  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).
