{"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/optimal-lottery-tickets-via-subset-sum","title":"Optimal Lottery Tickets via Subset Sum: Logarithmic Over-Parameterization is Sufficient","arxiv_id":null,"date":"2020-12-01","proceeding":"NeurIPS 2020 12","authors":["Ankit Pensia","Shashank Rajput","Alliot Nagle","Harit Vishwakarma","Dimitris Papailiopoulos"],"abstract":"The strong lottery ticket hypothesis (LTH) postulates that one can approximate any target neural network by only pruning the weights of a sufficiently over-parameterized random network.  A recent work by Malach et al. [MYSS20] establishes the first theoretical analysis for the strong LTH: one can provably approximate a neural network of width $d$ and depth $l$, by pruning a random one that is a factor $O(d^4 l^2)$ wider and twice as deep. This polynomial over-parameterization requirement is at odds with recent experimental research that achieves good approximation with networks that are a small factor wider than the target. In this work, we close the gap and offer an exponential improvement to the over-parameterization requirement for the existence of lottery tickets. We show that any target network of width $d$ and depth $l$ can be approximated by pruning a random network that is a factor $O(log(dl))$ wider and twice as deep.  Our analysis heavily relies on connecting pruning random ReLU networks to random instances of the Subset Sum problem. We then show that this logarithmic over-parameterization is essentially optimal for constant depth networks. Finally, we verify several of our theoretical insights with experiments.\n\n","url_abs":"http://proceedings.neurips.cc/paper/2020/hash/1b742ae215adf18b75449c6e272fd92d-Abstract.html","url_pdf":"http://proceedings.neurips.cc/paper/2020/file/1b742ae215adf18b75449c6e272fd92d-Paper.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":"optimal-lottery-tickets-via-subset-sum","repo_url":"https://github.com/acnagle/optimal-lottery-tickets","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[{"method_slug":"pruning","method_name":"Pruning"},{"method_slug":"relu","method_name":"ReLU"}],"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}