{"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/riemannian-approach-to-batch-normalization","title":"Riemannian approach to batch normalization","arxiv_id":"1709.09603","date":"2017-09-27","proceeding":"NeurIPS 2017 12","authors":["Minhyung Cho","Jaehyung Lee"],"abstract":"Batch Normalization (BN) has proven to be an effective algorithm for deep\nneural network training by normalizing the input to each neuron and reducing\nthe internal covariate shift. The space of weight vectors in the BN layer can\nbe naturally interpreted as a Riemannian manifold, which is invariant to linear\nscaling of weights. Following the intrinsic geometry of this manifold provides\na new learning rule that is more efficient and easier to analyze. We also\npropose intuitive and effective gradient clipping and regularization methods\nfor the proposed algorithm by utilizing the geometry of the manifold. The\nresulting algorithm consistently outperforms the original BN on various types\nof network architectures and datasets.","url_abs":"http://arxiv.org/abs/1709.09603v3","url_pdf":"http://arxiv.org/pdf/1709.09603v3.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":"riemannian-approach-to-batch-normalization","repo_url":"https://github.com/MinhyungCho/riemannian-batch-normalization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"gradient-clipping","method_name":"Gradient Clipping"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.09603","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1709.09603"}},"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/MinhyungCho/riemannian-batch-normalization","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_fixture":1,"unverified":14},"by_repo_kind":{"official":{"samples":15,"ran":1,"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":"fc52a4f8f0232e03","entry":"max_pool_2x2","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"vgg.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/vgg.py","link_basis":"harvester_set","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fc52a4f8f0232e03"}},{"code_sha256_prefix":"54506dae8da322c4","entry":"base_layer","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"layers.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/layers.py","link_basis":"first_harvest_node","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":"54506dae8da322c4"}},{"code_sha256_prefix":"e914acda806d78f7","entry":"convolution_layer","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"layers.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/layers.py","link_basis":"first_harvest_node","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":"e914acda806d78f7"}},{"code_sha256_prefix":"70fc2aa75cced4dd","entry":"full_connection_layer","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"layers.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/layers.py","link_basis":"first_harvest_node","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":"70fc2aa75cced4dd"}},{"code_sha256_prefix":"58f9e6060387bde3","entry":"horizontal_flip","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"preprocessing.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/preprocessing.py","link_basis":"first_harvest_node","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":"58f9e6060387bde3"}},{"code_sha256_prefix":"dc3d2192f81072ab","entry":"model","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"models.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/models.py","link_basis":"first_harvest_node","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":"dc3d2192f81072ab"}},{"code_sha256_prefix":"bd5bded8d7f19b2d","entry":"norm","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"gutils.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/gutils.py","link_basis":"first_harvest_node","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":"bd5bded8d7f19b2d"}},{"code_sha256_prefix":"fb298171b3f88688","entry":"pad_images","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"preprocessing.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/preprocessing.py","link_basis":"first_harvest_node","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":"fb298171b3f88688"}},{"code_sha256_prefix":"ddcdc91ea92220df","entry":"random_crop_and_flip","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"preprocessing.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/preprocessing.py","link_basis":"first_harvest_node","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":"ddcdc91ea92220df"}},{"code_sha256_prefix":"274446b4f9b3634d","entry":"read_images","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"svhn_input.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/svhn_input.py","link_basis":"first_harvest_node","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":"274446b4f9b3634d"}},{"code_sha256_prefix":"6ab99cf9752f685f","entry":"read_in_all_images","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"cifar100_input.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/cifar100_input.py","link_basis":"first_harvest_node","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":"6ab99cf9752f685f"}},{"code_sha256_prefix":"b0868a6a8461d6eb","entry":"read_in_all_images","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"cifar10_input.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/cifar10_input.py","link_basis":"first_harvest_node","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":"b0868a6a8461d6eb"}},{"code_sha256_prefix":"0b7624fd734a793f","entry":"reduce_shape","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"grassmann_optimizer.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/grassmann_optimizer.py","link_basis":"first_harvest_node","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":"0b7624fd734a793f"}},{"code_sha256_prefix":"ad3df8560af52b30","entry":"unit","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"gutils.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/gutils.py","link_basis":"first_harvest_node","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":"ad3df8560af52b30"}},{"code_sha256_prefix":"716e13312f5ab3a4","entry":"xTy","repo":"MinhyungCho/riemannian-batch-normalization","repo_kind":"official","path":"gutils.py","file_url":"https://github.com/MinhyungCho/riemannian-batch-normalization/blob/HEAD/gutils.py","link_basis":"first_harvest_node","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":"716e13312f5ab3a4"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}