# Signature and Log-signature for the Study of Empirical Distributions Generated with GANs

arXiv: https://arxiv.org/abs/2203.03226 · HTML: https://mlsanity.com/paper/2203.03226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 65 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [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)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Video-to-Video Synthesis](https://mlsanity.com/paper/1808.06601/) (2018)
- [PIXOR: Real-time 3D Object Detection from Point Clouds](https://mlsanity.com/paper/1902.06326/) (2019)
- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)

## Abstract (arXiv)

In this paper, we bring forward the use of the recently developed Signature Transform as a way to measure the similarity between image distributions and provide detailed acquaintance and extensive evaluations. We are the first to pioneer RMSE and MAE Signature, along with log-signature as an alternative to measure GAN convergence, a problem that has been extensively studied. We are also forerunners to introduce analytical measures based on statistics to study the goodness of fit of the GAN sample distribution that are both efficient and effective. Current GAN measures involve lots of computation normally done at the GPU and are very time consuming. In contrast, we diminish the computation time to the order of seconds and computation is done at the CPU achieving the same level of goodness. Lastly, a PCA adaptive t-SNE approach, which is novel in this context, is also proposed for data visualization.