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

arXiv: https://arxiv.org/abs/2609.29630 · HTML: https://mlsanity.com/paper/2609.29630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 20 of 20)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Topic Modeling in Embedding Spaces](https://mlsanity.com/paper/1907.04907/) (2019)
- [Top2Vec: Distributed Representations of Topics](https://mlsanity.com/paper/2008.09470/) (2020)
- [Pre-training is a Hot Topic: Contextualized Document Embeddings Improve Topic Coherence](https://mlsanity.com/paper/2004.03974/) (2020)
- [HDLTex: Hierarchical Deep Learning for Text Classification](https://mlsanity.com/paper/1709.08267/) (2017)
- [Is Automated Topic Model Evaluation Broken?: The Incoherence of Coherence](https://mlsanity.com/paper/2107.02173/) (2021)
- [Effective Neural Topic Modeling with Embedding Clustering Regularization](https://mlsanity.com/paper/2306.04217/) (2023)
- [FASTopic: Pretrained Transformer is a Fast, Adaptive, Stable, and Transferable Topic Model](https://mlsanity.com/paper/2405.17978/) (2024)
- [Towards the TopMost: A Topic Modeling System Toolkit](https://mlsanity.com/paper/2309.06908/) (2023)
- [Correlation Coefficients and Semantic Textual Similarity](https://mlsanity.com/paper/1905.07790/) (2019)
- [Neural Topic Modeling by Incorporating Document Relationship Graph](https://mlsanity.com/paper/2009.13972/) (2020)
- [Fast Spectral Ranking for Similarity Search](https://mlsanity.com/paper/1703.06935/) (2017)
- [Topic Modeling as Multi-Objective Contrastive Optimization](https://mlsanity.com/paper/2402.07577/) (2024)
- [Hubness Reduction Improves Sentence-BERT Semantic Spaces](https://mlsanity.com/paper/2311.18364/) (2023)
- [A Rank-Based Similarity Metric for Word Embeddings](https://mlsanity.com/paper/1805.01923/) (2018)
- [CAST: Corpus-Aware Self-similarity Enhanced Topic modelling](https://mlsanity.com/paper/2410.15136/) (2024)
- [E-LDA: Toward Interpretable LDA Topic Models with Strong Guarantees in Logarithmic Parallel Time](https://mlsanity.com/paper/2506.07747/) (2025)

## Abstract (arXiv)

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. MARETopicCorr 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. MARETopicDiff 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.