网络教学的统计力学
Statistical Mechanics of Online Learning for Ensemble Teachers
摘要：
我们分析了线性感知器组成的模型中的学生的泛化性能：一个真正的老师，合奏教师，和学生。在在线学习的框架下，利用统计力学对学生的泛化误差进行了分析计算，证明了当学习率为$η<1$时，集合教师的个数$K$越大，泛化误差越小。另一方面，当为$η>1$时，性质完全相反。如果合奏教师的多样性足够丰富，真教师和学生之间的方向余弦在$η\to 0$和$K \to \infty$的极限下变为1。
英文摘要：
We analyze the generalization performance of a student in a model composed of linear perceptrons: a true teacher, ensemble teachers, and the student. Calculating the generalization error of the student analytically using statistical mechanics in the framework of on-line learning, it is proven that when learning rate $η<1$, the larger the number $K$ and the variety of the ensemble teachers are, the smaller the generalization error is. On the other hand, when $η>1$, the properties are completely reversed. If the variety of the ensemble teachers is rich enough, the direction cosine between the true teacher and the student becomes unity in the limit of $η\to 0$ and $K \to \infty$.
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