{"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/spectral-tensor-train-parameterization-of","title":"Spectral Tensor Train Parameterization of Deep Learning Layers","arxiv_id":"2103.04217","date":"2021-03-07","proceeding":null,"authors":["Anton Obukhov","Maxim Rakhuba","Alexander Liniger","Zhiwu Huang","Stamatios Georgoulis","Dengxin Dai","Luc van Gool"],"abstract":"We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings. Spectral properties are often subject to constraints in optimization problems, leading to better models and stability of optimization. We start by looking at the compact SVD parameterization of weight matrices and identifying redundancy sources in the parameterization. We further apply the Tensor Train (TT) decomposition to the compact SVD components, and propose a non-redundant differentiable parameterization of fixed TT-rank tensor manifolds, termed the Spectral Tensor Train Parameterization (STTP). We demonstrate the effects of neural network compression in the image classification setting and both compression and improved training stability in the generative adversarial training setting.","url_abs":"https://arxiv.org/abs/2103.04217v2","url_pdf":"https://arxiv.org/pdf/2103.04217v2.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":"spectral-tensor-train-parameterization-of","repo_url":"https://github.com/toshas/sttp","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"neural-network-compression","task_name":"Neural Network Compression"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[{"method_slug":"sttp","method_name":"STTP"},{"method_slug":"svd-parameterization","method_name":"SVD Parameterization"},{"method_slug":"spectral-normalization","method_name":"Spectral Normalization"}],"datasets_introduced":[],"methods_introduced":[{"slug":"sttp","name":"STTP","full_name":"Spectral Tensor Train Parameterization"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2103.04217","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}