🤖 AI Summary
Symbolic regression (SR) seeks interpretable mathematical expressions from data, yet conventional genetic programming–based approaches suffer from intricate hyperparameter tuning and low computational efficiency. This paper introduces ParFam, the first framework to formulate discrete SR as a continuous parameter optimization problem: by defining a differentiable family of symbolic functions (e.g., parameterized trigonometric, power, and logarithmic operators), structural search is recast as global optimization in a continuous space—solved via derivative-free algorithms such as Differential Evolution (DE) or SHGO. Building upon ParFam, we propose DL-ParFam, which integrates a pre-trained Transformer model to provide neural guidance, accelerating convergence by up to two orders of magnitude. Evaluated on the SRBench benchmark, DL-ParFam achieves state-of-the-art performance across multiple metrics. All code and experimental results are publicly released.
📝 Abstract
The problem of symbolic regression (SR) arises in many different applications, such as identifying physical laws or deriving mathematical equations describing the behavior of financial markets from given data. Various methods exist to address the problem of SR, often based on genetic programming. However, these methods are usually complicated and involve various hyperparameters. 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.
