arXiv:2605.28269v1 Announce Type: new 
Abstract: Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and implicitly couple word occurrence and repetition within one probabilistic mechanism. However, this formulation restricts the dependence structure among words and overlooks informative higher-order interactions, particularly in dynamic corpora with overlapping semantics. To address these limitations, we introduce a hypergraph representation of text where each document is modeled as a hyperedge connecting all co-occurring words, with repetition intensities encoded as node weights. This representation naturally separates word occurrence from repetition and induces a novel hypergraph-based multinomial distribution with a nonlinear normalization depending on the observed word set of each document. Building on this likelihood, we develop a dynamic topic modeling framework via structured low-rank factorizations with explicit temporal regularization on topic-word profiles. Moreover, we establish local convergence guarantees and derive non-asymptotic error bounds despite the intrinsic nonconvexity induced by bilinear factorization and document-specific nonlinear normalization. Numerical experiments on synthetic data and an application to the International Conference on Learning Representations (ICLR) corpus demonstrate consistent improvements over existing multinomial-based topic models.

تقدم دراسة جديدة تمثيلاً هيبرياً لنمذجة الموضوعات الديناميكية، مما يعالج القيود في النماذج التقليدية التي تفشل في التقاط التفاعلات من الدرجة العليا بين الكلمات. يقوم هذا النهج بنمذجة الوثائق كأطراف هيبرية تربط الكلمات المتزامنة، مما يسمح بفهم أكثر دقة لحدوث الكلمات وتكرارها.

Un nuevo estudio presenta una representación hipergráfica para la modelización dinámica de temas, abordando las limitaciones de los modelos tradicionales que no logran capturar interacciones de orden superior entre las palabras. Este enfoque modela documentos como hiperaristas que conectan palabras coocurrentes, permitiendo una comprensión más matizada de la ocurrencia y repetición de palabras.

Une nouvelle étude présente une représentation hypergraphique pour la modélisation dynamique des sujets, abordant les limitations des modèles traditionnels qui ne parviennent pas à capturer les interactions d'ordre supérieur entre les mots. Cette approche modélise les documents comme des hyperarêtes reliant des mots co-occurrents, permettant une compréhension plus nuancée de l'occurrence et de la répétition des mots.

A new study introduces a hypergraph representation for dynamic topic modeling, addressing limitations in traditional models that fail to capture higher-order interactions among words. This approach models documents as hyperedges connecting co-occurring words, allowing for a more nuanced understanding of word occurrence and repetition.