Functional Semantics Analysis in Deep Neural Networks

Deep neural networks (DNNs) have achieved remarkable success in various domains, yet their lack of interpretability remains a critical limitation. To address this challenge, functional networks have emerged as an interpretable framework for understanding the internal workings of DNNs. Functional networks examine the statistical dependencies between activation values of neurons, thereby unraveling the functional organization of DNNs. In this work, we propose the classified functional network, which enables the analysis of the functional organization within DNN models specific to different classes of data. By introducing the distance metric between classified functional networks, we present the semantic map and hierarchical clustering as tools to delve into the functional semantic relationships within DNNs. Our results demonstrate that models exhibit similar functional organizations for classes with similar semantics. These observed semantic relationships arise from the similarity between functional connectivities, as opposed to the similarity between activation values. Furthermore, our experiments demonstrate the existence of hierarchical functional semantic relationships within DNNs. These insights into the functional organization of DNNs not only deepen our understanding of models but also provide potential avenues for enhancing their interpretability.