A Theoretical Study on Solving Continual Learning

Continual learning (CL) learns a sequence of tasks incrementally. There are two popular CL settings, class incremental learning (CIL) and task incremental learning (TIL). A major challenge of CL is catastrophic forgetting (CF). While several techniques are available to effectively overcome CF for TIL, CIL remains to be challenging due to the additional difficulty of inter-task class separation. So far little theoretical work has been done to provide a principled guidance and necessary and sufficient conditions for solving the CIL problem. This paper performs such a study. It first probabilistically decomposes the CIL problem into two subproblems: within-task prediction (WP) and task-id prediction (TP). It further proves that TP is correlated with out-of-distribution (OOD) detection. The key result is that regardless of whether WP and TP or OOD detection are defined explicitly or implicitly by a CIL algorithm, good WP and good TP or OOD detection are necessary and sufficient for good CIL performances. Additionally, TIL is simply WP. Based on the theoretical result, new CIL methods are also designed, which outperform strong baselines in both CIL and TIL settings by a large margin. 4