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

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.