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arXiv 2505.20970cs.LG

持续学习中表征偏移的度量:线性变换视角

Measuring Representational Shifts in Continual Learning: A Linear Transformation Perspective

Department of Electrical \& Electronic Engineering, Yonsei University, Seoul, South Korea;Department of Statistics;Data Science, Yonsei University, Seoul, South Korea

Joonkyu Kim, Yejin Kim, Jy-yong Sohn

AI总结:

该研究从线性变换视角提出表征差异指标以度量持续学习中的表征遗忘,通过理论分析得出层深度、网络宽度与遗忘速度的关联规律,并在Split-CIFAR100、ImageNet1K数据集上验证了理论结论。

摘要:

在持续学习场景中,对先前学习任务的灾难性遗忘是一个关键问题,因此有效度量此类遗忘至关重要。近年来,人们对表征遗忘(即在隐藏层度量的遗忘)的关注日益增长。本文首次对表征遗忘进行了理论分析,并利用该分析更好地理解持续学习的行为。首先,我们提出了一种名为表征差异的新指标,用于度量通过持续学习训练的模型的两个快照所构建的表征空间之间的差异。我们证明,所提出的指标可作为表征遗忘的有效替代指标,同时保持分析上的可处理性。其次,通过对该指标的数学分析,我们得出了关于表征遗忘动态的几个关键发现:随着层索引的增加,遗忘发生得更快、程度更高,而增加网络宽度则会减缓遗忘过程。第三,我们在真实图像数据集(包括Split-CIFAR100和ImageNet1K)上通过实验验证了我们的理论发现。

英文摘要:

In continual learning scenarios, catastrophic forgetting of previously learned tasks is a critical issue, making it essential to effectively measure such forgetting. Recently, there has been growing interest in focusing on representation forgetting, the forgetting measured at the hidden layer. In this paper, we provide the first theoretical analysis of representation forgetting and use this analysis to better understand the behavior of continual learning. First, we introduce a new metric called representation discrepancy, which measures the difference between representation spaces constructed by two snapshots of a model trained through continual learning. We demonstrate that our proposed metric serves as an effective surrogate for the representation forgetting while remaining analytically tractable. Second, through mathematical analysis of our metric, we derive several key findings about the dynamics of representation forgetting: the forgetting occurs more rapidly to a higher degree as the layer index increases, while increasing the width of the network slows down the forgetting process. Third, we support our theoretical findings through experiments on real image datasets, including Split-CIFAR100 and ImageNet1K.

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。

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