Establishment of Information Physics based on algebraic geometry
| Project/Area Number |
18079007
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
WATANABE Sumio Tokyo Institute of Technology, 精密工学研究所, 教授 (80273118)
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| Co-Investigator(Kenkyū-buntansha) |
山崎 啓介 東京工業大学, 精密工学研究所 (60376936)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAZAKI Keisuke 東京工業大学, 精密工学研究所, 助教 (60376936)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥45,800,000 (Direct Cost: ¥45,800,000)
Fiscal Year 2009: ¥13,200,000 (Direct Cost: ¥13,200,000)
Fiscal Year 2008: ¥14,000,000 (Direct Cost: ¥14,000,000)
Fiscal Year 2007: ¥14,000,000 (Direct Cost: ¥14,000,000)
Fiscal Year 2006: ¥4,600,000 (Direct Cost: ¥4,600,000)
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| Keywords | 代数幾何 / 情報物理学 / 学習理論 / 特異点論 / 超関数論 / 確率過程論 / 特異モデル / 実対数閾植 / 特異ゆらぎ / 学習の状態方程式 / 特異点 / 双有理不変量 / 実対数閾値 / ゼータ関数 / 広中の定理 / 佐藤幹夫のb関数 / 対数正規値 / 状態方程式 / 特異点解消定理 / 代数解析 / 厳密な数理物理 |
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| Research Abstract |
Almost all learning machines used in information science are singular because they have degenerate Fisher Information matrices. Regular statistical theory can not be applied to singular learning machines. In this research, we established new information physics theory for singular learning machines based on higher dimensional algebraic geometry, and clarified that the asymptotic behaviors of generalization and training errors are determined by two birational invariants. Based on new theory, we derived a widely applicable information criterion, by which the generalization error can be estimated from training error in both singular and regular learning machines.
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Report
(6 results)
Research Products
(89 results)
