FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows

Aditya Kallappa, Sandeep Nagar, Girish Varma

2023

Abstract

Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible k × k convolutions that are efficient in training and sampling passes. Though these attempts have improved the expressivity and sampling efficiency, they severely lagged behind Glow which used only 1×1 convolutions in terms of sampling time. Also, many of the approaches mask a large number of parameters of the underlying convolution, resulting in lower expressivity on a fixed run-time budget. We propose a k × k convolutional layer and Deep Normalizing Flow architecture which i.) has a fast parallel inversion algorithm with running time O(nk2) (n is height and width of the input image and k is kernel size), ii.) masks the minimal amount of learnable parameters in a layer. iii.) gives better forward pass and sampling times comparable to other k ×k convolution-based models on real-world benchmarks. We provide an implementation of the proposed parallel algorithm for sampling using our invertible convolutions on GPUs. Benchmarks on CIFAR-10, ImageNet, and CelebA datasets show comparable perf

Paper Citation

in Harvard Style

Kallappa A., Nagar S. and Varma G. (2023). FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows. In Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 5: VISAPP; ISBN 978-989-758-634-7, SciTePress, pages 338-348. DOI: 10.5220/0011876600003417

in Bibtex Style

@conference{visapp23,
author={Aditya Kallappa and Sandeep Nagar and Girish Varma},
title={FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows},
booktitle={Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 5: VISAPP},
year={2023},
pages={338-348},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011876600003417},
isbn={978-989-758-634-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 5: VISAPP
TI - FInC Flow: Fast and Invertible k × k Convolutions for Normalizing Flows
SN - 978-989-758-634-7
AU - Kallappa A.
AU - Nagar S.
AU - Varma G.
PY - 2023
SP - 338
EP - 348
DO - 10.5220/0011876600003417
PB - SciTePress