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arXiv 2106.15416cs.LGcs.AIstat.ML
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一次和少样本学习的高维可分性

High-dimensional separability for one- and few-shot learning

University of Leicester(莱斯特大学);Lobachevsky University(罗巴切夫斯基大学);Norwegian University of Science and Technology(挪威科技大学)

Alexander N. Gorban, Bogdan Grechuk, Evgeny M. Mirkes, Sergey V. Stasenko, Ivan Y. Tyukin

摘要:

这项工作是由一个实际问题驱动的:人工智能(AI)错误的纠正。这些纠正应该是快速的和非迭代的。为了解决这个问题,而不修改传统的人工智能系统,我们提出了特殊的“外部”设备,校正器。基本校正器由两部分组成,一个分类器将具有高错误风险的情况与传统AI系统工作良好的情况分开,另一个是对具有潜在错误的情况的新决策。校正器的输入信号可以是传统AI系统的输入、其内部信号和输出。如果数据的内在维数足够高,那么用于纠正少量错误的分类器可以非常简单。根据维度效应的祝福,即使是简单而强大的Fisher判别式也可以用于AI校正器的一次性学习。随机分离定理为这种一次学习提供了数学基础。然而,随着所需校正器数量的增加,数据的聚类结构变得重要,并且需要一个新的随机分离定理。我们拒绝了经典的假设的数据分布的规律性,并假设数据可以有一个细粒度的结构,许多集群和峰值的概率密度。提出并证明了细粒度数据的随机分离定理。提出了粒数据的多校正器。通过在CIFAR-10数据集上使用深度卷积神经网络纠正错误和学习新的对象类别的示例,证明了多校正器技术的优势。综述了非经典高维数据分析的关键问题,以及监督、半监督和领域自适应主成分分析的基本预处理步骤。

英文摘要:

This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special `external' devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher's discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a fine-grained structure with many clusters and peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. The multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including supervised, semi-supervised and domain adaptation Principal Component Analysis.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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