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arXiv 0705.2318cs.LGcond-mat.dis-nn
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非线性统计力学在线学习

Statistical Mechanics of Nonlinear On-line Learning for Ensemble Teachers

Kobe City College of Technology(神户市立工业高等专门学校);Kobe University(神户大学);The University of Tokyo(东京大学);RIKEN Brain Science Institute(理化学研究所脑科学研究所)

Hideto Utsumi, Seiji Miyoshi, Masato Okada

摘要:

我们分析了一个学生的泛化性能的非线性感知器组成的模型:一个真正的老师,合奏教师,和学生。我们计算的泛化误差的学生分析或数值使用统计力学的框架内的在线学习。我们处理两个著名的学习规则:Hebbian学习和感知器学习。结果表明,非线性模型表现出与线性模型不同的性质。此外,它是澄清,赫布学习和感知器学习表现出质的不同的行为从对方。在Hebbian学习中,我们可以解析地得到解。在这种情况下,泛化误差单调减小。泛化误差的稳定值与学习率无关。教师人数越多,教师群体的多样性越大,泛化误差越小。在感知器学习中,我们必须数值地获得解决方案。在这种情况下,泛化误差的动力学行为是非单调的。学习率越小,教师人数越多;集成教师种类越多,泛化误差的最小值越小。

英文摘要:

We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using statistical mechanics in the framework of on-line learning. We treat two well-known learning rules: Hebbian learning and perceptron learning. As a result, it is proven that the nonlinear model shows qualitatively different behaviors from the linear model. Moreover, it is clarified that Hebbian learning and perceptron learning show qualitatively different behaviors from each other. In Hebbian learning, we can analytically obtain the solutions. In this case, the generalization error monotonically decreases. The steady value of the generalization error is independent of the learning rate. The larger the number of teachers is and the more variety the ensemble teachers have, the smaller the generalization error is. In perceptron learning, we have to numerically obtain the solutions. In this case, the dynamical behaviors of the generalization error are non-monotonic. The smaller the learning rate is, the larger the number of teachers is; and the more variety the ensemble teachers have, the smaller the minimum value of the generalization error is.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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