  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.
