{"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/divide-and-conquer-networks","title":"Divide and Conquer Networks","arxiv_id":"1611.02401","date":"2016-11-08","proceeding":"ICLR 2018 1","authors":["Alex Nowak-Vila","David Folqué","Joan Bruna"],"abstract":"We consider the learning of algorithmic tasks by mere observation of\ninput-output pairs. Rather than studying this as a black-box discrete\nregression problem with no assumption whatsoever on the input-output mapping,\nwe concentrate on tasks that are amenable to the principle of divide and\nconquer, and study what are its implications in terms of learning. This\nprinciple creates a powerful inductive bias that we leverage with neural\narchitectures that are defined recursively and dynamically, by learning two\nscale-invariant atomic operations: how to split a given input into smaller\nsets, and how to merge two partially solved tasks into a larger partial\nsolution. Our model can be trained in weakly supervised environments, namely by\njust observing input-output pairs, and in even weaker environments, using a\nnon-differentiable reward signal. Moreover, thanks to the dynamic aspect of our\narchitecture, we can incorporate the computational complexity as a\nregularization term that can be optimized by backpropagation. We demonstrate\nthe flexibility and efficiency of the Divide-and-Conquer Network on several\ncombinatorial and geometric tasks: convex hull, clustering, knapsack and\neuclidean TSP. Thanks to the dynamic programming nature of our model, we show\nsignificant improvements in terms of generalization error and computational\ncomplexity.","url_abs":"http://arxiv.org/abs/1611.02401v7","url_pdf":"http://arxiv.org/pdf/1611.02401v7.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":"divide-and-conquer-networks","repo_url":"https://github.com/alexnowakvila/DiCoNet","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"inductive-bias","task_name":"Inductive Bias"}],"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}