$\partial$SLASH: Probabilistic Circuits for Fast Neural Answer Set Programming

Exact probabilistic inference is #P-hard and CPU-bound, and current neurosymbolic systems utilizing GPUs are approximate by design. Nonetheless, whether exact inference is cheap, can be read off the program. $\partial$SLASH compiles an answer-set program into a reasoning graph. It is a directed graph, implemented as a graph neural network and executed alongside deep neural networks on GPUs. Testing the graph for decomposability and determinism confirms it to be a probabilistic circuit. Hence, one message-passing sweep returns the exact query probability and the gradients of weighted model counting. Where the exactness fails, the offending disjunction goes to cutset sampling under a Hoeffding bound, which on visual question answering still beats every approximate baseline at every clause length, by up to $15$ percentage points. Further, it surpasses the one second per epoch barrier on neurosymbolic benchmarks being an order of magnitude faster than the exact solvers. $\partial$SLASH sums $100$ MNIST digits representing $10^{100}$ possible worlds, none of which are enumerated, at $99\%$ digit accuracy on a single GPU