SymbolicArena: A Unified Infrastructure for Benchmark Distillation and Dynamic Evaluation in Symbolic Regression
Ziwen Zhang, Xiju Wu, Yuheng Jing, Runxiang Wang, Boxiao Wang, Yifan Zang, Yifan Zhang, Yang Wang, Kai Li, Yifan Zhang, Huilin Xu, Jian Cheng
Abstract
Symbolic regression (SR) seeks concise and interpretable mathematical expressions from data for scientific equation discovery. Existing SR benchmarks face a tradeoff between evaluation cost and benchmark validity. Repeated evaluation of large task pools is expensive, and compact benchmarks lack systematic evidence of preserved task diversity and algorithm discriminability. SymbolicArena provides a unified infrastructure for benchmark distillation and dynamic evaluation. The framework standardizes 664 heterogeneous tasks with executable ground truth expressions and distills the Full Task Set into Core50, a validated benchmark of 50 tasks. The distillation process preserves task coverage and algorithm discrimination under explicit balance constraints. SymbolicArena applies a unified execution protocol to heterogeneous SR algorithms and produces comparable outputs and search trajectories. Multi Axis Evaluation characterizes numerical quality, symbolic quality, and search behavior. Core50 reduces evaluation workload by 92.5% and maintains agreement with Full Task Set evaluations. Experiments show that SymbolicArena achieves 72.6% to 86.7% lower approximation error than alternative selectors, further supporting its fidelity to the Full Task Set. Evaluation reveals a substantial gap between numerical fitting and symbolic recovery across current SR methods, suggesting that reliable equation recovery remains an open challenge.