PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEs

Dániel Rácz, Mihály Petreczky, Bálint Daróczy
7/7/2023
cs.LG

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Abstract

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.

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Cite this paper

@article{rcz2023bounds,
  title  = {PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEs},
  author = {Dániel Rácz and Mihály Petreczky and Bálint Daróczy},
  year   = {2023},
  eprint = {2307.03630},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2307.03630v1}
}

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