PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEs
This work addresses theoretical guarantees for neural ODEs, which are incremental as it extends existing PAC bounds to a specific class of systems.
The paper tackles the problem of learning neural ordinary differential equations (neural ODEs) by embedding them into linear parameter-varying (LPV) systems, and provides probably approximately correct (PAC) bounds under stability that do not depend on the integration interval.
We consider the problem of learning Neural Ordinary Differential Equations (neural ODEs) within the context of Linear Parameter-Varying (LPV) systems in continuous-time. LPV systems contain bilinear systems which are known to be universal approximators for non-linear systems. Moreover, a large class of neural ODEs can be embedded into LPV systems. As our main contribution we provide Probably Approximately Correct (PAC) bounds under stability for LPV systems related to neural ODEs. The resulting bounds have the advantage that they do not depend on the integration interval.