Multiexpression Symbolic Regression and Its Circuit Design Case

Symbolic regression is commonly considered in wide-ranging applications due to its inherent capability for learning both structure and weighting parameters of an interpretable model. However, for those scenarios that require fitting multiple expressions (MEs) synchronously, existing symbolic regression algorithms need to run multiple times step by step asynchronously for fitting such a group of expressions. Due to lacking mechanisms to explicitly capture and leverage the relationships between these expressions, the coupling information among MEs will be lost in this approach. A multiexpression symbolic regression algorithm (ME-SR) is proposed in this article to address the issue in learning MEs. Additionally, a methodology for extracting the approximate maximum common subexpression (aMCSE) among these MEs is suggested to disclose the relationships. A new metric is formulated to measure the quality of an aMCSE in ME-SR by imitating the concept of intersection over union. Furthermore, an adaptive cross matrix is incorporated into the algorithm to balance the search efforts between intertask and intratask domains. The proposed ME-SR demonstrates superior performance when compared to its counterparts of single expression symbolic regression on the designed test set. Finally, the efficacy of the method is well verified by a real-world circuit design case.