Enabling Explainable Fusion in Deep Learning With Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multilayer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic-gradient-descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables explainable artificial intelligence (XAI). Synthetic validation experiments are provided, and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy, and our previously established XAI indices shed light on the quality of our data, model, and its decisions.

I. Introduction

Data are ubiquitous in today's technological era. This is both a blessing and a curse, as we are swimming in sensors but drowning in data. In order to cope with these data, many systems employ data/information fusion. For example, you are right now combining multiple sources of data, e.g., taste, smell, touch, vision, hearing, memories, etc. In remote sensing, it is common practice to combine lidar, hyperspectral, visible, radar, and/or other variable spectral–spatial–temporal resolution sensors to detect objects, perform earth observations, etc. This is the same story for computer vision, smart cars, Big Data, and numerous other thrusts. While the last decade has seen great strides in topics like deep learning, the reality is that our understanding of fusion in the context of neural networks (NNs) (and therefore deep learning) has not witnessed similar growth. Most approaches to fusion in NNs are ad hoc (specialized for a particular application), and/or they are neither well understood nor explainable (i.e., how are the data being combined and why should we trust system outputs).