Novel class discovery (NCD) aims to infer novel categories in an unlabeled dataset by leveraging prior knowledge of a labeled set comprising disjoint but related classes. Given that most existing literature focuses primarily on utilizing supervised knowledge from a labeled set at the methodology level, this paper considers the question: Is supervised knowledge always helpful at different levels of semantic relevance? To proceed, we first establish a novel metric, so-called transfer flow, to measure the semantic similarity between labeled/unlabeled datasets. To show the validity of the proposed metric, we build up a large-scale benchmark with various degrees of semantic similarities between labeled/unlabeled datasets on ImageNet by leveraging its hierarchical class structure. The results based on the proposed benchmark show that the proposed transfer flow is in line with the hierarchical class structure; and that NCD performance is consistent with the semantic similarities (measured by the proposed metric). Next, by using the proposed transfer flow, we conduct various empirical experiments with different levels of semantic similarity, yielding that supervised knowledge may hurt NCD performance. Specifically, using supervised information from a low-similarity labeled set may lead to a suboptimal result as compared to using pure self-supervised knowledge. These results reveal the inadequacy of the existing NCD literature which usually assumes that supervised knowledge is beneficial. Finally, we develop a pseudo-version of the transfer flow as a practical reference to decide if supervised knowledge should be used in NCD. Its effectiveness is supported by our empirical studies, which show that the pseudo transfer flow (with or without supervised knowledge) is consistent with the corresponding accuracy based on various datasets. Code is released at https://github.com/J-L-O/SK-Hurt-NCD

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