# Learning Discrete Structured Representations by Adversarially Maximizing Mutual Information

arXiv: https://arxiv.org/abs/2004.03991 · HTML: https://mlsanity.com/paper/2004.03991/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Hidden Schema Networks](https://mlsanity.com/paper/2207.03777/) (2022)
- [MICO: Selective Search with Mutual Information Co-training](https://mlsanity.com/paper/2209.04378/) (2022)
- [Multi-View Clustering from the Perspective of Mutual Information](https://mlsanity.com/paper/2302.08743/) (2023)
- [UpSkill: Mutual Information Skill Learning for Structured Response Diversity in LLMs](https://mlsanity.com/paper/2602.22296/) (2026)
- [Integrating Semantics and Neighborhood Information with Graph-Driven Generative Models for Document Retrieval](https://mlsanity.com/paper/2105.13066/) (2021)

## Abstract (arXiv)

We propose learning discrete structured representations from unlabeled data by maximizing the mutual information between a structured latent variable and a target variable. Calculating mutual information is intractable in this setting. Our key technical contribution is an adversarial objective that can be used to tractably estimate mutual information assuming only the feasibility of cross entropy calculation. We develop a concrete realization of this general formulation with Markov distributions over binary encodings. We report critical and unexpected findings on practical aspects of the objective such as the choice of variational priors. We apply our model on document hashing and show that it outperforms current best baselines based on discrete and vector quantized variational autoencoders. It also yields highly compressed interpretable representations.