# CFNN: Continued Fraction Neural Network

arXiv: https://arxiv.org/abs/2603.20634 · HTML: https://mlsanity.com/paper/2603.20634/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Resnet in Resnet: Generalizing Residual Architectures](https://mlsanity.com/paper/1603.08029/) (2016)
- [Rational neural networks](https://mlsanity.com/paper/2004.01902/) (2020)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [Gradient Boosting Neural Networks: GrowNet](https://mlsanity.com/paper/2002.07971/) (2020)
- [Neural networks and rational functions](https://mlsanity.com/paper/1706.03301/) (2017)
- [Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learning](https://mlsanity.com/paper/2410.16105/) (2024)
- [CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractions](https://mlsanity.com/paper/2506.05586/) (2025)
- [From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic](https://mlsanity.com/paper/2601.18702/) (2026)

## Abstract (arXiv)

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.