CFNN: Continued Fraction Neural Network

• URL: http://arxiv.org/abs/2603.20634v1
• Date: Sat, 21 Mar 2026 04:06:21 GMT
• Title: CFNN: Continued Fraction Neural Network
• Abstract summary: We introduce Continued Neural Fraction Networks (CFNNs), integrating continued fractions with gradient-based optimization to provide a rational inductive bias''<n> Benchmarks show CFNNs consistently outperformLayers in precision with one to two orders of magnitude fewer parameters, exhibiting up to a 47-fold improvement in robustness and physical consistency.
• Score: 3.515482938869358
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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