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The bits-back argument suggests that latent variable models can be turnedinto lossless compression schemes. Translating the bits-back argument intoefficient and practical lossless compression schemes for general latentvariable models, however, is still an open problem. Bits-Back with AsymmetricNumeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makesbits-back coding practically feasible for latent variable models with onelatent layer, but it is inefficient for hierarchical latent variable models. Inthis paper we propose Bit-Swap, a new compression scheme that generalizesBB-ANS and achieves strictly better compression rates for hierarchical latentvariable models with Markov chain structure. Through experiments we verify thatBit-Swap results in lossless compression rates that are empirically superior toexisting techniques. Our implementation is available athttps://github.com/fhkingma/bitswap.

Bit-Swap: Recursive Bits-Back Coding for Lossless Compression with Hierarchical Latent Variables