Lipschitz continuous

[[concept]]

lipschitz stable / continuous

A function $f : x \to y$ is $c -$ Lipschtiz stable/continuous if

| | f (x) - f (x^{'}) | | \leq c | | x - x^{'} | | \forall x, x^{'}

or if $| | f^{'} (x) | | \leq c \forall x$

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GNNs inherit stability from their layers
Lipschitz filters are stable to additive perturbations
Lipschitz graphon filter
continuity for linear functions
convergence bound for graph convolutions
graph convolutions are stable to perturbations in the data and coefficients
integral Lipschitz filters are stable to relative perturbations
integral lipschitz filters are stable to dilations
lipschitz graph convolutions of graph signals converge to lipschitz graphon filters
lipschitz graph filter
stability-discriminability tradeoff for Lipschitz filters
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