# 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

Download#### 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