  Over-parameterized models can perfectly learn various types of data
distributions, however, generalization error is usually lower for real data in
comparison to artificial data. This suggests that the properties of data
distributions have an impact on generalization capability. This work focuses on
the search space defined by the input data and assumes that the correlation
between labels of neighboring input values influences generalization. If
correlation is low, the randomness of the input data space is high leading to
high generalization error. We suggest to measure the randomness of an input
data space using Maurer's universal. Results for synthetic classification tasks
and common image classification benchmarks (MNIST, CIFAR10, and Microsoft's
cats vs. dogs data set) find a high correlation between the randomness of input
data spaces and the generalization error of deep neural networks for binary
classification problems.
