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Deep learning and symbolic reasoning are complementary techniques for an intelligent system. However, principled combinations of these techniques are typically limited in scalability, rendering them ill-suited for real-world applications. We propose Scallop, a system that builds upon probabilistic deductive databases, to bridge this gap. The key insight underlying Scallop is a provenance framework that introduces a tunable parameter to specify the level of reasoning granularity. Scallop thereby i) generalizes exact probabilistic reasoning, ii) asymptotically reduces computational cost, and iii) provides relative accuracy guarantees. On synthetic tasks involving mathematical and logical reasoning, Scallop scales significantly better without sacrificing accuracy compared to DeepProbLog, a principled neural logic programming approach. Scallop also scales to a newly created real-world Visual Question Answering (VQA) benchmark that requires multi-hop reasoning, achieving 84.22% accuracy and outperforming two VQA-tailored models based on Neural Module Networks and transformers by 12.42% and 21.66% respectively. 

Incorporating symbolic reasoning into machine learning algorithms is a promising approach to improve performance on learning tasks that re- quire logical reasoning. We study the problem of generating a programmatic variant of referring expressions that we call referring relational pro- grams. In particular, given a symbolic representation of an image and a target object in that image, the goal is to generate a relational program that uniquely identifies the target object in terms of its attributes and its relations to other objects in the image. We propose a neurosymbolic program synthesis algorithm that combines a policy neural network with enumerative search to generate such relational programs. The policy neural net- work employs a program interpreter that provides immediate feedback on the consequences of the decisions made by the policy, and also takes into account the uncertainty in the symbolic representation of the image. We evaluate our algorithm on challenging benchmarks based on the CLEVR dataset, and demonstrate that our approach significantly outperforms several baselines.