Using task-specific components within a neural network in continual learning (CL) is a compelling strategy to address the stability-plasticity dilemma in fixed-capacity models without access to past data. Current methods focus only on selecting a sub-network for a new task that reduces forgetting of past tasks. However, this selection could limit the forward transfer of relevant past knowledge that helps in future learning. Our study reveals that satisfying both objectives jointly is more

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... nging when a unified classifier is used for all classes of seen tasks-class-Incremental Learning (class-IL)-as it is prone to ambiguities between classes across tasks. Moreover, the challenge increases when the semantic similarity of classes across tasks increases. To address this challenge, we propose a new CL method, named AFAF, that aims to Avoid Forgetting and Allow Forward transfer in class-IL using fix-capacity models. AFAF allocates a sub-network that enables selective transfer of relevant knowledge to a new task while preserving past knowledge, reusing some of the previously allocated components to utilize the fixed-capacity, and addressing class-ambiguities when similarities exist. The experiments show the effectiveness of AFAF in providing models with multiple CL desirable properties, while outperforming state-of-the-art methods on various challenging benchmarks with different semantic similarities.