Statistical mechanics of learning and optimization 学習と最適化の統計力学
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著者
書誌事項
- タイトル
-
Statistical mechanics of learning and optimization
- タイトル別名
-
学習と最適化の統計力学
- 著者名
-
井上, 純一
- 著者別名
-
イノウエ, ジュンイチ
- 学位授与大学
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東京工業大学
- 取得学位
-
博士 (理学)
- 学位授与番号
-
乙第3193号
- 学位授与年月日
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1998-06-30
注記・抄録
博士論文
identifier:oai:t2r2.star.titech.ac.jp:99001217
目次
- 論文目録 / (0002.jp2)
- Contents / p7 (0007.jp2)
- 1 Introduction / p9 (0008.jp2)
- 1.1 What is learning? / p9 (0008.jp2)
- 1.2 Neural network model / p11 (0009.jp2)
- 1.3 Several learning algorithms / p13 (0010.jp2)
- 1.4 What is generalization? / p23 (0015.jp2)
- 1.5 Optimization problem / p29 (0018.jp2)
- 1.6 Overview of this thesis / p34 (0021.jp2)
- 2 The Model System for Unrealizable Rule / p37 (0022.jp2)
- 3 Off-Line Learning / p41 (0024.jp2)
- 3.1 Statistical mechanics / p41 (0024.jp2)
- 3.2 Replica calculations of learning curves / p43 (0025.jp2)
- 3.3 Simulations for the two-dimensional case / p56 (0032.jp2)
- 3.4 Summary / p61 (0034.jp2)
- 4 On-Line Learning / p63 (0035.jp2)
- 4.1 Background / p63 (0035.jp2)
- 4.2 Dynamics of noiseless learning / p64 (0036.jp2)
- 4.3 Learning under output noise in the teacher signal / p76 (0042.jp2)
- 4.4 Optimization of learning rate / p86 (0047.jp2)
- 4.5 Optimized learning with output noise / p94 (0051.jp2)
- 4.6 Optimal learning without unknown parameters / p96 (0052.jp2)
- 4.7 Hebbian learning with queries / p99 (0053.jp2)
- 4.8 Avoiding over-training by a weight-decay term / p104 (0056.jp2)
- 4.9 Summary / p105 (0056.jp2)
- 5 Learning Processes in Non-Monotonic Perceptrons / p109 (0058.jp2)
- 5.1 The model system and dynamical equations / p109 (0058.jp2)
- 5.2 Hebbian and Perceptron learning algorithms / p110 (0059.jp2)
- 5.3 AdaTron learning algorithm / p116 (0062.jp2)
- 5.4 Optimized learning / p118 (0063.jp2)
- 5.5 Summary / p125 (0066.jp2)
- 6 Optimization by Simulated Annealing / p129 (0068.jp2)
- 6.1 Annealing schedule / p129 (0068.jp2)
- 6.2 Inhomogeneous Markov chain / p130 (0069.jp2)
- 6.3 Weak ergodicity / p131 (0069.jp2)
- 6.4 Example for q < 1 / p134 (0071.jp2)
- 6.5 More general transition probability / p137 (0072.jp2)
- 6.6 Discussion / p138 (0073.jp2)
- 7 Summary and Concluding Remarks / p141 (0074.jp2)
- A Evaluation of 《lnZ(β)》 / p145 (0076.jp2)
- B Stability of the R.S solution / p149 (0078.jp2)
- C Derivation of the differential equations of the on-line dynamics / p151 (0079.jp2)
- D Integrals / p153 (0080.jp2)
- E The weight function in the modified AdaTron learning algorithm / p161 (0084.jp2)
- F Derivation of the Fokker-Planck equation / p163 (0085.jp2)
