The Multi-Task Learning (MTL) leverages the inter-relationship across tasks and is useful for applications with limited data. Existing works articulate different task relationship assumptions, whose validity is vital to successful multi-task training. We observe that, in many scenarios, the inter-relationship across tasks varies across different groups of data (i.e., topic), which we call within-topic task relationship hypothesis. In this case, current MTL models with homogeneous task relationship assumption cannot fully exploit different task relationships among different groups of data. Based on this observation, in this paper, we propose a generalized topic-wise multi-task architecture, to capture the within-topic task relationship, which can be combined with any existing MTL designs. Further, we propose a new specialized MTL design, topic-task-sparsity, along with two different types of sparsity constraints. The architecture, combined with the topic-task-sparsity design, constructs our proposed TOMATO model. The experiments on both synthetic and 4 real-world datasets show that our proposed models consistently outperform 6 state-of-the-art models and 2 baselines with improvement from $5%$ to $46%$ in terms of task-wise comparison, demonstrating the validity of the proposed within-topic task relationship hypothesis. We release the source codes and datasets of TOMATO at: https://github.com/JasonLC506/MTSEM.