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Continual learning (CL) learns a sequence of tasks incre- mentally. This paper studies the challenging CL setting of class-incremental learning (CIL). CIL has two key chal- lenges: catastrophic forgetting (CF) and inter-task class sep- aration (ICS). Despite numerous proposed methods, these issues remain persistent obstacles. This paper proposes a novel CIL method, called Kernel Linear Discriminant Analy- sis (KLDA), that can effectively avoid CF and ICS problems. It leverages only the powerful features learned in a foundation model (FM). However, directly using these features proves suboptimal. To address this, KLDA incorporates the Radial Basis Function (RBF) kernel and its Random Fourier Fea- tures (RFF) to enhance the feature representations from the FM, leading to improved performance. When a new task ar- rives, KLDA computes only the mean for each class in the task and updates a shared covariance matrix for all learned classes based on the kernelized features. Classification is performed using Linear Discriminant Analysis. Our empir- ical evaluation using text and image classification datasets demonstrates that KLDA significantly outperforms baselines. Remarkably, without relying on replay data, KLDA achieves accuracy comparable to joint training of all classes, which is considered the upper bound for CIL performance. The KLDA code is available at https://github.com/salehmomeni/klda. 

Existing continual learning (CL) methods mainly rely on fine-tuning or adapting large language mod- els (LLMs). They still suffer from catastrophic for- getting (CF). Little work has been done to exploit in-context learning (ICL) to leverage the extensive knowledge within LLMs for CL without updating any parameters. However, incrementally learning each new task in ICL necessitates adding training examples from each class of the task to the prompt, which hampers scalability as the prompt length in- creases. This issue not only leads to excessively long prompts that exceed the input token limit of the underlying LLM but also degrades the model’s performance due to the overextended context. To address this, we introduce InCA, a novel approach that integrates an external continual learner (ECL) with ICL to enable scalable CL without CF. The ECL is built incrementally to pre-select a small subset of likely classes for each test instance. By restricting the ICL prompt to only these selected classes, InCA prevents prompt lengths from becom- ing excessively long, while maintaining high per- formance. Experimental results demonstrate that InCA significantly outperforms existing CL base- lines, achieving substantial performance gains.