We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

翻译：我们提出了一种新方法，通过使用不变集传播来确保神经常微分方程（ODE）满足输出规范。该方法利用一类控制屏障函数，将输出规范转化为对学习系统参数和输入的约束条件。这种设计使得我们只需在训练和推理过程中修改受约束的参数/输入，即可实现输出规范保证。此外，我们证明了通过数据控制的神经ODE进行不变集传播，不仅保持了泛化性能，还通过实现系统参数/输入的因果操控，产生了额外的鲁棒性提升。我们将该方法应用于一系列表示学习任务中，包括物理动力学建模、凸性特征刻画以及自动驾驶车辆的安全避障控制。