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.

我们展示了神经ODE可以通过解一组全局优化问题进行验证，为此，我们介绍了随机Lagrangian可达性（SLR）技术，并引入了前向模式伴随灵敏度方法来计算梯度，最终我们为SLR建立了渐近和非渐近收敛率。

关于具有随机保证的神经ODE验证