[2602.23467] On the Limits of Interpretable Machine Learning in Quintic Root Classification

Mathematics > Numerical Analysis arXiv:2602.23467 (math) [Submitted on 26 Feb 2026] Title:On the Limits of Interpretable Machine Learning in Quintic Root Classification Authors:Rohan Thomas, Majid Bani-Yaghoub View a PDF of the paper titled On the Limits of Interpretable Machine Learning in Quintic Root Classification, by Rohan Thomas and 1 other authors View PDF Abstract:Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a structured benchmark. We tested an extensive set of ML models, including decision trees, logistic regression, support vector machines, random forest, gradient boosting, XGBoost, symbolic regression, and neural networks. Neural networks achieved strong in-distribution performance on quintic classification using raw coefficients alone (84.3% + or - 0.9% balanced accuracy), whereas decision trees perform substantially worse (59.9% + or - 0.9\%). However, when provided with an explicit feature capturing sign changes at critical points, decision trees match neural performance (84.2% + or - 1.2%) and yield explicit classification rules. Knowledge distillation reveals that this single invariant accounts for 97.5% of the extracted decision structure. Out-of-distribution, data-efficiency, and noise robustness analyses indicate that neural networks learn continuous, data-dependent geometr...