Large language models (LLMs) with their strong zero-shot topic extraction capabilities offer an alternative to probabilistic topic modelling and closed-set topic classification approaches. As zero-shot topic extractors, LLMs are expected to understand human instructions to generate relevant and non-hallucinated topics based on the given documents. However, LLM-based topic modelling approaches often face difficulties in generating topics with adherence to granularity as specified in human instructions, often resulting in many near-duplicate topics. Furthermore, methods for addressing hallucinated topics generated by LLMs have not yet been investigated. In this paper, we focus on addressing the issues of topic granularity and hallucinations for better LLM-based topic modelling. To this end, we introduce a novel approach that leverages Direct Preference Optimisation (DPO) to fine-tune open-source LLMs, such as Mistral-7B. Our approach does not rely on traditional human annotation to rank preferred answers but employs a reconstruction pipeline to modify raw topics generated by LLMs, thus enabling a fast and efficient training and inference framework. Comparative experiments show that our fine-tuning approach not only significantly improves the LLM's capability to produce more coherent, relevant, and precise topics, but also reduces the number of hallucinated topics.

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