iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Coder

It was estimated that the world produced $59 ZB$ ($5.9 \times 10^{13} GB$) of data in 2020, resulting in the enormous costs of both data storage and transmission. Fortunately, recent advances in deep generative models have spearheaded a new class of so-called "neural compression" algorithms, which significantly outperform traditional codecs in terms of compression ratio. Unfortunately, the application of neural compression garners little commercial interest due to its limited bandwidth; therefore, developing highly efficient frameworks is of critical practical importance. In this paper, we discuss lossless compression using normalizing flows which have demonstrated a great capacity for achieving high compression ratios. As such, we introduce iFlow, a new method for achieving efficient lossless compression. We first propose Modular Scale Transform (MST) and a novel family of numerically invertible flow transformations based on MST. Then we introduce the Uniform Base Conversion System (UBCS), a fast uniform-distribution codec incorporated into iFlow, enabling efficient compression. iFlow achieves state-of-the-art compression ratios and is $5\times$ quicker than other high-performance schemes. Furthermore, the techniques presented in this paper can be used to accelerate coding time for a broad class of flow-based algorithms.