Signature and Log-signature for the Study of Empirical Distributions Generated with GANs
This work addresses the need for faster and more efficient convergence measurement and goodness-of-fit evaluation in GANs, which is incremental as it builds on existing distribution similarity problems.
The paper tackles the problem of measuring similarity between image distributions generated by GANs, introducing Signature and log-signature transforms as efficient alternatives to existing methods, reducing computation time to seconds on a CPU while maintaining effectiveness.
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.