Sym-Q: Adaptive Symbolic Regression via Sequential Decision-Making

Symbolic regression holds great potential for uncovering underlying mathematical and physical relationships from empirical data. While existing transformer-based models have recently achieved significant success in this domain, they face challenges in terms of generalizability and adaptability. Typically, in cases where the output expressions do not adequately fit experimental data, the models lack efficient mechanisms to adapt or modify the expression. This inflexibility hinders their application in real-world scenarios, particularly in discovering unknown physical or biological relationships. Inspired by how human experts refine and adapt expressions, we introduce Symbolic Q-network (Sym-Q), a novel reinforcement learning-based model that redefines symbolic regression as a sequential decision-making task. Sym-Q leverages supervised demonstrations and refines expressions based on reward signals indicating the quality of fitting precision. Its distinctive ability to manage the complexity of expression trees and perform precise step-wise updates significantly enhances flexibility and efficiency. Our results demonstrate that Sym-Q excels not only in recovering underlying mathematical structures but also uniquely learns to efficiently refine the output expression based on reward signals, thereby discovering underlying expressions. Sym-Q paves the way for more intuitive and impactful discoveries in physical science, marking a substantial advancement in the field of symbolic regression.