Sum-product networks (SPNs) are a promis-ing avenue for probabilistic modeling andhave been successfully applied to varioustasks. However, some theoretic propertiesabout SPNs are not yet well understood. Inthis paper we fill some gaps in the theoreticfoundation of SPNs. First, we show that theweights of any complete and consistent SPNcan be transformed into locally normalizedweights without changing the SPN distribu-tion. Second, we show that consistent SPNscannot model distributions significantly (ex-ponentially) more compactly than decompos-able SPNs. As a third contribution, we ex-tend the inference mechanisms known forSPNs with finite states to generalized SPNswith arbitrary input distributions.

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