FInC Flow: Fast and Invertible $k \times k$ Convolutions for Normalizing Flows

• URL: http://arxiv.org/abs/2301.09266v1
• Date: Mon, 23 Jan 2023 04:31:03 GMT
• Title: FInC Flow: Fast and Invertible $k \times k$ Convolutions for Normalizing Flows
• Authors: Aditya Kallappa, Sandeep Nagar, Girish Varma
• Abstract summary: Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models. We propose a $k times k$ convolutional layer and Deep Normalizing Flow architecture.
• Score: 2.156373334386171
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $k \times k$ 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 $1 \times 1$ 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 $k \times k$ convolutional layer and Deep Normalizing Flow architecture which i.) has a fast parallel inversion algorithm with running time O$(n k^2)$ ($n$ 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 $k \times k$ 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 performance to previous works regarding bits per dimension while significantly improving the sampling time.

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