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

2026-01-06 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

This paper, "Fibonacci-Driven Recursive Ensembles: Algorithms, Convergence, and Learning Dynamics," is the third part of a trilogy, focusing on the algorithmic and dynamical foundations of recursive ensemble learning. It introduces second-order recursive architectures where each predictor depends on its two immediate predecessors, contrasting with classical first-order boosting methods. The work presents a general family of recursive weight-update algorithms, including Fibonacci and tribonacci recursions, and their continuous-time limits as systems of differential equations. The authors establish global convergence conditions, spectral stability criteria, and non-asymptotic generalization bounds using Rademacher and algorithmic stability analyses. Experimental results with kernel ridge regression, spline smoothers, and random Fourier feature models demonstrate that these recursive flows consistently improve approximation and generalization compared to static weighting and first-order boosting.

Key takeaway

For AI Researchers and Scientists developing advanced ensemble learning methods, adopting Fibonacci-driven recursive ensembles can lead to faster convergence and improved generalization. Your models will benefit from the inherent memory and momentum, especially when using adaptive golden-ratio step-size policies to ensure stability and prevent overfitting. Explore implementing the proposed Fibonacci Boosting or orthogonalized variants to enhance approximation accuracy beyond traditional first-order boosting techniques.

Key insights

Second-order recursive ensembles with memory offer improved learning dynamics and generalization over first-order methods.

Principles

• Ensembles can be dynamical systems, not just static aggregates.
• Memory in learning processes can stabilize and accelerate convergence.
• The golden ratio acts as a stability threshold for recursive ensembles.

Method

Recursive ensemble learning uses a second-order update $F_{t+1}=\beta_{t}F_{t}+\gamma_{t}F_{t-1}+\eta_{t}h_{t}$, where $h_t$ is a base learner trained on residuals. Algorithms include Fibonacci Boosting, Rao–Blackwellized flows, and orthogonalized ensembles, often with golden-ratio adaptive step sizes.

In practice

• Implement second-order recursions for ensemble learning.
• Apply golden-ratio adaptive step sizes for stability.
• Consider Rao–Blackwellization for variance reduction in randomized base learners.

Topics

• Fibonacci Ensembles
• Recursive Learning Dynamics
• Ensemble Convergence Theory
• Golden Ratio Stability
• Fibonacci Boosting

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.