In radial basis function neural network (RBFNN) based real-time learning tasks, forgetting mechanisms are widely used such that the neural network can keep its sensitivity to new data. However, with forgetting mechanisms, some useful knowledge will get lost simply because they are learned a long time ago, which we refer to as the passive knowledge forgetting phenomenon. To address this problem, this paper proposes a real-time training method named selective memory recursive least squares (SMRLS) in which the classical forgetting mechanisms are recast into a memory mechanism. Different from the forgetting mechanism, which mainly evaluates the importance of samples according to the time when samples are collected, the memory mechanism evaluates the importance of samples through both temporal and spatial distribution of samples. With SMRLS, the input space of the RBFNN is evenly divided into a finite number of partitions and a synthesized objective function is developed using synthesized samples from each partition. In addition to the current approximation error, the neural network also updates its weights according to the recorded data from the partition being visited. Compared with classical training methods including the forgetting factor recursive least squares (FFRLS) and stochastic gradient descent (SGD) methods, SMRLS achieves improved learning speed and generalization capability, which are demonstrated by corresponding simulation results.

翻译：在基于径向基函数神经网络（RBFNN）的实时学习任务中，遗忘机制被广泛使用，以使神经网络能够保持对新数据的敏感性。然而，采用遗忘机制时，某些有用知识仅因学习时间久远而丢失，我们称之为被动知识遗忘现象。为解决这一问题，本文提出一种名为选择性记忆递归最小二乘法（SMRLS）的实时训练方法，其中将经典遗忘机制重塑为记忆机制。与主要依据样本采集时间评估样本重要性的遗忘机制不同，记忆机制通过样本的时空分布共同评估其重要性。采用SMRLS方法，RBFNN的输入空间被均匀划分为有限数量的分区，并利用每个分区的合成样本构建合成目标函数。除当前近似误差外，神经网络还根据所访问分区的记录数据更新权重。与遗忘因子递归最小二乘法（FFRLS）和随机梯度下降法（SGD）等经典训练方法相比，SMRLS在仿真结果中展现出更快的学习速度和更强的泛化能力。