  Symbolic regression (SR) methods attempt to learn mathematical expressions
that approximate the behavior of an observed system. However, when dealing with
multivariate systems, they often fail to identify the functional form that
explains the relationship between each variable and the system's response. To
begin to address this, we propose an explainable neural SR method that
generates univariate symbolic skeletons that aim to explain how each variable
influences the system's response. By analyzing multiple sets of data generated
artificially, where one input variable varies while others are fixed,
relationships are modeled separately for each input variable. The response of
such artificial data sets is estimated using a regression neural network (NN).
Finally, the multiple sets of input-response pairs are processed by a
pre-trained Multi-Set Transformer that solves a problem we termed Multi-Set
Skeleton Prediction and outputs a univariate symbolic skeleton. Thus, such
skeletons represent explanations of the function approximated by the regression
NN. Experimental results demonstrate that this method learns skeleton
expressions matching the underlying functions and outperforms two GP-based and
two neural SR methods.
