持续学习的数学基础
Mathematics of Continual Learning
AI总结：
本教程回顾持续学习与自适应滤波的基本原理，通过比较分析揭示两者联系，以增强持续学习的数学基础并拓展研究方向。
摘要：
持续学习是机器学习中的一个新兴课题，旨在解决按顺序呈现给学习者的多个任务，同时不遗忘先前学过的任务。近年来，许多基于深度学习的持续学习方法被提出，然而现有持续学习方法背后的数学基础仍不完善。另一方面，自适应滤波是信号处理中的一个经典课题，拥有丰富且数学上严谨的方法历史。然而，其在理解持续学习基础中的作用一直被低估。在本教程中，我们回顾了持续学习和自适应滤波两者的基本原理，并进行了比较分析，突出了它们之间的多个联系。这些联系使我们能够基于自适应滤波的现有结果来增强持续学习的数学基础，利用现有的持续学习方法扩展自适应滤波的见解，并讨论由自适应滤波的历史发展所启示的持续学习的几个研究方向。
英文摘要：
Continual learning is an emerging subject in machine learning that aims to solve multiple tasks presented sequentially to the learner without forgetting previously learned tasks. Recently, many deep learning based approaches have been proposed for continual learning, however the mathematical foundations behind existing continual learning methods remain underdeveloped. On the other hand, adaptive filtering is a classic subject in signal processing with a rich history of mathematically principled methods. However, its role in understanding the foundations of continual learning has been underappreciated. In this tutorial, we review the basic principles behind both continual learning and adaptive filtering, and present a comparative analysis that highlights multiple connections between them. These connections allow us to enhance the mathematical foundations of continual learning based on existing results for adaptive filtering, extend adaptive filtering insights using existing continual learning methods, and discuss a few research directions for continual learning suggested by the historical developments in adaptive filtering.
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。
