  We present a novel Auxiliary Truth enhanced Genetic Algorithm (GA) that uses
logical or mathematical constraints as a means of data augmentation as well as
to compute loss (in conjunction with the traditional MSE), with the aim of
increasing both data efficiency and accuracy of symbolic regression (SR)
algorithms. Our method, logic-guided genetic algorithm (LGGA), takes as input a
set of labelled data points and auxiliary truths (ATs) (mathematical facts
known a priori about the unknown function the regressor aims to learn) and
outputs a specially generated and curated dataset that can be used with any SR
method. Three key insights underpin our method: first, SR users often know
simple ATs about the function they are trying to learn. Second, whenever an SR
system produces a candidate equation inconsistent with these ATs, we can
compute a counterexample to prove the inconsistency, and further, this
counterexample may be used to augment the dataset and fed back to the SR system
in a corrective feedback loop. Third, the value addition of these ATs is that
their use in both the loss function and the data augmentation process leads to
better rates of convergence, accuracy, and data efficiency. We evaluate LGGA
against state-of-the-art SR tools, namely, Eureqa and TuringBot on 16 physics
equations from "The Feynman Lectures on Physics" book. We find that using these
SR tools in conjunction with LGGA results in them solving up to 30.0% more
equations, needing only a fraction of the amount of data compared to the same
tool without LGGA, i.e., resulting in up to a 61.9% improvement in data
efficiency.

Neural and Evolutionary Computing;Artificial Intelligence;Machine Learning;Symbolic Computation