Measuring Representational Shifts in Continual Learning: A Linear Transformation Perspective
This work addresses the problem of catastrophic forgetting for researchers in continual learning, providing theoretical insights and a new metric, but it is incremental as it builds on existing representation forgetting concepts.
The paper tackles catastrophic forgetting in continual learning by introducing a new metric called representation discrepancy to measure representation forgetting, and through theoretical analysis and experiments on datasets like Split-CIFAR100 and ImageNet1K, it finds that forgetting increases with layer depth and decreases with network width.
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.