Kong Yajing, Liu Liu, Chen Huanhuan, Kacprzyk Janusz, Tao Dacheng
IEEE Trans Neural Netw Learn Syst. 2024 Nov;35(11):16196-16210. doi: 10.1109/TNNLS.2023.3292359. Epub 2024 Oct 29.
Neural networks tend to suffer performance deterioration on previous tasks when they are applied to multiple tasks sequentially without access to previous data. The problem is commonly known as catastrophic forgetting, a significant challenge in continual learning (CL). To overcome the catastrophic forgetting, regularization-based CL methods construct a regularization-based term, which can be considered as the approximation loss function of previous tasks, to penalize the update of parameters. However, the rigorous theoretical analysis of regularization-based methods is limited. Therefore, we theoretically analyze the forgetting and the convergence properties of regularization-based methods. The theoretical results demonstrate that the upper bound of the forgetting has a relationship with the maximum eigenvalue of the Hessian matrix. Hence, to decrease the upper bound of the forgetting, we propose eiGenvalues ExplorAtion Regularization-based (GEAR) method, which explores the geometric properties of the approximation loss of prior tasks regarding the maximum eigenvalue. Extensive experimental results demonstrate that our method mitigates catastrophic forgetting and outperforms existing regularization-based methods.
当神经网络在不访问先前数据的情况下依次应用于多个任务时，它们往往会在先前任务上出现性能下降。这个问题通常被称为灾难性遗忘，是持续学习（CL）中的一个重大挑战。为了克服灾难性遗忘，基于正则化的持续学习方法构建了一个基于正则化的项，它可以被视为先前任务的近似损失函数，以惩罚参数的更新。然而，对基于正则化方法的严格理论分析是有限的。因此，我们从理论上分析了基于正则化方法的遗忘和收敛特性。理论结果表明，遗忘的上限与海森矩阵的最大特征值有关。因此，为了降低遗忘的上限，我们提出了基于特征值探索正则化（GEAR）的方法，该方法探索了先前任务近似损失关于最大特征值的几何性质。大量实验结果表明，我们的方法减轻了灾难性遗忘，并且优于现有的基于正则化的方法。
