# Sparsemax and Relaxed Wasserstein for Topic Sparsity

arXiv: https://arxiv.org/abs/1810.09079 · HTML: https://mlsanity.com/paper/1810.09079/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2018.

## Built on by (most cited first, 9 of 9)

- [Is Automated Topic Model Evaluation Broken?: The Incoherence of Coherence](https://mlsanity.com/paper/2107.02173/) (2021)
- [Topic Modelling Meets Deep Neural Networks: A Survey](https://mlsanity.com/paper/2103.00498/) (2021)
- [A Survey on Neural Topic Models: Methods, Applications, and Challenges](https://mlsanity.com/paper/2401.15351/) (2024)
- [Neural Attention-Aware Hierarchical Topic Model](https://mlsanity.com/paper/2110.07161/) (2021)
- [Sparse Autoencoders are Topic Models](https://mlsanity.com/paper/2511.16309/) (2025)
- [Optimal transport with some directed distances](https://mlsanity.com/paper/2105.05989/) (2021)
- [Reinforcement Learning for Topic Models](https://mlsanity.com/paper/2305.04843/) (2023)
- [Dynamic Topic Language Model on Heterogeneous Children's Mental Health Clinical Notes](https://mlsanity.com/paper/2312.14180/) (2023)
- [A Unifying Framework for Some Directed Distances in Statistics](https://mlsanity.com/paper/2203.00863/) (2022)

## Abstract (arXiv)

Topic sparsity refers to the observation that individual documents usually focus on several salient topics instead of covering a wide variety of topics, and a real topic adopts a narrow range of terms instead of a wide coverage of the vocabulary. Understanding this topic sparsity is especially important for analyzing user-generated web content and social media, which are featured in the form of extremely short posts and discussions. As topic sparsity of individual documents in online social media increases, so does the difficulty of analyzing the online text sources using traditional methods. In this paper, we propose two novel neural models by providing sparse posterior distributions over topics based on the Gaussian sparsemax construction, enabling efficient training by stochastic backpropagation. We construct an inference network conditioned on the input data and infer the variational distribution with the relaxed Wasserstein (RW) divergence. Unlike existing works based on Gaussian softmax construction and Kullback-Leibler (KL) divergence, our approaches can identify latent topic sparsity with training stability, predictive performance, and topic coherence. Experiments on different genres of large text corpora have demonstrated the effectiveness of our models as they outperform both probabilistic and neural methods.