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The key of referring expression comprehension lies in capturing the cross-modal visual-linguistic relevance. Existing works typically model the cross-modal relevance in each image, where the anchor object/expression and their positive expression/object have the same attribute as the negative expression/object, but with different attribute values. These objects/expressions are exclusively utilized to learn the implicit representation of the attribute by a pair of different values, which however impedes the accuracies of the attribute representations, expression/object representations, and their cross-modal relevances since each anchor object/expression usually has multiple attributes while each attribute usually has multiple potential values. To this end, we investigate a novel REC problem named Group-based REC, where each object/expression is simultaneously employed to construct the multiple triplets among the semantically similar images. To tackle the explosion of the negatives and the differentiation of the anchor-negative relevance scores, we propose the multi-group self-paced relevance learning schema to adaptively assign within-group object-expression pairs with different priorities based on their cross-modal relevances. Since the average cross-modal relevance varies a lot across different groups, we further design an across-group relevance constraint to balance the bias of the group priority. Experiments on three standard REC benchmarks demonstrate the effectiveness and superiority of our method.