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#1 Understanding the Forgetting of (Replay-based) Continual Learning via Feature Learning: Angle Matters [PDF1] [Copy] [Kimi] [REL]

Authors: Hongyi Wan, Shiyuan Ren, Wei Huang, Miao Zhang, Xiang Deng, Yixin Bao, Liqiang Nie

Continual learning (CL) is crucial for advancing human-level intelligence, but its theoretical understanding, especially regarding factors influencing forgetting, is still relatively limited. This work aims to build a unified theoretical framework for understanding CL using feature learning theory. Different from most existing studies that analyze forgetting under linear regression model or lazy training, we focus on a more practical two-layer convolutional neural network (CNN) with polynomial ReLU activation for sequential tasks within a signal-noise data model. Specifically, we theoretically reveal how the angle between task signal vectors influences forgetting that: *acute or small obtuse angles lead to benign forgetting, whereas larger obtuse angles result in harmful forgetting*. Furthermore, we demonstrate that the replay method alleviates forgetting by expanding the range of angles corresponding to benign forgetting. Our theoretical results suggest that mid-angle sampling, which selects examples with moderate angles to the prototype, can enhance the replay method's ability to mitigate forgetting. Experiments on synthetic and real-world datasets confirm our theoretical results and highlight the effectiveness of our mid-angle sampling strategy.

Subject: ICML.2025 - Poster