Beyond the Gegenbauer Paradigm: q-Orthogonal Kernels for Machine Learning

arXiv:2608.03482 · cs.LG, stat.ML · Submitted 2026-08-04 · Read on arXiv

Álvaro Sánchez-Paniagua Ríos, Juan P. Llerena, Alberto Lastra, Nuria Torrado, Edmundo J. Huertas

cs.LG, stat.ML

Submitted: 2026-08-04

Comments: 27 pages, 4 figures, 9 tables. Source code and experimental pipeline available at https://github.com/Kokechacho/SVMs-QSVMs

Code: https://github.com/Kokechacho/SVMs-QSVMs

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 20× in this paper · explained in 1 episode
• Benchmark — 4× in this paper · explained in 2 episodes
• Hyperparameters — 4× in this paper · explained in 2 episodes
• Radial Basis Function — 4× in this paper
• Regularization — 4× in this paper · explained in 3 episodes
• Computational Efficiency — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 14 episodes
• Bayesian Optimization — 2× in this paper · explained in 3 episodes
• Computational Biology — 2× in this paper · explained in 2 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Overfitting — 2× in this paper · explained in 2 episodes
• Active Learning — 1× in this paper · explained in 6 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Data Leakage — 1× in this paper · explained in 2 episodes
• False Negatives — 1× in this paper · explained in 2 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Pairwise Comparisons — 1× in this paper · explained in 2 episodes
• Papers — 1× in this paper · explained in 3 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Practical application improvement to Quantum SVM: theory to practice
• Radial basis function kernel optimization for Support Vector Machine classifiers
• An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations
• OptunaHub: A Platform for Black-Box Optimization

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks