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

arXiv 2307.03630 ↗First posted 7 Jul 2023cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 21 of its 43 references that are in the map. First posted on arXiv 7 Jul 2023.

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References · 21

  1. 2018Neural Ordinary Differential Equationscited by 3,779
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  3. 2022On Neural Differential Equationscited by 268
  4. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
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  6. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
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  11. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 44
  12. 2020Logarithmic Regret for Adversarial Online Controlcited by 41
9 more
  1. 2022Do Residual Neural Networks discretize Neural Ordinary Differential Equations?cited by 27
  2. 2021Framing RNN as a kernel method: A neural ODE approachcited by 23
  3. 2020Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradientscited by 22
  4. 2023Generalization bounds for neural ordinary differential equations and deep residual networkscited by 21
  5. 2022Robust Classification using Contractive Hamiltonian Neural ODEscited by 13
  6. 2020Learning Recurrent Neural Net Models of Nonlinear Systemscited by 11
  7. 2021Reduced-order modeling of LPV systems in the Loewner frameworkcited by 3
  8. 2021LPV Modeling of Nonlinear Systems: A Multi-Path Feedback Linearization Approachcited by 1
  9. 2023Learning Stable and Robust Linear Parameter-Varying State-Space Modelscited by 1

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