# Combating Mode Collapse in GANs via Manifold Entropy Estimation

arXiv: https://arxiv.org/abs/2208.12055 · HTML: https://mlsanity.com/paper/2208.12055/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Feedback Network for Image Super-Resolution](https://mlsanity.com/paper/1903.09814/) (2019)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Consistency Regularization for Generative Adversarial Networks](https://mlsanity.com/paper/1910.12027/) (2019)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [Generative Adversarial Networks (GANs Survey): Challenges, Solutions, and Future Directions](https://mlsanity.com/paper/2005.00065/) (2020)
- [No MCMC for me: Amortized sampling for fast and stable training of energy-based models](https://mlsanity.com/paper/2010.04230/) (2020)
- [Cooperative Training of Descriptor and Generator Networks](https://mlsanity.com/paper/1609.09408/) (2016)
- [Learning Descriptor Networks for 3D Shape Synthesis and Analysis](https://mlsanity.com/paper/1804.00586/) (2018)
- [Maximum Entropy Generators for Energy-Based Models](https://mlsanity.com/paper/1901.08508/) (2019)
- [AniGAN: Style-Guided Generative Adversarial Networks for Unsupervised Anime Face Generation](https://mlsanity.com/paper/2102.12593/) (2021)
- [Learning Energy-based Spatial-Temporal Generative ConvNets for Dynamic Patterns](https://mlsanity.com/paper/1909.11975/) (2019)

## Built on by (most cited first, 4 of 4)

- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Critic](https://mlsanity.com/paper/2405.00987/) (2024)
- [Dynamically Masked Discriminator for Generative Adversarial Networks](https://mlsanity.com/paper/2306.07716/) (2023)
- [Improving GAN Training via Feature Space Shrinkage](https://mlsanity.com/paper/2303.01559/) (2023)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEE