A Manifold-Aware Topic Modeling Approach via Rank-Based Prototypes

arXiv:2609.29630v1 Announce Type: cross Abstract: Recent topic models leverage pretrained embeddings, but neural architectures produce latent representations without grounding in specific texts, and clustering-based pipelines assign representative documents only post hoc, relying on absolute distances distorted by hubness and anisotropy in high-dimensional spaces. We introduce MARETopic, a training-free framework that casts topic discovery as rank-based prototype selection. After projecting embeddings onto a low-dimensional manifold, MARETopic builds ranked lists encoding ordinal neighborhood structure. A greedy algorithm selects exactly K exemplar documents, real corpus texts, whose neighborhoods cover the corpus. Two variants share this criterion. MARETopic$\text{Corr}$ scores candidates with a query performance predictor and a rank correlation measure, leading Purity and NMI on the two benchmarks with the most categories, ahead of both neural and clustering-based topic models. MARETopic$\text{Diff}$ scores them with a rank-based diffusion matrix, needs neither measure, and runs 1.7 to 1.9 times faster. Without a single gradient update, MARETopic leads topic coherence on two of three datasets. A novel inter-topic Maximal Marginal Relevance step raises vocabulary diversity at little cost in coherence. Our code is available at https://github.com/thcastilho/maretopic.