Inclusion–Exclusion Integral Neural Networks: A Framework for Explainable AI with Non-Additive Measures

Abstract

This study introduces the inclusion–exclusion integral neural network (IEINN) and its accompanying open-source Python library, a novel framework designed to enhance the interpretability of neural networks by leveraging non-additive monotone measures and polynomial operations. The proposed architecture integrates the inclusion–exclusion integral into the network structure, enabling direct extraction of structured information from the learned parameters. We develop a Python-based IEINN library, implemented using PyTorch, to facilitate efficient model training and integration. The library includes several preprocessing methods for parameter initialization, such as normalization based on minimum and maximum values, percentiles, and standard deviations, which enhance training stability and convergence. Additionally, the framework supports various computational operations, including t-norms and t-conorms, allowing flexible modeling of interactions among input variables. The proposed framework is publicly available as an open-source library on GitHub (AoiHonda-lab/IEI-NeuralNetwork), facilitating further research and practical applications in explainable AI.