We study the problem of combining neural networks with symbolic reasoning. Recently introduced frameworks for Probabilistic Neurosymbolic Learning (PNL), such as DeepProbLog, perform exponential-time exact inference, limiting the scalability of PNL solutions. We introduce Approximate Neurosymbolic Inference (A-NeSI): a new framework for PNL that uses neural networks for scalable approximate inference. A-NeSI 1) performs approximate inference in polynomial time without changing the semantics of probabilistic logics; 2) is trained using data generated by the background knowledge; 3) can generate symbolic explanations of predictions; and 4) can guarantee the satisfaction of logical constraints at test time, which is vital in safety-critical applications. Our experiments show that A-NeSI is the first end-to-end method to solve three neurosymbolic tasks with exponential combinatorial scaling. Finally, our experiments show that A-NeSI achieves explainability and safety without a penalty in performance.

翻译：我们研究神经网络与符号推理相结合的问题。最近引入的概率神经符号学习框架（如DeepProbLog）采用指数级时间精确推理，限制了PNL方法的可扩展性。本文提出近似神经符号推理（A-NeSI）：一种基于神经网络实现可扩展近似推理的新型PNL框架。A-NeSI具备以下特性：1）在不改变概率逻辑语义的前提下，实现多项式时间内的近似推理；2）利用背景知识生成的数据进行训练；3）可生成预测的符号解释；4）能在测试阶段确保逻辑约束的满足性，这对安全关键型应用至关重要。实验表明，A-NeSI是首个能够以指数级组合规模解决三个神经符号任务任务的端到端方法。此外，实验证明A-NeSI在实现可解释性与安全性的同时，不牺牲模型性能。