Comprehending the rich semantics in an image and ordering them in linguistic order are essential to compose a visually-grounded and linguistically coherent description for image captioning. Modern techniques commonly capitalize on a pre-trained object detector/classifier to mine the semantics in an image, while leaving the inherent linguistic ordering of semantics under-exploited. In this paper, we propose a new recipe of Transformer-style structure, namely Comprehending and Ordering Semantics Networks (COS-Net), that novelly unifies an enriched semantic comprehending and a learnable semantic ordering processes into a single architecture. Technically, we initially utilize a cross-modal retrieval model to search the relevant sentences of each image, and all words in the searched sentences are taken as primary semantic cues. Next, a novel semantic comprehender is devised to filter out the irrelevant semantic words in primary semantic cues, and meanwhile infer the missing relevant semantic words visually grounded in the image. After that, we feed all the screened and enriched semantic words into a semantic ranker, which learns to allocate all semantic words in linguistic order as humans. Such sequence of ordered semantic words are further integrated with visual tokens of images to trigger sentence generation. Empirical evidences show that COS-Net clearly surpasses the state-of-the-art approaches on COCO and achieves to-date the best CIDEr score of 141.1% on Karpathy test split. Source code is available at \url{https://github.com/YehLi/xmodaler/tree/master/configs/image_caption/cosnet}.
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