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Lipschitz Flow-box Theorem
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Lipschitz Flow-box Theorem
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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.
Forward citations
Cited by 3 Pith papers
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A Theory of Saddle Escape in Deep Nonlinear Networks
Derives exact Frobenius norm imbalance identity for deep nonlinear networks, classifies activations into four classes, and obtains critical-depth escape time law τ★ = Θ(ε^{-(r-2)}) from reduction to scalar ODE on perm...
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A Theory of Saddle Escape in Deep Nonlinear Networks
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.
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A Theory of Saddle Escape in Deep Nonlinear Networks
An exact norm-imbalance identity classifies activations into four classes and reduces deep nonlinear training flow to a scalar ODE that predicts saddle escape time scaling as ε to the power of minus (r-2) for r bottle...
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