Current Challenges of Symbolic Regression: Optimization, Selection, Model Simplification, and Benchmarking

• URL: http://arxiv.org/abs/2512.01682v1
• Date: Mon, 01 Dec 2025 13:48:07 GMT
• Title: Current Challenges of Symbolic Regression: Optimization, Selection, Model Simplification, and Benchmarking
• Authors: Guilherme Seidyo Imai Aldeia,
• Abstract summary: Symbolic Regression (SR) aims to discover mathematical expressions that describe the relationship between variables.<n>Current methods must be constantly re-evaluated to understand the SR landscape.<n>This thesis addresses these challenges through a sequence of studies conducted throughout the doctorate.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symbolic Regression (SR) is a regression method that aims to discover mathematical expressions that describe the relationship between variables, and it is often implemented through Genetic Programming, a metaphor for the process of biological evolution. Its appeal lies in combining predictive accuracy with interpretable models, but its promise is limited by several long-standing challenges: parameters are difficult to optimize, the selection of solutions can affect the search, and models often grow unnecessarily complex. In addition, current methods must be constantly re-evaluated to understand the SR landscape. This thesis addresses these challenges through a sequence of studies conducted throughout the doctorate, each focusing on an important aspect of the SR search process. First, I investigate parameter optimization, obtaining insights into its role in improving predictive accuracy, albeit with trade-offs in runtime and expression size. Next, I study parent selection, exploring $ε$-lexicase to select parents more likely to generate good performing offspring. The focus then turns to simplification, where I introduce a novel method based on memoization and locality-sensitive hashing that reduces redundancy and yields simpler, more accurate models. All of these contributions are implemented into a multi-objective evolutionary SR library, which achieves Pareto-optimal performance in terms of accuracy and simplicity on benchmarks of real-world and synthetic problems, outperforming several contemporary SR approaches. The thesis concludes by proposing changes to a famous large-scale symbolic regression benchmark suite, then running the experiments to assess the symbolic regression landscape, demonstrating that a SR method with the contributions presented in this thesis achieves Pareto-optimal performance.

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