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
-
1998-06-30
注記・抄録
博士論文
資料形態 : テキストデータ プレーンテキスト
コレクション : 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文
identifier:oai:t2r2.star.titech.ac.jp:99001217
目次
- 論文目録
- Contents
- 1 Introduction
- 1.1 What is learning?
- 1.2 Neural network model
- 1.3 Several learning algorithms
- 1.4 What is generalization?
- 1.5 Optimization problem
- 1.6 Overview of this thesis
- 2 The Model System for Unrealizable Rule
- 3 Off-Line Learning
- 3.1 Statistical mechanics
- 3.2 Replica calculations of learning curves
- 3.3 Simulations for the two-dimensional case
- 3.4 Summary
- 4 On-Line Learning
- 4.1 Background
- 4.2 Dynamics of noiseless learning
- 4.3 Learning under output noise in the teacher signal
- 4.4 Optimization of learning rate
- 4.5 Optimized learning with output noise
- 4.6 Optimal learning without unknown parameters
- 4.7 Hebbian learning with queries
- 4.8 Avoiding over-training by a weight-decay term
- 4.9 Summary
- 5 Learning Processes in Non-Monotonic Perceptrons
- 5.1 The model system and dynamical equations
- 5.2 Hebbian and Perceptron learning algorithms
- 5.3 AdaTron learning algorithm
- 5.4 Optimized learning
- 5.5 Summary
- 6 Optimization by Simulated Annealing
- 6.1 Annealing schedule
- 6.2 Inhomogeneous Markov chain
- 6.3 Weak ergodicity
- 6.4 Example for q < 1
- 6.5 More general transition probability
- 6.6 Discussion
- 7 Summary and Concluding Remarks
- A Evaluation of 《lnZ(β)》
- B Stability of the R.S solution
- C Derivation of the differential equations of the on-line dynamics
- D Integrals
- E The weight function in the modified AdaTron learning algorithm
- F Derivation of the Fokker-Planck equation
