtube.
• Score: 14.490826225393096
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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