The human brain excels at lifelong learning by not only encoding information in sparse activation codes but also leveraging rich semantic structures and relationships between newly encountered and previously learned objects. This ability to utilize semantic similarities is crucial for efficient learning and knowledge consolidation, yet is often underutilized in current continual learning approaches. To bridge this gap, we propose Semantic-Aware Representation Learning (SARL) which employs sparse activations and a principled approach to evaluate similarities between objects encountered across different tasks and subsequently uses them to guide representation learning. Using these relationships, SARL enhances the reusability of features and reduces interference between tasks. This approach empowers the model to adapt to new information while maintaining stability, significantly improving performance in complex incremental learning scenarios. Our analysis demonstrates that SARL achieves a superior balance between plasticity and stability by harnessing the underlying semantic structure.