A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix
This work addresses catastrophic forgetting for continual learning systems, offering a theoretical analysis and incremental method improvement.
The paper tackles catastrophic forgetting in continual learning by analyzing how task similarity affects forgetting and introduces the NTK overlap matrix as a measure. It proposes a PCA-based variant of Orthogonal Gradient Descent, showing it reduces forgetting on classical datasets.
Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets.