Large language models (LLM)'s are increasingly used for topic modeling outperforming classical topic models such as LDA. Commonly, pre-trained LLM encoders such as BERT are used out-of-the-box despite the fact that fine-tuning is known to improve LLMs considerably. The challenge lies in obtaining a suitable (labeled) dataset for fine-tuning. In this paper, we use the recent idea to use bag of sentences as the elementary unit in computing topics. In turn, we derive an approach FT-Topic to perform unsupervised fine-tuning relying primarily on two steps for constructing a training dataset in an automatic fashion. First, a heuristic method to identifies pairs of sentence groups that are either assumed to be of the same or different topics. Second, we remove sentence pairs that are likely labeled incorrectly. The dataset is then used to fine-tune an encoder LLM, which can be leveraged by any topic modeling approach using embeddings. However, in this work, we demonstrate its effectiveness by deriving a novel state-of-the-art topic modeling method called SenClu, which achieves fast inference through an expectation-maximization algorithm and hard assignments of sentence groups to a single topic, while giving users the possibility to encode prior knowledge on the topic-document distribution. Code is at \url{https://github.com/JohnTailor/FT-Topic}
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