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CFNN: Continued Fraction Neural Network

arXiv 2603.20634 ↗First posted 21 Mar 2026cs.LG cs.AIcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 16 of its 40 references that are in the map. First posted on arXiv 21 Mar 2026.

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16 of 40 references.

References · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,120
  3. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,413
  4. 2018On the Spectral Bias of Neural Networkscited by 1,321
  5. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  6. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
  7. 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
  8. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  9. 2016Resnet in Resnet: Generalizing Residual Architecturescited by 110
  10. 2020Rational neural networkscited by 75
  11. 2025Nested Learning: The Illusion of Deep Learning Architecturescited by 69
  12. 2020Gradient Boosting Neural Networks: GrowNetcited by 46
4 more
  1. 2017Neural networks and rational functionscited by 40
  2. 2024Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learningcited by 14
  3. 2025CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractionscited by 3
  4. 2026From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmeticcited by 1

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