论文标题
LGML：逻辑指导机器学习
LGML: Logic Guided Machine Learning
论文作者
论文摘要
我们介绍了逻辑指导的机器学习（LGML），这是一种新颖的方法，可以共生结合机器学习（ML）和逻辑求解器，以便从数据中学习数学功能的目标。 LGML由两个阶段组成，即学习相和具有纠正反馈回路的逻辑相，从而从输入数据中学习符号表达式，逻辑相交叉验证了与已知的辅助真理的学习表达的一致性。如果不一致，逻辑阶段将“反例”反馈到学习相。重复此过程，直到学习的表达与辅助真理一致。使用LGML，我们能够学习与毕达哥拉斯定理和正弦函数相对应的表达式，与基于开箱即用的多层perceptron（MLP）的方法相比，数据效率的数量级提高了几个数量级。
We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers with the goal of learning mathematical functions from data. LGML consists of two phases, namely a learning-phase and a logic-phase with a corrective feedback loop, such that, the learning-phase learns symbolic expressions from input data, and the logic-phase cross verifies the consistency of the learned expression with known auxiliary truths. If inconsistent, the logic-phase feeds back "counterexamples" to the learning-phase. This process is repeated until the learned expression is consistent with auxiliary truth. Using LGML, we were able to learn expressions that correspond to the Pythagorean theorem and the sine function, with several orders of magnitude improvements in data efficiency compared to an approach based on an out-of-the-box multi-layered perceptron (MLP).
