# Hybrid deep additive neural networks

arXiv: https://arxiv.org/abs/2411.09175 · HTML: https://mlsanity.com/paper/2411.09175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 14 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
- [Sparse additive models in high dimensions with wavelets](https://mlsanity.com/paper/2207.04083/) (2022)

## Abstract (arXiv)

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large number of parameters, primarily due to their reliance on the linear combination structure. Meanwhile, additive regression has been a popular alternative to linear regression in statistics. In this work, we introduce novel deep neural networks that incorporate the idea of additive regression. Our neural networks share architectural similarities with Kolmogorov-Arnold networks but are based on simpler yet flexible activation and basis functions. Additionally, we introduce several hybrid neural networks that combine this architecture with that of traditional neural networks. We derive their universal approximation properties and demonstrate their effectiveness through simulation studies and a real-data application. The numerical results indicate that our neural networks generally achieve better performance than traditional neural networks while using fewer parameters.