In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph Neural Networks. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We do not aim to give a complete and exhaustive treatment, but we isolate few concepts to give a fast introduction to the subject. We provide some appendices to complement our treatment discussing Kullback-Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation Theorem.

翻译：在本文中，我们旨在为数学家和物理学家提供关于深度学习与几何深度学习（重点聚焦于图神经网络）这些新兴且成功算法的内在运作机制作简要介绍，并附上少量进一步阅读的关键参考文献。我们概述了这些算法的核心要素：评分函数与损失函数，并解释了模型训练的主要步骤。我们不追求全面详尽的论述，而是提炼出几个关键概念，以便快速入门该主题。我们还提供了若干附录以补充说明，涵盖Kullback-Leibler散度、回归、多层感知机以及通用逼近定理。