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In the era of rapid paper publications in various venues, automatic citation recommendations would be highly useful to researchers when they write papers. Local citation recommendation aims to recommend possible papers to cite given local citation contexts. Previous work mainly computes the similarity score between citation contexts and cited papers on a one-to-one basis, which is quite time-consuming. We train a pair of neural network encoders that map citation contexts and all possible cited papers to the same vector space, respectively. After that, we index the positions of all cited papers in the vector space. This makes our process for searching recommended papers considerably faster. On the other hand, existing methods tend to recommend papers that are highly similar to each other, which makes recommendations lack diversity. Therefore, we extend our algorithm to perform multi-topic recommendations. We generate multi-topic training examples based on the index we mentioned earlier. Furthermore, we specially design a multi-group contrastive learning method to train our model so that it can distinguish different topics. Empirical experiments show that our model outperforms previous methods by a wide margin. Our model is also light weighted and has been deployed online so that researchers can use it to obtain recommended citations for their own paper in real-time. • Proposed FLCR algorithm with sentence-transformer & k-d tree. • Introduced multi-topic citation recommendation for diverse contexts. • Developed large-scale dataset with 1.7 million citation contexts for evaluation. • Demonstrated significant performance improvement over previous methods. • Deployed demo for real-time citation recommendations. [ABSTRACT FROM AUTHOR]