臺灣博碩士論文加值系統

本篇論文主要探討以廣義 adaline網路為基礎的近似函數的學習法則。廣義adaline神經元包含一個接收場向量及一個多態激發函數，激發函數的輸入是多變量刺激在接收場向量上的投影特徵，輸出是嵌入式Gaussian陣列的標準化反應。我們將建構有效監督式學習法則的數學模型，具體目標包含強化投影特徵的有效性、提升Gaussian元件的利用率及降低訓練集的近似誤差。我們得到混合式的整數及線性規劃模型，並利用平均場退火理論及最陡坡降法求取該架構之最佳解。經過嚴密的推導，我們得到三個交互動態方程祖，具體實踐新的監督式學習法則。實驗的結果顯示，新的學習法則可以找到訓練集中隱含的內在生成對應函數。

This work explores the learning process of a network of generalized adalines for function approximation. A generalized adaline contains a receptive field and a multi-state activation function, of which the output is the normalized response of an embedded Gaussian array and the input is the feature extracted by the receptive field from a multi-component stimulus. The supervised learning process is modeled by a mathematical framework, addressing on subjects of extracting the most effective feature, maximizing utilization of Gaussian units, and fitting criteria proposed by training samples. The mathematical framework is a mixed integer and linear programming, and can be solved by a hybrid of the mean field annealing and the gradient descent methods. As a result, we have three sets of interactive dynamics for the new supervised learning process. Numerical simulations show that the learning process is able to generate essential internal representations for the mapping underlying training samples.

1.Neural Organization of Generalized Adalines
A. Adalines 1
B. Generalized Adalines 3
C. A Network of Generalized Adalines 6
2.A Mathematical Framework for Learning Neural Approximation 7
3.Neural Dynamics 12
4.Numerical Simulations and Discussions
A.The first strategy for simulating interactive dynamics 16
B.The second strategy for simulating interactive
dynamics 19
5.Conclusions 21
Appendix
References

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