# Elastic Interaction Energy-Based Generative Model: Approximation in Feature Space

arXiv: https://arxiv.org/abs/2303.10553 · HTML: https://mlsanity.com/paper/2303.10553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 19 Mar 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [Sobolev GAN](https://mlsanity.com/paper/1711.04894/) (2017)
- [Improving MMD-GAN Training with Repulsive Loss Function](https://mlsanity.com/paper/1812.09916/) (2018)
- [Auto-Encoding Variational Neural Machine Translation](https://mlsanity.com/paper/1807.10564/) (2018)
- [Boltzmann Encoded Adversarial Machines](https://mlsanity.com/paper/1804.08682/) (2018)

## Built on by (most cited first, 1 of 1)

- [Stability Analysis Framework for Particle-based Distance GANs with Wasserstein Gradient Flow](https://mlsanity.com/paper/2307.01879/) (2023)

## Abstract (arXiv)

In this paper, we propose a novel approach to generative modeling using a loss function based on elastic interaction energy (EIE), which is inspired by the elastic interaction between defects in crystals. The utilization of the EIE-based metric presents several advantages, including its long range property that enables consideration of global information in the distribution. Moreover, its inclusion of a self-interaction term helps to prevent mode collapse and captures all modes of distribution. To overcome the difficulty of the relatively scattered distribution of high-dimensional data, we first map the data into a latent feature space and approximate the feature distribution instead of the data distribution. We adopt the GAN framework and replace the discriminator with a feature transformation network to map the data into a latent space. We also add a stabilizing term to the loss of the feature transformation network, which effectively addresses the issue of unstable training in GAN-based algorithms. Experimental results on popular datasets, such as MNIST, FashionMNIST, CIFAR-10, and CelebA, demonstrate that our EIEG GAN model can mitigate mode collapse, enhance stability, and improve model performance.