CFNN: Continued Fraction Neural Network

About

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.

Chao Wang, Xuancheng Zhou, Ruilin Hou, Xiaoyu Cheng, Ruiyi Ding · 2026

Related benchmarks

Task	Dataset	Result
Classification	Waveform real-world (test)	Accuracy89	7
Classification	Magic real-world (test)	Accuracy88	7
Classification	Credit Card real-world (test)	Accuracy82	7
Classification	Sentiment real-world (test)	Accuracy88	7
Classification	Quora real-world (test)	Accuracy94	7
Classification	CIFAR10 real-world (test)	Accuracy47	7
Thermal-load regression	UCI Energy Efficiency single-target thermal-load regression	MSE7.13	5
Feature Importance Ranking Alignment	UCI Energy Efficiency	Spearman Correlation0.6944	4