Most neural architectures admit a GSVD representation making the nonlinear portion left-invertible and norm-preserving before the final linear layer.
ReLU is globally1-Lipschitz; smooth activations with bounded derivative on a compact interval are Lipschitz there by the mean-value theorem
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A Generalized Singular Value Theory for Neural Networks
Most neural architectures admit a GSVD representation making the nonlinear portion left-invertible and norm-preserving before the final linear layer.