新神经网络用加法结构提升性能，参数更少效果更好。
Hybrid deep additive neural networks
- 用加法回归思想替代线性组合，设计新型深层网络
- 仿真与真实数据均显示：性能优于传统网络，参数更少
- 适合追求高效高精度模型的科研与工程人员
传统神经网络（多层感知机）在数据科学中广泛应用，但表现有时不佳，且参数量大，主要源于其依赖线性组合结构。加法回归是统计学中线性回归的流行替代方法。本文提出一种融合加法回归思想的新型深度神经网络，其架构与柯尔莫戈罗夫-阿诺德网络相似，但采用更简单灵活的激活函数和基函数。此外，我们设计了多种混合神经网络，将该结构与传统网络结合。推导了其通用逼近性质，并通过模拟研究和真实数据应用验证了有效性。数值结果表明，所提网络通常在性能上优于传统网络，同时使用更少参数。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。