On the Universality of Augmented Invertible Networks
Invertible networks;pseudo-invertible;hamiltonian;symplectic;coupling layer;universality
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@misc{
bizzi2024on,
title={On the Universality of Augmented Invertible Networks},
author={Arthur Bizzi and Karl Igor Martins Guerra},
year={2024},
url={https://openreview.net/forum?id=sohdkxQ5H5}
}
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.
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~Arthur_Bizzi1 ~Karl_Igor_Martins_Guerra1
Arthur Bizzi Karl Igor Martins Guerra
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Invertible networks pseudo-invertible hamiltonian symplectic coupling layer universality
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bizzi|on_the_universality_of_augmented_invertible_networks
learning theory
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On the Universality of Augmented Invertible Networks
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