Evolutional Math: Cross-Validated Island-Model Genetic Programming for Interpretable Symbolic Regression on Small, Wide Datasets

Symbolic regression via genetic programming routinely fails on small, wide datasets - a regime common in clinical-trial monitoring, biostatistics, and engineering pilot studies - by converging on bloated, overfit expressions that exploit correlation rather than prediction. We present Evolutional Math, an open-source genetic programming system that combines four design choices to yield compact, interpretable formulas in this regime. First, fitness is measured by R-squared on held-out cross-validation folds rather than Pearson correlation on the training set, eliminating single-variable shortcuts that correlate but mis-scale. Second, a multi-island architecture runs independent populations seeded with distinct operator subsets (algebraic, logarithmic, trigonometric, and full) with ring-topology migration every M generations, preventing the search from collapsing into one region of formula space. Third, a structural deduplication scheme treats formulas differing only in constants as equivalent, so the elite archive contains structurally distinct candidates rather than near-duplicate variants. Fourth, top-k individuals undergo numerical constant refinement via scipy L-BFGS-B after each migration phase, decoupling structure search from parameter fitting. We evaluate the system on synthetic benchmarks of the form log(x_i) * x_j / (x_k * c), trigonometric mixtures, and an anonymized clinical site-monitoring dataset with 24 rows and approximately 290 candidate numeric features. The system consistently recovers compact ground-truth structures with R-squared at or above 0.99 within tens of thousands of unique formula evaluations. A reference implementation is released under a noncommercial source-available license.

Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines

Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic structure rather than numerical optimization, against standard baselines on image and tabular classification across varying training-set sizes. We find that AML trained only on training data without using validation or cross-validation outperforms a family of cross-validated baseline methods including CNNs on small to medium image datasets (50--2000 training examples). On tabular datasets in the same size range, XGBoost is overall the best performing method, but AML is nonetheless comparable to methods incorporating task-specific biases such as LightGBM and random forests. AML achieves this competitive performance across two very different types of datasets using a generic algebraic inductive bias, rather than the modality-specific biases built into standard baselines like CNNs for images or XGBoost for tabular data, and requires no cross validation because it has no task-dependent hyperparameters to tune.