用复数莱默变换激活函数提升神经网络效率与可解释性
Efficient and Interpretable Neural Networks Using Complex Lehmer Transform
- 引入加权莱默变换激活函数，支持实数与复数域自适应特征选择
- 单层即可达到顶尖性能，计算效率显著优于现有模型
- 适合需要透明决策过程的高可信场景，如医疗与金融建模
我们提出一种高效且可解释的神经网络，采用新型激活函数——加权莱默变换。该函数实现自适应特征选择，并拓展至复数域，能够捕捉数据中的相位敏感性与层次关系。相比现有机器学习模型，其具备更强的可解释性与透明度，有助于深入理解模型功能与决策机制。我们分析了实值与复值莱默激活单元的数学性质，并展示了其在建模非线性交互中的应用。实验表明，所提神经网络在基准数据集上达到具有竞争力的准确率，同时显著提升计算效率。单层实值或复值莱默激活单元即能实现业界领先性能，在效率与可解释性之间取得良好平衡。
原文摘要 · Abstract (English)
We propose an efficient and interpretable neural network with a novel activation function called the weighted Lehmer transform. This new activation function enables adaptive feature selection and extends to the complex domain, capturing phase-sensitive and hierarchical relationships within data. Notably, it provides greater interpretability and transparency compared to existing machine learning models, facilitating a deeper understanding of its functionality and decision-making processes. We analyze the mathematical properties of both real-valued and complex-valued Lehmer activation units and demonstrate their applications in modeling nonlinear interactions. Empirical evaluations demonstrate that our proposed neural network achieves competitive accuracy on benchmark datasets with significantly improved computational efficiency. A single layer of real-valued or complex-valued Lehmer activation units is shown to deliver state-of-the-art performance, balancing efficiency with interpretability.
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