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We study the task of smoothing a circuit, i.e., ensuring that all children ofa plus-gate mention the same variables. Circuits serve as the building blocksof state-of-the-art inference algorithms on discrete probabilistic graphicalmodels and probabilistic programs. They are also important for discrete densityestimation algorithms. Many of these tasks require the input circuit to besmooth. However, smoothing has not been studied in its own right yet, and onlya trivial quadratic algorithm is known. This paper studies efficient smoothingfor structured decomposable circuits. We propose a near-linear time algorithmfor this task and explore lower bounds for smoothing decomposable circuits,using existing results on range-sum queries. Further, for the important case ofAll-Marginals, we show a more efficient linear-time algorithm. We validateexperimentally the performance of our methods.

Smoothing Structured Decomposable Circuits