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：我们研究了将神经网络与符号推理相结合的问题。近期引入的概率神经符号学习框架（如DeepProbLog）采用指数时间精确推理，限制了概率神经符号学习解决方案的可扩展性。我们提出近似神经符号推理（A-NeSI）：一种利用神经网络进行可扩展近似推理的新型概率神经符号学习框架。A-NeSI具备以下特性：1）在不改变概率逻辑语义的前提下，以多项式时间执行近似推理；2）利用背景知识生成的数据进行训练；3）能够生成预测结果的符号解释；4）可在测试阶段保证逻辑约束的满足，这对安全关键应用至关重要。实验表明，A-NeSI是首个以端到端方式解决具有指数组合复杂度的三项神经符号任务的方法。最终，我们的实验证明A-NeSI在实现可解释性与安全性的同时，未对性能造成损失。