超越存储容量：数据驱动的可满足性转换
Beyond the storage capacity: data driven satisfiability transition
摘要：
数据结构对神经网络的性质有着巨大的影响，但它在已建立的理论框架中的重要性却知之甚少。在这里，我们计算的Vapnik-Chervonenkis熵的内核机器上的数据分组到相等的标签子集。与非结构化场景不同的是，熵在训练集的大小上是非单调的，并且除了存储容量之外还显示了一个额外的临界点。值得注意的是，相同的行为发生在边缘分类器中，即使是随机标记的数据，如通过识别编码过渡的突触体积所阐明的。这些研究结果揭示了方面的表现力躺在压缩描述所提供的存储容量，他们指出了更现实的界限为泛化误差的神经网络的路径。
英文摘要：
Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine operating on data grouped into equally labelled subsets. At variance with the unstructured scenario, entropy is non-monotonic in the size of the training set, and displays an additional critical point besides the storage capacity. Remarkably, the same behavior occurs in margin classifiers even with randomly labelled data, as is elucidated by identifying the synaptic volume encoding the transition. These findings reveal aspects of expressivity lying beyond the condensed description provided by the storage capacity, and they indicate the path towards more realistic bounds for the generalization error of neural networks.
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