IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression

TL;DR

This paper analyzes the theoretical properties of integer discrete flows for lossless compression, refutes previous claims about their flexibility, and proposes architectural improvements that enhance performance and efficiency.

Contribution

It provides a proof that integer discrete flows are more flexible than previously claimed and introduces architectural modifications that improve compression performance.

Findings

Integer discrete flows are more flexible than earlier believed.

Architectural modifications lead to better compression performance.

A simplified model with fewer layers matches or exceeds previous results.

Abstract

In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete nature makes them particularly suitable for lossless compression with entropy coding schemes. We start by investigating a recent theoretical claim that states that invertible flows for discrete random variables are less flexible than their continuous counterparts. We demonstrate with a proof that this claim does not hold for integer discrete flows due to the embedding of data with finite support into the countably infinite integer lattice. Furthermore, we zoom in on the effect of gradient bias due to the straight-through estimator in integer discrete flows, and demonstrate that its influence is highly dependent on architecture choices and less prominent than previously thought. Finally, we show how different architecture modifications improve the performance of this model class for lossless compression, and that they also enable more efficient compression: a model with half the number of flow layers performs on par with or better than the original integer discrete flow model.