On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units-Steepest Gradient Descent and Natural Gradient Descent-
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- Inoue Masato
- Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute Department of Otolaryngology, Head and Neck Surgery, Graduate School of Medicine, Kyoto University
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- Park Hyeyoung
- Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute
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- Okada Masato
- Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute “Intelligent Cooperation and Control”, PRESTO, JST
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抄録
The permutation symmetry of the hidden units in multilayer perceptrons causes the saddle structure and plateaus of the learning dynamics in gradient learning methods. The correlation of the weight vectors of hidden units in a teacher network is thought to affect this saddle structure, resulting in a prolonged learning time, but this mechanism is still unclear. In this paper, we discuss it with regard to soft committee machines and on-line learning using statistical mechanics. Conventional gradient descent needs more time to break the symmetry as the correlation of the teacher weight vectors rises. On the other hand, no plateaus occur with natural gradient descent regardless of the correlation for the limit of a low learning rate. Analytical results support these dynamics around the saddle point.
収録刊行物
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- Journal of the Physical Society of Japan
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Journal of the Physical Society of Japan 72 (4), 805-810, 2003
一般社団法人 日本物理学会
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詳細情報 詳細情報について
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- CRID
- 1390001204183166976
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- NII論文ID
- 210000104721
- 110001954444
- 130004538409
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- NII書誌ID
- AA00704814
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- BIBCODE
- 2003JPSJ...72..805I
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- ISSN
- 13474073
- 00319015
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- NDL書誌ID
- 6507452
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可