Dynamic Topic Modeling with a Higher-Order Hypergraphical Representation
Authors: Hanjia Gao, Hanwen Ye, Qing Nie, Annie Qu
Organizations: Department of Statistics, University of California, Irvine · Department of Mathematics and Department of Developmental & Cell Biology, University of California, Irvine · Department of Statistics and Applied Probability, University of California, Santa Barbara
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.
Traditional topic models are effective at uncovering latent themes in large text collections. However, due to their reliance on bag-of-words representations, they struggle to capture semantically abstract features. While some neural variants use richer representations, they are similarly constrained by expressing topics as word lists, which limits their ability to articulate complex topics. We introduce Mechanistic Topic Models (MTMs), a class of topic models that operate on interpretable features learned by sparse autoencoders (SAEs). By defining topics over this semantically rich space, MTMs can reveal deeper conceptual themes with expressive feature descriptions. Moreover, uniquely among topic models, MTMs enable controllable text generation using topic steering vectors. To properly evaluate MTM topics against word list approaches, we propose \textit{topic judge}, an LLM-based pairwise comparison evaluation framework. Across eight datasets, MTMs match or exceed traditional and neural baselines on coherence metrics, are consistently preferred by topic judge, and enable effective LLM steering.
Carolina Zheng, Nicolas Beltran-Velez, Sweta Karlekar +5
Topic models summarize large text corpora, but top-ranked words often provide only a limited representation of topic semantics. Sparse autoencoders (SAEs) offer a way to move beyond word-level descriptors by extracting interpretable features from dense representations, yet how feature interpretability relates to topic-inference quality remains unclear. We introduce \textbf{MonoTM}, an interpretable topic modeling framework that decouples these roles. Across three benchmark corpora, we show that document--topic mixture estimation and semantic interpretation favor different SAE configurations and feature subsets. MonoTM estimates mixtures from the full SAE bag-of-features representation and, with them fixed, learns topic descriptors over a separate vocabulary of corpus-grounded semantic features. This design preserves global topic structure while representing topics with semantic units more meaningful than individual words, making them more useful for downstream corpus analysis.
Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling. Hypergraph generation remains challenging because incidence structures are discrete, sparse, and governed by heterogeneous higher-order interactions. Existing generators often rely on implicit latent spaces or continuous incidence decoders, which provide limited mechanistic interpretation of how node-hyperedge incidences arise. To address these limitations, we propose HYVINT, an intensity-driven hypergraph generative framework. Our key innovations are twofold: (i) we develop an intensity-driven incidence formation mechanism for hypergraphs that links latent interaction strength to binary incidence, and (ii) we derive a tractable lower-bound variational estimator for learning latent representations. We provide generation error bounds with asymptotic convergence rates and empirically show that HYVINT achieves strong fidelity while maintaining substantial novelty and diversity on synthetic and real-world hypergraphs.