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Continual learning (CL) requires a model to continually learn new tasks with incremental available information while retaining previous knowledge. Despite the numerous previous approaches to CL, most of them still suffer forgetting, expensive memory cost, or lack sufficient theoretical understanding. While different CL training regimes have been extensively studied empirically, insufficient attention has been paid to the underlying theory. In this paper, we establish a probabilistic framework to analyze information flow through layers in networks for sequential tasks and its impact on learning performance. Our objective is to optimize the information preservation between layers while learning new tasks. This manages task-specific knowledge passing throughout the layers while maintaining model performance on previous tasks. Our analysis provides novel insights into information adaptation within the layers during incremental task learning. We provide empirical evidence and practically highlight the performance improvement across multiple tasks. Code is available at https://github.com/Sekeh-Lab/InformationFlow-CL.