An Exact Solver for Satisfiability Modulo Counting with Probabilistic Circuits
Keywords: Satisfiabilty, Satisfiability Modulo Counting, Uncertainty in AI, Statistical AI
TL;DR: We propose an exact solver for Satisfiability Modulo Counting with probabilistic circuits
Abstract: Satisfiability Modulo Counting (SMC) is a general language to reason about problems integrating statistical and symbolic artificial intelligence. An SMC formula is an SAT formula in which the truth values of a few Boolean predicates are determined by model counting, or equivalently, probabilistic inference. Existing solvers optimize surrogate objectives and hence provide no formal guarantee. Hence, an exact solver is desperately in need. However, the direct integration of satisfiability and probabilistic inference solvers results in slow SMC solving because of many back-and-forth invocations of both solvers. We develop KOCO-SMC, a fast exact SMC solver, exploiting the fact that many similar probabilistic inferences are needed throughout SMC solving. We compile the probabilistic inference part of SMC solving into probabilistic circuits, supporting efficient lower and upper-bound computation. Experiment results in several real-world applications demonstrate that our approach provides exact solutions, much better than those from approximate solvers, while is more efficient than direct integration with the current exact solvers.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 4810
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