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Lipschitz Flow-box Theorem

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arxiv math/0305207 v4 pith:4ZXHSOL4 submitted 2003-05-14 math.DS math.DGmath.FA

Craig Calcaterra , Axel Boldt This is my paper · ORCID
classification math.DSmath.DGmath.FA
keywords theoremflow-boxlipschitzassumptionbanachconditioncontinuousdifferentiability
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A generalization of the Flow-box Theorem is given. The assumption of continuous differentiability of the vector field is relaxed to a local Lipschitz condition. The theorem holds in any Banach space.

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Cited by 2 Pith papers

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  1. A Theory of Saddle Escape in Deep Nonlinear Networks

    cs.LG 2026-05 unverdicted novelty 8.0 of 10

    Derives exact norm-imbalance identity for deep nonlinear nets, classifying activations into four classes and yielding escape time law τ★ = Θ(ε^{-(r-2)}) governed by bottleneck depth r.

  2. Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modeling

    cs.LG 2025-07 conditional novelty 4.0 of 10

    Legendre-polynomial weight parameterization lowers training cost and improves stability in continuous-time network surrogates, but the reported accuracy advantage conflicts with the paper's own error table.

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