# Rational ANOVA Networks

arXiv: https://arxiv.org/abs/2602.04006 · HTML: https://mlsanity.com/paper/2602.04006/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [AutoGluon-Tabular: Robust and Accurate AutoML for Structured Data](https://mlsanity.com/paper/2003.06505/) (2020)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [Rational neural networks](https://mlsanity.com/paper/2004.01902/) (2020)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)
- [Real-TabPFN: Improving Tabular Foundation Models via Continued Pre-training With Real-World Data](https://mlsanity.com/paper/2507.03971/) (2025)
- [Neural networks and rational functions](https://mlsanity.com/paper/1706.03301/) (2017)
- [Kolmogorov-Arnold Fourier Networks](https://mlsanity.com/paper/2502.06018/) (2025)

## Built on by (most cited first, 2 of 2)

- [AgriWorld:A World Tools Protocol Framework for Verifiable Agricultural Reasoning with Code-Executing LLM Agents](https://mlsanity.com/paper/2602.15325/) (2026)
- [A Scalable Curiosity-Driven Game-Theoretic Framework for Long-Tail Multi-Label Learning in Data Mining](https://mlsanity.com/paper/2602.15330/) (2026)

## Abstract (arXiv)

Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address this using splines, they often suffer from computational inefficiency and boundary instability. We propose the Rational-ANOVA Network (RAN), a foundational architecture grounded in functional ANOVA decomposition and Pad'e-style rational approximation. RAN models f(x) as a composition of main effects and sparse pairwise interactions, where each component is parameterized by a stable, learnable rational unit. Crucially, we enforce a strictly positive denominator, which avoids poles and numerical instability while capturing sharp transitions and near-singular behaviors more efficiently than polynomial bases. This ANOVA structure provides an explicit low-order interaction bias for data efficiency and interpretability, while the rational parameterization significantly improves extrapolation. Across controlled function benchmarks and vision classification tasks (e.g., CIFAR-10) under matched parameter and compute budgets, RAN matches or surpasses parameter-matched MLPs and learnable-activation baselines, with better stability and throughput. Code is available at https://github.com/jushengzhang/Rational-ANOVA-Networks.git.