Learning the expansion basis instead of choosing it: a gated orthogonal-polynomial functional link network for diabetes risk classification

Single layer functional link networks remain attractive for clinical risk screening because they train in milliseconds, expose every coefficient to inspection and run on hardware that cannot host a deep model. Their accuracy, however, hinges on a design decision usually made by hand and defended after the fact, namely which family of orthogonal functions should expand the input. Comparative studies of Legendre and Chebyshev expansions, including the one that motivated this work, have reached conflicting conclusions. We remove the decision from the designer and hand it to the learner. The proposed adaptive gated orthogonal polynomial functional link network expands every attribute simultaneously in four function families and learns a temperature annealed gate deciding, separately for each attribute, how those families are mixed. Capacity is controlled by a shrinkage term growing with expansion order, motivated by the decay of orthogonal expansion coefficients of smooth functions, and by a group sparsity term applied through a proximal step. Legendre, Chebyshev and trigonometric functional link networks are recovered exactly as degenerate gates, so the architecture strictly generalises the models it replaces. Under nested cross validation on three public diabetes cohorts, against nine baselines including random forests and two gradient boosting libraries, the proposed network attains the highest Matthews correlation on the Pima cohort and joins the leading statistical group overall while using one to three orders of magnitude fewer parameters. We further show that the fixed threshold, accuracy oriented protocol of earlier functional link studies badly overstates the clinical usefulness of these classifiers on imbalanced cohorts.