{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/signature-and-log-signature-for-the-study-of","title":"Signature and Log-signature for the Study of Empirical Distributions Generated with GANs","arxiv_id":"2203.03226","date":"2022-03-07","proceeding":null,"authors":["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.","url_abs":"https://arxiv.org/abs/2203.03226v3","url_pdf":"https://arxiv.org/pdf/2203.03226v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"signature-and-log-signature-for-the-study-of","repo_url":"https://github.com/decurtoydiaz/signatures","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"CPU"},{"task_slug":"data-visualization","task_name":"Data Visualization"},{"task_slug":null,"task_name":"GPU"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"instance-segmentation","task_name":"Instance Segmentation"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"aspp","method_name":"ASPP"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"deeplabv3","method_name":"DeepLabv3"},{"method_slug":"dilated-convolution","method_name":"Dilated Convolution"},{"method_slug":"mae","method_name":"MAE"},{"method_slug":"pca","method_name":"PCA"},{"method_slug":"spatial-pyramid-pooling","method_name":"Spatial Pyramid Pooling"}],"datasets_introduced":[{"slug":"nasa-perseverance","name":"NASA Perseverance","full_name":""}],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-afhq-cat","task":"Image Generation","dataset":"AFHQ Cat","model":"Stylegan2-ada (NVIDIA pre-trained)","rank_in_archive_order":8,"of":8,"metrics":{"MAE Signature":"45968","MAE log-signature":"22297","RMSE Signature":"61450","RMSE log-signature":"29201"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-afhq-dog","task":"Image Generation","dataset":"AFHQ Dog","model":"Stylegan2-ada (NVIDIA pre-trained)","rank_in_archive_order":6,"of":6,"metrics":{"MAE Signature":"30441","MAE log-signature":"24612","RMSE Signature":"38861","RMSE log-signature":"31686"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-afhq-wild","task":"Image Generation","dataset":"AFHQ Wild","model":"Stylegan2-ada (NVIDIA pre-trained)","rank_in_archive_order":5,"of":5,"metrics":{"MAE Signature":"25578","MAE log-signature":"20359","RMSE Signature":"33306","RMSE log-signature":"26622"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-metfaces","task":"Image Generation","dataset":"MetFaces","model":"t-Stylegan3-ada (NVIDIA pre-trained)","rank_in_archive_order":1,"of":3,"metrics":{"MAE Signature":"19872","MAE log-signature":"13761","RMSE Signature":"30894","RMSE log-signature":"21560"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-metfaces","task":"Image Generation","dataset":"MetFaces","model":"r-Stylegan3-ada (NVIDIA pre-trained)","rank_in_archive_order":2,"of":3,"metrics":{"MAE Signature":"22799","MAE log-signature":"16539","RMSE Signature":"34977","RMSE log-signature":"24707"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-metfaces","task":"Image Generation","dataset":"MetFaces","model":"Stylegan2-ada (NVIDIA pre-trained)","rank_in_archive_order":3,"of":3,"metrics":{"MAE Signature":"23428","MAE log-signature":"18071","RMSE Signature":"33247","RMSE log-signature":"25685"},"uses_additional_data":false},{"leaderboard":"/sota/image-generation-on-nasa-perseverance","task":"Image Generation","dataset":"NASA Perseverance","model":"Stylegan2-ada","rank_in_archive_order":1,"of":1,"metrics":{"MAE Signature":"9086","MAE log-signature":"5717","RMSE Signature":"11601","RMSE log-signature":"7397"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}