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Recently, slow dynamics in learning of neural networks has been known to be closely related to singularities, which exist in parameter spaces of hierarchical learning models. To show the influence of singular structure on learning dynamics, we take statistical mechanical approaches and investigate online-learning dynamics under various learning scenario with different relationship between optimum and singularities. From the investigation, we found a quasi-plateau phenomenon which differs fromdoi:10.1143/ptps.157.275 fatcat:zff5ioeifvbf7jgylg6syfo4fq