{"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/comb-tensor-networks-vs-matrix-product-states","title":"Comb Tensor Networks vs. Matrix Product States: Enhanced Efficiency in High-Dimensional Spaces","arxiv_id":"2412.06857","date":"2024-12-08","proceeding":null,"authors":["Danylo Kolesnyk","Yelyzaveta Vodovozova"],"abstract":"Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product States (MPS) architectures. Here, we demonstrate that beyond a certain threshold in data and bond dimensions, a comb-shaped tensor network architecture can yield more efficient contractions than a standard MPS. This finding suggests that for continuous and high-dimensional data distributions, transitioning from MPS to a comb tensor network representation can substantially reduce computational overhead while maintaining accuracy.","url_abs":"https://arxiv.org/abs/2412.06857v1","url_pdf":"https://arxiv.org/pdf/2412.06857v1.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":"comb-tensor-networks-vs-matrix-product-states","repo_url":"https://github.com/DanyloKolesnyk/QuantumMLChronicles","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"tensor-networks","task_name":"Tensor Networks"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}