Probabilistic circuits (PCs) are tractable probabilistic models, enabling exact and efficient computation of many queries. When modeling images with PCs, one key step in the learning pipeline is decorrelation. Since RGB channels in pixels are highly correlated in natural images, learning is instead performed on a transformed pixel space with much lower channel-wise correlation, making the learning task easier. However, the transformations are not bijective; there are values in the modeled space not realizable as images in the original space. In particular, probability mass is ‘leaked’ to such invalid values during learning on the transformed space. Moreover, the resulting model does not enable tractable inference on the original space. We propose to use bitblasting – representing a distribution over complex objects as a distribution over bits – to address these problems. We show that the relationship between the original and transformed spaces can be encoded exactly and succinctly in the structure of the PC, removing the leakage problem, improving modeling performance, and providing a tractable model over the original space. Preliminary empirical results support our approach.

@inproceedings{GargTPM25,
  author    = {Garg, Poorva and Wang, Benjie and Broadrick, Oliver and Van den Broeck, Guy and Millstein, Todd},
  title     = {Bitblasting for Constrained Decorrelation in Tractable Image Modeling},
  booktitle = {Proceedings of the UAI Workshop on Tractable Probabilistic Modeling (TPM)},
  url       = "https://starai.cs.ucla.edu/papers/GargTPM25.pdf",
  month     = 7,
  year      = {2025},
  keywords  = {workshop}
}