标题： 现代关联记忆方法 显示英文标题

标题： Modern Methods in Associative Memory

摘要： 关联记忆，如著名的霍普菲尔德网络，是描述全循环神经网络的优雅模型，其基本任务是存储和检索信息。 在过去的几年中，由于关于它们的信息存储能力的新理论结果，以及它们与最先进的AI架构（如Transformer和扩散模型）之间的关系，它们引起了广泛关注。 这些联系为通过关联记忆的理论视角来解释传统AI网络的计算提供了可能性。 此外，这些网络的新拉格朗日公式使得设计强大的分布式模型成为可能，这些模型可以学习有用的表示，并指导新型架构的设计。 本教程提供了一个易于理解的关联记忆介绍，强调该研究领域中使用的现代语言和方法，并包含实践性的数学推导和编码笔记本。 显示英文摘要

摘要： Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest due to novel theoretical results pertaining to their information storage capabilities, and their relationship with SOTA AI architectures, such as Transformers and Diffusion Models. These connections open up possibilities for interpreting the computation of traditional AI networks through the theoretical lens of Associative Memories. Additionally, novel Lagrangian formulations of these networks make it possible to design powerful distributed models that learn useful representations and inform the design of novel architectures. This tutorial provides an approachable introduction to Associative Memories, emphasizing the modern language and methods used in this area of research, with practical hands-on mathematical derivations and coding notebooks.