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In this paper, we explore text classification with extremely weak supervision, i.e., only relying on the surface text of class names. This is a more challenging setting than the seed-driven weak supervision, which allows a few seed words per class. We opt to attack this problem from a representation learning perspective -- ideal document representations should lead to nearly the same results between clustering and the desired classification. In particular, one can classify the same corpus differently (e.g., based on topics and locations), so document representations should be adaptive to the given class names. We propose a novel framework X-Class to realize the adaptive representations. Specifically, we first estimate class representations by incrementally adding the most similar word to each class until inconsistency arises. Following a tailored mixture of class attention mechanisms, we obtain the document representation via a weighted average of contextualized word representations. With the prior of each document assigned to its nearest class, we then cluster and align the documents to classes. Finally, we pick the most confident documents from each cluster to train a text classifier. Extensive experiments demonstrate that X-Class can rival and even outperform seed-driven weakly supervised methods on 7 benchmark datasets. Our dataset and code are released at https://github.com/ZihanWangKi/XClass/ .