  The bits-back argument suggests that latent variable models can be turned
into lossless compression schemes. Translating the bits-back argument into
efficient and practical lossless compression schemes for general latent
variable models, however, is still an open problem. Bits-Back with Asymmetric
Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes
bits-back coding practically feasible for latent variable models with one
latent layer, but it is inefficient for hierarchical latent variable models. In
this paper we propose Bit-Swap, a new compression scheme that generalizes
BB-ANS and achieves strictly better compression rates for hierarchical latent
variable models with Markov chain structure. Through experiments we verify that
Bit-Swap results in lossless compression rates that are empirically superior to
existing techniques. Our implementation is available at
https://github.com/fhkingma/bitswap.
