A coreset of an input set is its small summarization, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems (models/classifiers/loss functions). Coresets have been suggested for many fundamental problems, for example, in machine/deep learning, computer vision, databases, and theoretical computer science. This introductory paper was written following requests regarding the many inconsistent coreset definitions, lack of source code, the required deep theoretical background from different fields, and the dense papers that make it hard for beginners to apply and develop coresets. The article provides folklore, classic, and simple results including step-by-step proofs and figures, for the simplest (accurate) coresets. Nevertheless, we did not find most of their constructions in the literature. Moreover, we expect that putting them together in a retrospective context would help the reader to grasp current results that usually generalize these fundamental observations. Experts might appreciate the unified notation and comparison table for existing results. Open source code is provided for all presented algorithms, to demonstrate their usage, and to support the readers who are more familiar with programming than mathematics.

中文翻译：

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精确核心组概述

输入集的核心集是它的小总结，对于给定的问题系列（模型/分类器/损失函数）。核心集已被建议用于许多基本问题，例如，机器/深度学习、计算机视觉、数据库和理论计算机科学。这篇介绍性论文是根据许多不一致的核心集定义、缺乏源代码、需要来自不同领域的深厚理论背景以及使初学者难以应用和开发核心集的密集论文的要求而编写的。本文为最简单（准确）的核心集提供了民间传说、经典和简单的结果，包括逐步证明和数字。尽管如此，我们没有在文献中找到他们的大部分结构。此外，我们希望将它们放在回顾性上下文中将有助于读者掌握通常概括这些基本观察的当前结果。专家可能会欣赏现有结果的统一符号和比较表。为所有呈现的算法提供了开源代码，以演示它们的用法，并为那些更熟悉编程而不是数学的读者提供支持。