{"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/discontinuous-piecewise-polynomial-neural","title":"Discontinuous Piecewise Polynomial Neural Networks","arxiv_id":"1505.04211","date":"2015-05-15","proceeding":null,"authors":["John Loverich"],"abstract":"An artificial neural network is presented based on the idea of connections\nbetween units that are only active for a specific range of input values and\nzero outside that range (and so are not evaluated outside the active range).\nThe connection function is represented by a polynomial with compact support.\nThe finite range of activation allows for great activation sparsity in the\nnetwork and means that theoretically you are able to add computational power to\nthe network without increasing the computational time required to evaluate the\nnetwork for a given input. The polynomial order ranges from first to fifth\norder. Unit dropout is used for regularization and a parameter free weight\nupdate is used. Better performance is obtained by moving from piecewise linear\nconnections to piecewise quadratic, even better performance can be obtained by\nmoving to higher order polynomials. The algorithm is tested on the MAGIC Gamma\nray data set as well as the MNIST data set.","url_abs":"http://arxiv.org/abs/1505.04211v2","url_pdf":"http://arxiv.org/pdf/1505.04211v2.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":"discontinuous-piecewise-polynomial-neural","repo_url":"https://github.com/jloveric/high-order-layers-torch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"polynomial-neural-networks","task_name":"Polynomial Neural Networks"}],"methods":[{"method_slug":"dropout","method_name":"Dropout"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}