{"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/parametric-machines-a-fresh-approach-to","title":"Parametric machines: a fresh approach to architecture search","arxiv_id":"2007.02777","date":"2020-07-06","proceeding":null,"authors":["Pietro Vertechi","Mattia G. Bergomi"],"abstract":"Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and we discuss how to find optimal architectures and parameters -- within those spaces -- to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small.","url_abs":"https://arxiv.org/abs/2007.02777v3","url_pdf":"https://arxiv.org/pdf/2007.02777v3.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":"parametric-machines-a-fresh-approach-to","repo_url":"https://github.com/limenresearch/kernelmachines.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"parametric-machines-a-fresh-approach-to","repo_url":"https://gitlab.com/VEOS-research/hypergraph_machines","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2007.02777","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}