CFNN: Continued Fraction Neural Network

2026-03-21

AI Summary

This work addresses the limitations of traditional multilayer perceptrons, which—due to spectral bias—struggle to efficiently model nonlinear functions exhibiting singularities or high curvature. To overcome this, the authors propose Continued Fraction Neural Networks (CFNNs), which integrate continued fraction structures with gradient-based optimization to introduce a “rational inductive bias.” This enables highly accurate modeling of complex asymptotic behaviors and discontinuities with markedly fewer parameters. Three stable implementation strategies—CFNN-Boost, CFNN-MoE, and CFNN-Hybrid—are introduced, preserving black-box flexibility while enhancing white-box interpretability, thereby establishing a “gray-box” modeling paradigm. Experiments demonstrate that CFNNs achieve comparable or superior accuracy with 1–2 orders of magnitude fewer parameters, up to 47× improved robustness to noise, and significantly enhanced physical consistency.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features without excessive parameters. We introduce Continued Fraction Neural Networks (CFNNs), integrating continued fractions with gradient-based optimization to provide a ``rational inductive bias.'' This enables capturing complex asymptotics and discontinuities with extreme parameter frugality. We provide formal approximation bounds demonstrating exponential convergence and stability guarantees. To address recursive instability, we develop three implementations: CFNN-Boost, CFNN-MoE, and CFNN-Hybrid. Benchmarks show CFNNs consistently outperform MLPs in precision with one to two orders of magnitude fewer parameters, exhibiting up to a 47-fold improvement in noise robustness and physical consistency. By bridging black-box flexibility and white-box transparency, CFNNs establish a reliable ``grey-box'' paradigm for AI-driven scientific research.

Problem

• non-linear functional manifolds
• singularities
• spectral bias
• high-curvature features
• parameter efficiency

Innovation

• Continued Fraction Neural Network
• rational inductive bias
• spectral bias mitigation
• parameter efficiency
• grey-box modeling