Efficient and Interpretable Neural Networks Using Complex Lehmer Transform

Abstract: 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.