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Existing generalization theories analyze the generalization performancemainly based on the model complexity and training process. The ignorance of thetask properties, which results from the widely used IID assumption, makes thesetheories fail to interpret many generalization phenomena or guide practicallearning tasks. In this paper, we propose a new Independent andTask-Identically Distributed (ITID) assumption, to consider the task propertiesinto the data generating process. The derived generalization bound based on theITID assumption identifies the significance of hypothesis invariance inguaranteeing generalization performance. Based on the new bound, we introduce apractical invariance enhancement algorithm from the perspective of modifyingdata distributions. Finally, we verify the algorithm and theorems in thecontext of image classification task on both toy and real-world datasets. Theexperimental results demonstrate the reasonableness of the ITID assumption andthe effectiveness of new generalization theory in improving practicalgeneralization performance.

A Generalization Theory based on Independent and Task-Identically Distributed Assumption