Symbolic Regression (SR) is a central problem in evolutionary computation concerned with identifying symbolic equations from data. In many scientific and engineering settings, observed data are governed by physical laws drawn from known but implicitly defined families of equations, where the exact symbolic form is unknown and difficult to enumerate a priori. In such settings, exact structural identification is more critical than arbitrary function approximation. We present an evolutionary SR approach for scientific equation identification in which large language models (LLMs) are integrated directly into the evolutionary process as guided variation operators. The method maintains a population of candidate symbolic expressions and evolves them over successive generations using fitness-based selection, structural diversity preservation, and stateful evolutionary memory. LLM guidance proposes structurally informed variations that exploit qualitative prior knowledge while remaining embedded within an evolutionary search framework. We evaluate the approach on the SRSD-Feynman benchmark, demonstrating robust rediscovery of scientific equations across easy and medium difficulty subsets, with competitive performance on harder instances. Results show that incorporating language-model guidance into evolutionary SR substantially improves search efficiency while preserving interpretability and the evolutionary character of the algorithm.
Jun Zhao, Kei Sen Fong, M. Motani· Proceedings of the Genetic a...· 0 citations
Symbolic regression (SR) is commonly benchmarked using relative Pareto analysis, where an algorithm is evaluated according to whether it dominates the other methods included in the comparison. While useful, this perspective does not reveal the true attainable limits of short, interpretable expressions, and conclusions may change depending on which competing methods are selected. In this work, we advocate benchmarking with absolute Pareto-optimal (APO) fronts instead. We construct APO fronts for 34 datasets from SRBench by exhaustively searching over short symbolic expressions and by fitting numerical constants with eight commonly used local optimization methods. The resulting fronts provide dataset-specific baselines for the best accuracy-complexity trade-offs attainable within a fixed primitive set. Comparing against the SR methods reported in SRBench shows that many current algorithms remain far from these fronts, especially in the regime of short expressions. We also find that the final fronts are relatively stable across numerical optimizers, suggesting that structural search is a more important bottleneck than constant fitting. These APO fronts provide a reusable benchmarking asset for the evolutionary computation community and a more stable reference point for measuring progress in SR.
Kei Sen Fong, M. Motani· Proceedings of the Genetic a...· 0 citations
In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize its confidence. Our reward scheme uses two functions for rewarding confidence verbalized by the LLM: one when the LLM is correct and a different one when the LLM is incorrect. With a poorly designed reward scheme, the LLM may be incentivized to answer incorrectly so that it can be confident that its answer is indeed incorrect, a phenomenon that we call confidence reward hacking. We propose the concept of non-hackable confidence reward schemes and define a spectrum of such reward schemes for RL confidence calibration training in LLMs. We demonstrate that selective confidence reward hacking can occur in practical datasets with reward schemes that are not designed to be non-hackable. We also demonstrate that the reward scheme with the best calibration to accuracy tradeoff depends on the dataset and the application, and propose using the reward scheme as a hyperparameter to optimize the tradeoffs in accordance to what is important for the application. The code of our experiments is available in https://anonymous.4open.science/r/rl-confidence-calibration-9ED4/README.md.
Chee Heng Tan, Zhuoyi Lin, M. Motani et al.· 0 citations
