{"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/product-of-tensors-and-description-of","title":"Product of Tensors and Description of Networks","arxiv_id":"2402.06768","date":"2024-02-09","proceeding":null,"authors":["Luca Chiantini","Giuseppe Alessio D'Inverno","Sara Marziali"],"abstract":"Any kind of network can be naturally represented by a Directed Acyclic Graph (DAG); additionally, activation functions can determine the reaction of each node of the network with respect to the signal(s) incoming. We study the characterization of the signal distribution in a network under the lens of tensor algebra. More specifically, we describe every activation function as tensor distributions with respect to the nodes, called \\textit{activation tensors}. The distribution of the signal is encoded in the \\textit{total tensor} of the network. We formally prove that the total tensor can be obtained by computing the \\textit{Batthacharya-Mesner Product} (BMP), an $n$-ary operation for tensors of order $n$, on the set of the activation tensors properly ordered and processed via two basic operations, that we call \\textit{blow} and \\textit{forget}. Our theoretical framework can be validated through the related code developed in Python.","url_abs":"https://arxiv.org/abs/2402.06768v2","url_pdf":"https://arxiv.org/pdf/2402.06768v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"product-of-tensors-and-description-of","repo_url":"https://github.com/marzialis/bmp-network","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}