Topic modeling aims to discover the distribution of topics within a corpus. The advanced comprehension and generative capabilities of large language models (LLMs) have introduced new avenues for topic modeling, particularly by prompting LLMs to generate topics and refine them by merging similar ones. However, this approach necessitates that LLMs generate topics with consistent granularity, thus relying on the exceptional instruction-following capabilities of closed-source LLMs (such as GPT-4) or requiring additional training. Moreover, merging based only on topic words and neglecting the fine-grained semantics within documents might fail to fully uncover the underlying topic structure. In this work, we propose a semi-supervised topic modeling method, LiSA, that combines LLMs with clustering to improve topic generation and distribution. Specifically, we begin with prompting LLMs to generate a candidate topic word for each document, thereby constructing a topic-level semantic space. To further utilize the mutual complementarity between them, we first cluster documents and candidate topic words, and then establish a mapping from document to topic in the LLM-guided assignment stage. Subsequently, we introduce a collaborative enhancement strategy to align the two semantic spaces and establish a better topic distribution. Experimental results demonstrate that LiSA outperforms state-of-the-art methods that utilize GPT-4 on topic alignment, and exhibits competitive performance compared to Neural Topic Models on topic quality. The codes are available at https://github.com/ljh986/LiSA.

Data quality and diversity are key to the construction of effective instruction-tuning datasets. With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. Notably, the model fine-tuned with 5% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73% on AlpacaEval and +6.89% on Wildbench.