# Theoretical Insights into the Use of Structural Similarity Index In Generative Models and Inferential Autoencoders

arXiv: https://arxiv.org/abs/2004.01864 · HTML: https://mlsanity.com/paper/2004.01864/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2020.

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

- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [GAS-NeXt: Few-Shot Cross-Lingual Font Generator](https://mlsanity.com/paper/2212.02886/) (2022)

## Abstract (arXiv)

Generative models and inferential autoencoders mostly make use of ℓ2 norm in their optimization objectives. In order to generate perceptually better images, this short paper theoretically discusses how to use Structural Similarity Index (SSIM) in generative models and inferential autoencoders. We first review SSIM, SSIM distance metrics, and SSIM kernel. We show that the SSIM kernel is a universal kernel and thus can be used in unconditional and conditional generated moment matching networks. Then, we explain how to use SSIM distance in variational and adversarial autoencoders and unconditional and conditional Generative Adversarial Networks (GANs). Finally, we propose to use SSIM distance rather than ℓ2 norm in least squares GAN.