On the Universality of Augmented Invertible Networks

Authors: Arthur Bizzi, Karl Igor Martins Guerra
Primary area: learning theory
Keywords: invertible networks, pseudo-invertible, hamiltonian, symplectic, coupling layer, universality

Abstract:
We revisit the universality of augmented invertible networks, reversible architectures that leverage zero padding to increase their expressiveness. Under mild hypotheses, we provide a short proof that a single augmented RevNet block is an universal approximator for Bi-Lipschitz homeomorphisms, which we then extend to Augmented Neural ODEs and i-ResNets. We demonstrate that augmenting these architectures with additional dimensions essentially trivializes their invertible structure, rendering them equivalent to encoder-decoder ensembles. We embrace this equivalence and argue for the use of augmented RevNets, which we demonstrate to be both faster and more expressive in low-dimensional numerical experiments, as compared to other approximately invertible models.

Decision: withdrawn
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