[2603.20634] CFNN: Continued Fraction Neural Network

Computer Science > Machine Learning arXiv:2603.20634 (cs) [Submitted on 21 Mar 2026] Title:CFNN: Continued Fraction Neural Network Authors:Chao Wang, Xuancheng Zhou, Ruilin Hou, Xiaoyu Cheng, Ruiyi Ding View a PDF of the paper titled CFNN: Continued Fraction Neural Network, by Chao Wang and 4 other authors View PDF HTML (experimental) 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. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs...