Jürgen Rahmel, Thomas Villmann

• In this report, we first propose a dichotomy of topology preserving network models based on the degree to which the structure of a network is determined by the given task. We then look closer at one of those groups and investigate the information that is contained in the graph structure of a topology preserving neural network. The task we have in mind is the usage of the network's topology for the retrieval of nearest neighbors of a neuron or a query, as it is of importance, e.g., in medical diagnosis systems. In general considerations, we propose certain properties of the structure and formulate the respective expectable results of network interpretation. From the results we conclude that both topology preservation as well as neuron distribution are highly influential for the network semantics. After a short survey on hierarchical models for data analysis, we propose a new network model that fits both needs. This so called SplitNet model dynamically constructs a hierarchically structured network that provides interpretability by neuron distribution, network topology and hierarchy of the network layers. We present empirical results for this new model and demonstrate its application in the medical domain of nerve lesion diagnosis. Further, we explain a view how the interpretation of the hierarchy in models like SplitNet can be understood in the context of integration of symbolic and connectionist learning.