Continual learning and machine unlearning are crucial challenges in machine learning, typically addressed separately. Continual learning focuses on adapting to new knowledge while preserving past information, whereas unlearning involves selectively forgetting specific subsets of data. In this paper, we introduce a novel framework that jointly tackles both tasks by leveraging controlled knowledge distillation. Our approach enables efficient learning with minimal forgetting and effective targeted unlearning. By incorporating a fixed memory buffer, the system supports learning new concepts while retaining prior knowledge. The distillation process is carefully managed to ensure a balance between acquiring new information and forgetting specific data as needed. Experimental results on benchmark datasets show that our method matches or exceeds the performance of existing approaches in both continual learning and machine unlearning. This unified framework is the first to address both challenges simultaneously, paving the way for adaptable models capable of dynamic learning and forgetting while maintaining strong overall performance.

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