Neural operators that are diffeomorphisms generally cannot be continuously discretized, but strongly monotone neural operators can, and bilipschitz neural operators decompose into strongly monotone layers plus a single isometry.
Universal approximation property of invertible neural networks
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Can neural operators always be continuously discretized?
Neural operators that are diffeomorphisms generally cannot be continuously discretized, but strongly monotone neural operators can, and bilipschitz neural operators decompose into strongly monotone layers plus a single isometry.