We propose a set of modifications that improve training time and likelihood estimation of hierarchical mixture models implemented via Probabilistic Circuits (PCs). Our proposal reduces the complexity of mutual information estimation in the structure learning step of PCs from quadratic to linear in the number of inputs, without sacrificing likelihood estimation performance on image datasets. We repurpose invertible transformations from the lossless compression community to improve likelihood estimation by a factor of up to 25% on benchmark image datasets, making PCs competitive with current standard codecs on low-resolution datasets. Despite our improvements, experiments with low- and high-resolution image datasets indicate that the advantage of lossless neural compression and PCs over standard codecs, such as WebP, disappears as the image size increases, motivating future work on practical lossless neural compression.

@inproceedings{SeveroDCC25,
  author    = {Severo, Daniel and Su, Jingtong and Liu, Anji and Johnson, Jeff and Karrer, Brian and Van den Broeck, Guy and Muckley, Matthew and Ullrich, Karen},
  title     = {Enhancing and Evaluating Probabilistic Circuits for High-Resolution Lossless Image Compression},
  booktitle = {Proceedings of the Data Compression Conference (DCC)},
  month     = 3,
  year      = {2025},
  url       = "https://starai.cs.ucla.edu/papers/SeveroDCC25.pdf",
  keywords  = {conference}
}