# Conjugate Energy-Based Models

arXiv: https://arxiv.org/abs/2106.13798 · HTML: https://mlsanity.com/paper/2106.13798/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 61 references that are in the map.
- First posted on arXiv 25 Jun 2021.

## Builds on (most cited first, 29 of 29)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Sequential Attend, Infer, Repeat: Generative Modelling of Moving Objects](https://mlsanity.com/paper/1806.01794/) (2018)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Flow Contrastive Estimation of Energy-Based Models](https://mlsanity.com/paper/1912.00589/) (2019)
- [Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling](https://mlsanity.com/paper/2003.06060/) (2020)
- [Improving Generative Imagination in Object-Centric World Models](https://mlsanity.com/paper/2010.02054/) (2020)
- [No MCMC for me: Amortized sampling for fast and stable training of energy-based models](https://mlsanity.com/paper/2010.04230/) (2020)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Cooperative Training of Descriptor and Generator Networks](https://mlsanity.com/paper/1609.09408/) (2016)
- [Learning Energy-Based Model with Variational Auto-Encoder as Amortized Sampler](https://mlsanity.com/paper/2012.14936/) (2020)
- [Exploiting Spatial Invariance for Scalable Unsupervised Object Tracking](https://mlsanity.com/paper/1911.09033/) (2019)
- [Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Model](https://mlsanity.com/paper/1812.10907/) (2018)
- [Joint Training of Variational Auto-Encoder and Latent Energy-Based Model](https://mlsanity.com/paper/2006.06059/) (2020)
- [Hybrid Discriminative-Generative Training via Contrastive Learning](https://mlsanity.com/paper/2007.09070/) (2020)
- [Bi-level Score Matching for Learning Energy-based Latent Variable Models](https://mlsanity.com/paper/2010.07856/) (2020)
- [Amortized Population Gibbs Samplers with Neural Sufficient Statistics](https://mlsanity.com/paper/1911.01382/) (2019)

## Built on by (most cited first, 2 of 2)

- [Guiding Energy-based Models via Contrastive Latent Variables](https://mlsanity.com/paper/2303.03023/) (2023)
- [Morse Neural Networks for Uncertainty Quantification](https://mlsanity.com/paper/2307.00667/) (2023)

## Abstract (arXiv)

In this paper, we propose conjugate energy-based models (CEBMs), a new class of energy-based models that define a joint density over data and latent variables. The joint density of a CEBM decomposes into an intractable distribution over data and a tractable posterior over latent variables. CEBMs have similar use cases as variational autoencoders, in the sense that they learn an unsupervised mapping from data to latent variables. However, these models omit a generator network, which allows them to learn more flexible notions of similarity between data points. Our experiments demonstrate that conjugate EBMs achieve competitive results in terms of image modelling, predictive power of latent space, and out-of-domain detection on a variety of datasets.