# Efficient and Interpretable Neural Networks Using Complex Lehmer Transform

arXiv: https://arxiv.org/abs/2501.15223 · HTML: https://mlsanity.com/paper/2501.15223/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 25 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Explainable Machine Learning for Scientific Insights and Discoveries](https://mlsanity.com/paper/1905.08883/) (2019)
- [Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead](https://mlsanity.com/paper/1811.10154/) (2018)
- [A Hybrid Complex-valued Neural Network Framework with Applications to Electroencephalogram (EEG)](https://mlsanity.com/paper/2207.14799/) (2022)

## Abstract (arXiv)

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.