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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. 

Software APIs exhibit rich diversity and complexity which not only renders them a common source of programming errors but also hinders program analysis tools for checking them. Such tools either expect a precise API specification, which requires program analysis expertise, or presume that correct API usages follow simple idioms that can be automatically mined from code, which suffers from poor accuracy. We propose a new approach that allows regular programmers to find API misuses. Our approach interacts with the user to classify valid and invalid usages of each target API method. It minimizes user burden by employing an active learning algorithm that ranks API usages by their likelihood of being invalid. We implemented our approach in a tool called ARBITRAR for C/C++ programs, and applied it to check the uses of 18 API methods in 21 large real-world programs, including OpenSSL and Linux Kernel. Within just 3 rounds of user interaction on average per API method, ARBITRAR found 40 new bugs, with patches accepted for 18 of them. Moreover, ARBITRAR finds all known bugs reported by a state-of-the-art tool APISAN in a benchmark suite comprising 92 bugs with a false positive rate of only 51.5% compared to APISAN’s 87.9% 

Optimizing molecules for desired properties is a fundamental yet challenging task in chemistry, material science, and drug discovery. This paper develops a novel algorithm for optimizing molecular properties via an Expectation- Maximization (EM) like explainable evolutionary process. The algorithm is designed to mimic human experts in the process of searching for desirable molecules and alternate between two stages: the first stage on explainable local search which identifies rationales, i.e., critical subgraph patterns accounting for desired molecular properties, and the second stage on molecule completion which explores the larger space of molecules containing good rationales. We test our approach against various baselines on a real-world multi-property optimization task where each method is given the same number of queries to the property oracle. We show that our evolution-by-explanation algorithm is 79% better than the best baseline in terms of a generic metric combining aspects such as success rate, novelty, and diversity. Human expert evaluation on optimized molecules shows that 60% of top molecules obtained from our methods are deemed successful. 

Inspired by the Thomson problem in physics where the distribution of multiple propelling electrons on a unit sphere can be modeled via minimizing some potential energy, hyperspherical energy minimization has demonstrated its potential in regularizing neural networks and improving their generalization power. In this paper, we first study the important role that hyperspherical energy plays in neural network training by analyzing its training dynamics. Then we show that naively minimizing hyperspherical energy suffers from some difficulties due to highly non-linear and non-convex optimization as the space dimensionality becomes higher, therefore limiting the potential to further improve the generalization. To address these problems, we propose the compressive minimum hyperspherical energy (CoMHE) as a more effective regularization for neural networks. Specifically, CoMHE utilizes projection mappings to reduce the dimensionality of neurons and minimizes their hyperspherical energy. According to different designs for the projection mapping, we propose several distinct yet well-performing variants and provide some theoretical guarantees to justify their effectiveness. Our experiments show that CoMHE consistently outperforms existing regularization methods, and can be easily applied to different neural networks.