ICLR 2025

Published as a conference paper at ICLR 2025
PARFAM—(NEURAL GUIDED) SYMBOLIC REGRES-
SION VIA CONTINUOUS GLOBAL OPTIMIZATION
Philipp Scholl, Katharina Bieker, Hillary Hauger & Gitta Kutyniok∗
Mathematical Institute
LMU Munich
Munich, Germany
scholl@math.lmu.de
ABSTRACT
The problem of symbolic regression (SR) arises in many different applications,
such as identifying physical laws or deriving mathematical equations describ-
ing the behavior of financial markets from given data. In this paper, we present
our new approach ParFam that utilizes parametric families of suitable symbolic
functions to translate the discrete symbolic regression problem into a continuous
one, resulting in a more straightforward setup compared to current state-of-the-
art methods. In combination with a global optimizer, this approach results in a
highly effective method to tackle the problem of SR. We theoretically analyze the
expressivity of ParFam and demonstrate its performance with extensive numerical
experiments based on the common SR benchmark suit SRBench, showing that we
achieve state-of-the-art results. Moreover, we present an extension incorporating
a pre-trained transformer network (DL-ParFam) to guide ParFam, accelerating the
optimization process by up to two magnitudes. Our code and results can be found
at https://github.com/Philipp238/parfam.
1
INTRODUCTION
Symbolic regression (SR) aims to discover concise and interpretable mathematical functions that
accurately model input-output relationships. This focus on simplicity is crucial for applications
requiring model analysis and trustworthiness, such as in physical or chemical sciences (Quade et al.,
2016; Angelis et al., 2023; Wang et al., 2019). SR finds broad application in diverse fields, including
ecosystem dynamics (Chen et al., 2019), solar power forecasting (Quade et al., 2016), financial
market analysis (Liu & Guo, 2023), materials science (He & Zhang, 2021), and robotics (Oplatkova
& Zelinka, 2007). The growing body of SR r...