In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We proved the fundamental relationship between proper sampling set and complexity of boolean circuit. Armed with this set of tools, we then introduce much more effective learning strategies. We show that with such learning strategies and learning dynamics, universal learning can be achieved, and requires much less data.

中文翻译：

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布尔函数的采样与学习

在本文中，我们将通过引入新工具来继续我们对通用学习机的研究。我们首先讨论布尔函数和布尔电路，并建立一套工具，即拟合极值和适当的采样集。我们证明了适当的采样集与布尔电路的复杂性之间的基本关系。有了这套工具，我们就可以引入更有效的学习策略。我们表明，通过这样的学习策略和学习动态，可以实现普遍学习，并且需要的数据要少得多。