On The Verification of Neural ODEs with Stochastic Guarantees

Abstract

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.

Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving

“…OptNet with CBFs has been used in neural networks as a filter for safe controls [36], but OptNet is not trainable, thus, potentially limiting the system's learning performance. In [14,25,59,16,17], safety guaranteed neural network controllers have been learned through verification-in-the-loop training. A safe neural network filter has been proposed in [15] for a specific vehicle model using verification methods.…”

Adversarial Training is Not Ready for Robot Learning

“…A more rigorous approach, albeit expensive, is to compute an upper-bound of the loss of each safety domain and minimize the upper bound via stochastic gradient descent [15], [53]. While computing an upper-bound of a network's output is difficult and may overestimate the true maximum, it provides certified guarantees on the worst-case loss.…”