A Seq2Seq approach to Symbolic Regression

Luca Biggio, Tommaso Bendinelli, Aurelien Lucchi, Giambattista Parascandolo

Abstract:

Deep neural networks have proved to be powerful function approximators. The
large hypothesis space they implicitly model allows them to fit very complicated
black-box functions to the training data. However, often the data generating
process is characterized by a concise and relatively simple functional form. This
is especially true in natural sciences, where elegant physical laws govern the
behaviour of the quantities of interest. In this work, we address this dichotomy
from the perspective of Symbolic Regression (SR). In particular, we apply a
fully-convolutional seq2seq model to map numerical data to the corresponding
symbolic equations. We demonstrate the effectiveness of our approach on a large
set of mathematical expressions by providing both a qualitative and a quantitative
analysis of our results. Additionally, we release our new equation-generator Python
library in order to facilitate benchmarking and stimulate new research on SR.