approach as training progresses. With the help of data softening and entropy regularization, we were
able to obtain consistently higher test set LL. Next, we compare our HCLT model (with regularization)
with the state-of-the-art PSDD (Strudel [17] and LearnPSDD [16]) and SPN (EinSumNet [13],
LearnSPN [18], ID-SPN [47], and RAT-SPN [48]) learning algorithms. Results are summarized
in Table 1. With proper regularization, HCLT out-performed all baselines in 10 out of 20 datasets.
Comparing with individual baselines, HCLT out-performs both PSDD learners on all datasets; HCLT
Tractable Regularization of Probabilistic Circuits