A Symbolic Hessian-Based Approach for Assessing Model Complexity in Symbolic Regression

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@InProceedings{haut:2025:GECCOcomp2,

• author = "Nathan Haut and Stuart Card and Mark Kotanchek",
• title = "A Symbolic Hessian-Based Approach for Assessing Model Complexity in Symbolic Regression",
• booktitle = "Proceedings of the 2025 Genetic and Evolutionary Computation Conference Companion",
• year = "2025",
• editor = "Aniko Ekart and Nelishia Pillay",
• pages = "615--618",
• address = "Malaga, Spain",
• series = "GECCO '25 Companion",
• month = "14-18 " # jul,
• organisation = "SIGEVO",
• publisher = "Association for Computing Machinery",
• publisher_address = "New York, NY, USA",
• keywords = "genetic algorithms, genetic programming, symbolic regression, smoothness, stability, symbolic hessian: Poster",
• isbn13 = "979-8-4007-1464-1",
• URL = "https://doi.org/10.1145/3712255.3726666",
• DOI = "doi:10.1145/3712255.3726666",
• size = "4 pages",
• abstract = "In this work, we develop a novel method for estimating model curvature to be used in model selection and evaluation in symbolic regression by symbolically evaluating the model's Hessian matrix at the maximum, minimum, and median points with respect to the response surface. We demonstrate that this estimator is unique from previous methods for computing model complexity and demonstrate that it is relatively computationally efficient. We further validate the method by showcasing that the estimator ranks equations in line with expectations while also exploring the impact of using the max, min, and median points as the references for assessing a model's curvature. Finally, we explore how the metric impacts evolutionary search when used during selection.",
• notes = "GECCO-2025 GP A Recombination of the 34th International Conference on Genetic Algorithms (ICGA) and the 30th Annual Genetic Programming Conference (GP)",

}

Genetic Programming entries for Nathaniel Haut Stu Card Mark Kotanchek

Citations