Fibonacci-Driven Recursive Ensembles: Algorithms, Convergence, and Learning Dynamics

TL;DR

This paper introduces Fibonacci-driven recursive ensemble algorithms that incorporate second-order dynamics, providing new convergence guarantees and demonstrating improved approximation and generalization in various models.

Contribution

It develops a novel class of recursive ensemble algorithms based on Fibonacci and higher-order recursions, with theoretical convergence analysis and practical improvements.

Findings

Recursive Fibonacci flows improve approximation accuracy.

The algorithms exhibit global convergence under certain conditions.

Experimental results show enhanced generalization in kernel and spline models.

Abstract

This paper develops the algorithmic and dynamical foundations of recursive ensemble learning driven by Fibonacci-type update flows. In contrast with classical boosting Freund and Schapire (1997); Friedman (2001), where the ensemble evolves through first-order additive updates, we study second-order recursive architectures in which each predictor depends on its two immediate predecessors. These Fibonacci flows induce a learning dynamic with memory, allowing ensembles to integrate past structure while adapting to new residual information. We introduce a general family of recursive weight-update algorithms encompassing Fibonacci, tribonacci, and higher-order recursions, together with continuous-time limits that yield systems of differential equations governing ensemble evolution. We establish global convergence conditions, spectral stability criteria, and non-asymptotic generalization bounds under Rademacher Bartlett and Mendelson (2002) and algorithmic stability analyses. The resulting theory unifies recursive ensembles, structured weighting, and dynamical systems viewpoints in statistical learning. Experiments with kernel ridge regression Rasmussen and Williams (2006), spline smoothers Wahba (1990), and random Fourier feature models Rahimi and Recht (2007) demonstrate that recursive flows consistently improve approximation and generalization beyond static weighting. These results complete the trilogy begun in Papers I and II: from Fibonacci weighting, through geometric weighting theory, to fully dynamical recursive ensemble learning systems.