Research & Papers

Evolutional Math: New GP system cracks small, wide data with R² ≥ 0.99

Overfits no more: island-model GP recovers true formulas from only 24 rows...

Deep Dive

Symbolic regression via genetic programming (GP) typically fails on small, wide datasets — regimes common in clinical trials, biostatistics, and engineering pilots — by producing bloated, overfit expressions that capture correlation but not true prediction. Enter Evolutional Math, an open-source GP system from Artem Andrianov at Cyntegrity Germany GmbH, released on arXiv (2606.28381). The system combines four design choices to yield compact, interpretable formulas: (1) fitness measured by R-squared on held-out cross-validation folds instead of Pearson correlation on training data, eliminating single-variable shortcuts; (2) a multi-island architecture with independent populations seeded with distinct operator subsets (algebraic, logarithmic, trigonometric, full) and ring-topology migration every M generations, preventing search collapse; (3) structural deduplication that treats formulas differing only in constants as equivalent, so the elite archive contains structurally distinct candidates; and (4) top-k individuals undergo numerical constant refinement via scipy L-BFGS-B after each migration phase, decoupling structure search from parameter fitting. On synthetic benchmarks (e.g., log(x_i) * x_j / (x_k * c), trigonometric mixtures) and an anonymized clinical site-monitoring dataset with 24 rows and ≈290 features, Evolutional Math consistently recovers compact ground-truth structures with R-squared ≥ 0.99 within tens of thousands of unique formula evaluations. The reference implementation is released under a noncommercial source-available license, making it accessible for researchers in high-stakes fields where interpretability is paramount. This work effectively bridges the gap between expressiveness and generalization in GP for challenging data regimes.

Key Points
  • Achieves R² ≥ 0.99 on a clinical dataset with only 24 rows and 290 features
  • Uses cross-validation fitness, multi-island migration, structural deduplication, and L-BFGS-B constant refinement
  • Open-source reference implementation available under a noncommercial license

Why It Matters

A practical GP solution for interpretable symbolic regression in small-data scenarios like clinical trials and engineering pilots.

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