Papers › Signature and Log-signature for the Study of Empirical Distributions Generated with GANs
Signature and Log-signature for the Study of Empirical Distributions Generated with GANs
Joaquim de Curtò, Irene de Zarzà, Hong Yan, Carlos T. Calafate
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
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Tasks
2 archive task tags without a task page not shown.
Datasets
Introduced by this paper, per the archive.
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Generation | AFHQ Cat | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature | 45968 | #8 of 8 | Archive leaderboard | report |
| Image Generation | AFHQ Cat | Stylegan2-ada (NVIDIA pre-trained) | MAE log-signature | 22297 | #8 of 8 | Archive leaderboard | report |
| Image Generation | AFHQ Cat | Stylegan2-ada (NVIDIA pre-trained) | RMSE Signature | 61450 | #8 of 8 | Archive leaderboard | report |
| Image Generation | AFHQ Cat | Stylegan2-ada (NVIDIA pre-trained) | RMSE log-signature | 29201 | #8 of 8 | Archive leaderboard | report |
| Image Generation | AFHQ Dog | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature | 30441 | #6 of 6 | Archive leaderboard | report |
| Image Generation | AFHQ Dog | Stylegan2-ada (NVIDIA pre-trained) | MAE log-signature | 24612 | #6 of 6 | Archive leaderboard | report |
| Image Generation | AFHQ Dog | Stylegan2-ada (NVIDIA pre-trained) | RMSE Signature | 38861 | #6 of 6 | Archive leaderboard | report |
| Image Generation | AFHQ Dog | Stylegan2-ada (NVIDIA pre-trained) | RMSE log-signature | 31686 | #6 of 6 | Archive leaderboard | report |
| Image Generation | AFHQ Wild | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature | 25578 | #5 of 5 | Archive leaderboard | report |
| Image Generation | AFHQ Wild | Stylegan2-ada (NVIDIA pre-trained) | MAE log-signature | 20359 | #5 of 5 | Archive leaderboard | report |
| Image Generation | AFHQ Wild | Stylegan2-ada (NVIDIA pre-trained) | RMSE Signature | 33306 | #5 of 5 | Archive leaderboard | report |
| Image Generation | AFHQ Wild | Stylegan2-ada (NVIDIA pre-trained) | RMSE log-signature | 26622 | #5 of 5 | Archive leaderboard | report |
| Image Generation | MetFaces | t-Stylegan3-ada (NVIDIA pre-trained) | MAE Signature | 19872 | #1 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | t-Stylegan3-ada (NVIDIA pre-trained) | MAE log-signature | 13761 | #1 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | t-Stylegan3-ada (NVIDIA pre-trained) | RMSE Signature | 30894 | #1 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | t-Stylegan3-ada (NVIDIA pre-trained) | RMSE log-signature | 21560 | #1 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | r-Stylegan3-ada (NVIDIA pre-trained) | MAE Signature | 22799 | #2 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | r-Stylegan3-ada (NVIDIA pre-trained) | MAE log-signature | 16539 | #2 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | r-Stylegan3-ada (NVIDIA pre-trained) | RMSE Signature | 34977 | #2 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | r-Stylegan3-ada (NVIDIA pre-trained) | RMSE log-signature | 24707 | #2 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | Stylegan2-ada (NVIDIA pre-trained) | MAE Signature | 23428 | #3 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | Stylegan2-ada (NVIDIA pre-trained) | MAE log-signature | 18071 | #3 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | Stylegan2-ada (NVIDIA pre-trained) | RMSE Signature | 33247 | #3 of 3 | Archive leaderboard | report |
| Image Generation | MetFaces | Stylegan2-ada (NVIDIA pre-trained) | RMSE log-signature | 25685 | #3 of 3 | Archive leaderboard | report |
| Image Generation | NASA Perseverance | Stylegan2-ada | MAE Signature | 9086 | #1 of 1 | Archive leaderboard | report |
| Image Generation | NASA Perseverance | Stylegan2-ada | MAE log-signature | 5717 | #1 of 1 | Archive leaderboard | report |
| Image Generation | NASA Perseverance | Stylegan2-ada | RMSE Signature | 11601 | #1 of 1 | Archive leaderboard | report |
| Image Generation | NASA Perseverance | Stylegan2-ada | RMSE log-signature | 7397 | #1 of 1 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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