LGML: Logic Guided Machine Learning
This addresses the challenge of data-efficient symbolic regression for mathematical functions, though it appears incremental as it builds on existing logic and ML techniques.
The authors tackled the problem of learning mathematical functions from data by introducing Logic Guided Machine Learning (LGML), which combines machine learning with logic solvers to ensure consistency with auxiliary truths, resulting in several orders of magnitude improvements in data efficiency compared to a standard MLP approach.
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).