{"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/alternating-local-enumeration-tnale-solving","title":"Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluations","arxiv_id":"2304.12875","date":"2023-04-25","proceeding":null,"authors":["Chao Li","Junhua Zeng","Chunmei Li","Cesar Caiafa","Qibin Zhao"],"abstract":"Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~\\cite{li2022permutation} showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, \\emph{greatly} reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is \\emph{reached} in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that $\\Omega(2^N)$ evaluations are typically required in TNLS for \\emph{reaching} the objective reduction in the neighborhood, while ideally $O(N^2R)$ evaluations are sufficient in TnALE, where $N$ denotes the tensor order and $R$ reflects the \\emph{``low-rankness''} of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.","url_abs":"https://arxiv.org/abs/2304.12875v3","url_pdf":"https://arxiv.org/pdf/2304.12875v3.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":"alternating-local-enumeration-tnale-solving","repo_url":"https://github.com/chaoliatriken/tnale","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.12875","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}