PAC bounds of continuous Linear Parameter-Varying systems related to
  neural ODEs
Dániel Rácz Mihály Petreczky Bálint Daróczy
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.