IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression
This work addresses theoretical and practical bottlenecks in lossless compression models for data compression applications, though it is incremental in improving an existing method.
The paper analyzes integer discrete flows for lossless compression, proving they are as flexible as continuous flows and showing that gradient bias effects are less significant than believed, with architectural modifications enabling a model with half the layers to match or exceed original performance.
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.