value for a given input data sample, the visualization of the resulting hierarchical modular representations becomes more difficult with a deeper and a larger scale network structure, since a cluster may contain units in mutually distant layers. Additionally, the number of possible cluster sizes increases with the scale (or the number of units) of a network, and so it is necessary to construct a method for automatically selecting a set of representative resolutions, instead of visualizing the entire hierarchical cluster structure.

Conclusion
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Finding a way to unravel the function of a trained LNN is an important issue in the machine learning field. While LNNs have achieved high prediction accuracy with various data sets, their highly complex and nonlinear parameters have made it difficult to interpret their internal inference mechanism. Recent studies have enabled us to decompose a trained LNN into simpler cluster structure, however, there is no method for (1) determining the optimal number of clusters, or (2) knowing whether the outputs of each cluster have a positive or negative correlation with the input and output dimension values. In this paper, we proposed a method for extracting the hierarchical modular representation of a trained LNN, which consists of sequential 