Where to spend approximation in neurosymbolic inference: APRICOT's tensor-train recompression cuts weighted model count error by orders of magnitude
Probabilistic neurosymbolic inference combines neural predictions with symbolic constraints by computing a weighted model count, which is #P-hard exactly, and existing methods each place approximation at a different stage. APRICOT unifies bottom-up compilation into a three-step pipeline and instantiates factor compilation and product recompression with tensor trains, yielding weighted model count estimates orders of magnitude more accurate than prior methods across six tasks in Sudoku, arithmetic reasoning and scene understanding, with better downstream learning where symbolic factors are tightly coupled.