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In AI, generalization refers to a model's ability to perform well on out-of-distribution data related to the given task, beyond the data it was trained on. For an AI agent to excel, it must also possess the continual learning capability, whereby an agent incrementally learns to perform a sequence of tasks without forgetting the previously acquired knowledge to solve the old tasks. Intuitively, generalization within a task allows the model to learn underlying features that can readily be applied to novel tasks, facilitating quicker learning and enhanced performance in subsequent tasks within a continual learning framework. Conversely, continual learning methods often include mechanisms to mitigate catastrophic forgetting, ensuring that knowledge from earlier tasks is retained. This preservation of knowledge over tasks plays a role in enhancing generalization for the ongoing task at hand. Despite the intuitive appeal of the interplay of both abilities, existing literature on continual learning and generalization has proceeded separately. In the preliminary effort to promote studies that bridge both fields, we first present empirical evidence showing that each of these fields has a mutually positive effect on the other. Next, building upon this finding, we introduce a simple and effective technique known as Shape-Texture Consistency Regularization (STCR), which caters to continual learning. STCR learns both shape and texture representations for each task, consequently enhancing generalization and thereby mitigating forgetting. Remarkably, extensive experiments validate that our STCR, can be seamlessly integrated with existing continual learning methods, including replay-free approaches. Its performance surpasses these continual learning methods in isolation or when combined with established generalization techniques by a large margin.