Patching Up Circuit Learning on Images

Probabilistic circuits (PCs) have emerged as generative models guaranteeing tractable probabilistic inference. However, tractability comes at the price of larger model sizes than in other neural generative models. As such, to scale PCs to high-dimensional data such as images, previous work has devised several parameter sharing techniques as well as fast evaluation protocols that consider learning PCs on independent image patches. In this work, we revisit this practice to highlight a surprising learnability issue: models that assume independence counterintuitively can yield better likelihoods than models that do not. To break this apparent bottleneck and to scale PCs further, we introduce a recursive parameter sharing construction (RePA) that fosters efficiency without assuming independence. In a set of rigorous experiments, we show that RePA can greatly reduce time and memory consumption while yielding competitive likelihoods.