Hybrid deep additive neural networks

TL;DR

This paper introduces hybrid deep additive neural networks that combine additive regression concepts with traditional neural network architectures, achieving better performance with fewer parameters.

Contribution

It presents novel neural network architectures inspired by additive regression, with proven universal approximation and improved efficiency over traditional neural networks.

Findings

Achieve better performance than traditional neural networks.

Use fewer parameters to reach comparable or superior results.

Demonstrated effectiveness through simulations and real-data applications.

Abstract

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.