Task Confusion and Catastrophic Forgetting in Class-Incremental Learning: A Mathematical Framework for Discriminative and Generative Modelings
This provides a theoretical foundation for class-incremental learning, addressing a key challenge in continual learning for AI systems that need to learn new classes over time.
The paper tackles the problem of task confusion in class-incremental learning, proving that optimal performance is impossible with discriminative modeling but feasible with generative modeling, as shown by their Infeasibility and Feasibility Theorems.
In class-incremental learning (class-IL), models must classify all previously seen classes at test time without task-IDs, leading to task confusion. Despite being a key challenge, task confusion lacks a theoretical understanding. We present a novel mathematical framework for class-IL and prove the Infeasibility Theorem, showing optimal class-IL is impossible with discriminative modeling due to task confusion. However, we establish the Feasibility Theorem, demonstrating that generative modeling can achieve optimal class-IL by overcoming task confusion. We then assess popular class-IL strategies, including regularization, bias-correction, replay, and generative classifier, using our framework. Our analysis suggests that adopting generative modeling, either for generative replay or direct classification (generative classifier), is essential for optimal class-IL.