  We propose the first practical learned lossless image compression system,
L3C, and show that it outperforms the popular engineered codecs, PNG, WebP and
JPEG 2000. At the core of our method is a fully parallelizable hierarchical
probabilistic model for adaptive entropy coding which is optimized end-to-end
for the compression task. In contrast to recent autoregressive discrete
probabilistic models such as PixelCNN, our method i) models the image
distribution jointly with learned auxiliary representations instead of
exclusively modeling the image distribution in RGB space, and ii) only requires
three forward-passes to predict all pixel probabilities instead of one for each
pixel. As a result, L3C obtains over two orders of magnitude speedups when
sampling compared to the fastest PixelCNN variant (Multiscale-PixelCNN).
Furthermore, we find that learning the auxiliary representation is crucial and
outperforms predefined auxiliary representations such as an RGB pyramid
significantly.
