# TMPNN: High-Order Polynomial Regression Based on Taylor Map Factorization

arXiv: https://arxiv.org/abs/2307.16105 · HTML: https://mlsanity.com/paper/2307.16105/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 30 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [CatBoost: gradient boosting with categorical features support](https://mlsanity.com/paper/1810.11363/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)
- [DNNR: Differential Nearest Neighbors Regression](https://mlsanity.com/paper/2205.08434/) (2022)
- [Physics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Accelerators](https://mlsanity.com/paper/2007.03555/) (2020)
- [Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study](https://mlsanity.com/paper/2209.07736/) (2022)
- [Regression-Enhanced Random Forests](https://mlsanity.com/paper/1904.10416/) (2019)
- [Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning](https://mlsanity.com/paper/1912.09986/) (2019)

## Abstract (arXiv)

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for constructing a high-order polynomial regression based on the Taylor map factorization. This method naturally implements multi-target regression and can capture internal relationships between targets. Additionally, we introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on UCI open access datasets, Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate that the proposed method performs comparable to the state-of-the-art regression methods and outperforms them on specific tasks.