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Signature and Log-signature for the Study of Empirical Distributions Generated with GANs
Joaquim de Curtò Irene de Zarzà Hong Yan Carlos T. Calafate
Abstract
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.
Code Repositories
Benchmarks
| Benchmark | Methodology | Metrics |
|---|---|---|
| image-generation-on-afhq-cat | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature: 45968 MAE log-signature: 22297 RMSE Signature: 61450 RMSE log-signature: 29201 |
| image-generation-on-afhq-dog | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature: 30441 MAE log-signature: 24612 RMSE Signature: 38861 RMSE log-signature: 31686 |
| image-generation-on-afhq-wild | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature: 25578 MAE log-signature: 20359 RMSE Signature: 33306 RMSE log-signature: 26622 |
| image-generation-on-metfaces | t-Stylegan3-ada (NVIDIA pre-trained) | MAE Signature: 19872 MAE log-signature: 13761 RMSE Signature: 30894 RMSE log-signature: 21560 |
| image-generation-on-metfaces | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature: 23428 MAE log-signature: 18071 RMSE Signature: 33247 RMSE log-signature: 25685 |
| image-generation-on-metfaces | r-Stylegan3-ada (NVIDIA pre-trained) | MAE Signature: 22799 MAE log-signature: 16539 RMSE Signature: 34977 RMSE log-signature: 24707 |
| image-generation-on-nasa-perseverance | Stylegan2-ada | MAE Signature: 9086 MAE log-signature: 5717 RMSE Signature: 11601 RMSE log-signature: 7397 |
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