论文标题
高维世界中的高维大脑：维度的祝福
High--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality
论文作者
论文摘要
现实的高维数据和高维表示是现代人工智能系统的固有特征和机器学习的应用。 “维度诅咒”的众所周知现象指出：在高维度中，许多问题变得成倍困难。最近，硬币的另一面是“维度的祝福”，引起了很多关注。事实证明，通用高维数据集具有相当简单的几何特性。因此，在高维空间中的复杂性与简单性之间存在基本的权衡。在这里，我们对最近的思想，结果和假设进行了简要的解释，内容及其与机器学习和神经科学相关的相关效果的祝福。
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.
