Numerous generalization bounds have been proposed in the literature as
potential explanations for the ability of neural networks to generalize in the
overparameterized setting. However, none of these bounds are tight. For
instance, in their paper ``Fantastic Generalization Measures and Where to Find
Them'', Jiang et al. (2020) examine more than a dozen generalization bounds,
and show empirically that none of them imply guarantees that can explain the
remarkable performance of neural networks. This raises the question of whether
tight generalization bounds are at all possible. We consider two types of
generalization bounds common in the literature: (1) bounds that depend on the
training set and the output of the learning algorithm. There are multiple
bounds of this type in the literature (e.g., norm-based and margin-based
bounds), but we prove mathematically that no such bound can be uniformly tight
in the overparameterized setting; (2) bounds that depend on the training set
and on the learning algorithm (e.g., stability bounds). For these bounds, we
show a trade-off between the algorithm's performance and the bound's tightness.
Namely, if the algorithm achieves good accuracy on certain distributions in the
overparameterized setting, then no generalization bound can be tight for it. We
conclude that generalization bounds in the overparameterized setting cannot be
tight without suitable assumptions on the population distribution.

神经网络在超参数化设置中的泛化界限无法达到紧致性，除非在总体分布上具备合适的假设。

奇妙的概括度量无处追寻

Fantastic Generalization Measures are Nowhere to be Found

Obtaining a dynamic population distribution is key to many decision-making
processes such as urban planning, disaster management and most importantly
helping the government to better allocate socio-technical supply. For the
aspiration of these objectives, good population data is essential. The
traditional method of collecting population data through the census is
expensive and tedious. In recent years, statistical and machine learning
methods have been developed to estimate population distribution. Most of the
methods use data sets that are either developed on a small scale or not
publicly available yet. Thus, the development and evaluation of new methods
become challenging. We fill this gap by providing a comprehensive data set for
population estimation in 98 European cities. The data set comprises a digital
elevation model, local climate zone, land use proportions, nighttime lights in
combination with multi-spectral Sentinel-2 imagery, and data from the Open
Street Map initiative. We anticipate that it would be a valuable addition to
the research community for the development of sophisticated approaches in the
field of population estimation.

研究人口分布，提供包括数字高程模型、本地气候区域、土地利用比例、夜间灯光和 Sentinel-2 的多光谱图像以及 Open Street Map 计划的数据，为人口估计的研究提供了一个全面的数据集。