Existing generalization theories analyze the generalization performance mainly based on the model complexity and training process. The ignorance of the task properties, which results from the widely used IID assumption, makes these theories fail to interpret many generalization phenomena or guide practical learning tasks. In this paper, we propose a new Independent and Task-Identically Distributed (ITID) assumption, to consider the task properties into the data generating process. The derived generalization bound based on the ITID assumption identifies the significance of hypothesis invariance in guaranteeing generalization performance. Based on the new bound, we introduce a practical invariance enhancement algorithm from the perspective of modifying data distributions. Finally, we verify the algorithm and theorems in the context of image classification task on both toy and real-world datasets. The experimental results demonstrate the reasonableness of the ITID assumption and the effectiveness of new generalization theory in improving practical generalization performance.
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