{"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/compressive-hyperspherical-energy","title":"Regularizing Neural Networks via Minimizing Hyperspherical Energy","arxiv_id":"1906.04892","date":"2019-06-12","proceeding":"CVPR 2020 6","authors":["Rongmei Lin","Weiyang Liu","Zhen Liu","Chen Feng","Zhiding Yu","James M. Rehg","Li Xiong","Le Song"],"abstract":"Inspired by the Thomson problem in physics where the distribution of multiple propelling electrons on a unit sphere can be modeled via minimizing some potential energy, hyperspherical energy minimization has demonstrated its potential in regularizing neural networks and improving their generalization power. In this paper, we first study the important role that hyperspherical energy plays in neural network training by analyzing its training dynamics. Then we show that naively minimizing hyperspherical energy suffers from some difficulties due to highly non-linear and non-convex optimization as the space dimensionality becomes higher, therefore limiting the potential to further improve the generalization. To address these problems, we propose the compressive minimum hyperspherical energy (CoMHE) as a more effective regularization for neural networks. Specifically, CoMHE utilizes projection mappings to reduce the dimensionality of neurons and minimizes their hyperspherical energy. According to different designs for the projection mapping, we propose several distinct yet well-performing variants and provide some theoretical guarantees to justify their effectiveness. Our experiments show that CoMHE consistently outperforms existing regularization methods, and can be easily applied to different neural networks.","url_abs":"https://arxiv.org/abs/1906.04892v2","url_pdf":"https://arxiv.org/pdf/1906.04892v2.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":"compressive-hyperspherical-energy","repo_url":"https://github.com/rmlin/CoMHE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1906.04892","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1906.04892"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/rmlin/CoMHE","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":3},"by_repo_kind":{"listed":{"samples":3,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"e2a9aaf74ba34fcd","entry":"load_test","repo":"rmlin/CoMHE","repo_kind":"listed","path":"adversarial_projection/cifar100_input_python.py","file_url":"https://github.com/rmlin/CoMHE/blob/HEAD/adversarial_projection/cifar100_input_python.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e2a9aaf74ba34fcd"}},{"code_sha256_prefix":"01a663a780ec75bf","entry":"load_train","repo":"rmlin/CoMHE","repo_kind":"listed","path":"adversarial_projection/cifar100_input_python.py","file_url":"https://github.com/rmlin/CoMHE/blob/HEAD/adversarial_projection/cifar100_input_python.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"01a663a780ec75bf"}},{"code_sha256_prefix":"7bb2163a72b8b7cc","entry":"loss2","repo":"rmlin/CoMHE","repo_kind":"listed","path":"adversarial_projection/loss.py","file_url":"https://github.com/rmlin/CoMHE/blob/HEAD/adversarial_projection/loss.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7bb2163a72b8b7cc"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}