{"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/constructions-in-combinatorics-via-neural","title":"Constructions in combinatorics via neural networks","arxiv_id":"2104.14516","date":"2021-04-29","proceeding":null,"authors":["Adam Zsolt Wagner"],"abstract":"We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy method, one can find explicit constructions and counterexamples to several open conjectures in extremal combinatorics and graph theory. Amongst the conjectures we refute are a question of Brualdi and Cao about maximizing permanents of pattern avoiding matrices, and several problems related to the adjacency and distance eigenvalues of graphs.","url_abs":"https://arxiv.org/abs/2104.14516v1","url_pdf":"https://arxiv.org/pdf/2104.14516v1.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":"constructions-in-combinatorics-via-neural","repo_url":"https://github.com/zawagner22/cross-entropy-for-combinatorics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"constructions-in-combinatorics-via-neural","repo_url":"https://github.com/dpaleka/cross-entropy-for-combinatorics","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"constructions-in-combinatorics-via-neural","repo_url":"https://github.com/ponyfat/graph-conjectures-counterexaples","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2104.14516","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}