We make three novel contributions to parameter learning and inference in probabilistic sentential decision diagrams (PSDDs). First, rather than traversing the entire PSDD during parameter learning for each dataset example, we pioneer the use of determinism to focus only on the activated partition. Second, we demonstrate how to prune deterministic computation in inference, thereby eliminating the need to propagate probability over every node in the network for each query. Third, we introduce a technique that parallelizes a single circuit evaluation, rather than parallelizing individual multiplications or layer-wise inference. For both learning and inference, experimental results on benchmark PSDDs from various application domains demonstrate state-of-the-art performance.