{"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/mean-field-theory-for-deep-dropout-networks","title":"Mean field theory for deep dropout networks: digging up gradient backpropagation deeply","arxiv_id":"1912.09132","date":"2019-12-19","proceeding":null,"authors":["Wei Huang","Richard Yi Da Xu","Weitao Du","Yutian Zeng","Yunce Zhao"],"abstract":"In recent years, the mean field theory has been applied to the study of neural networks and has achieved a great deal of success. The theory has been applied to various neural network structures, including CNNs, RNNs, Residual networks, and Batch normalization. Inevitably, recent work has also covered the use of dropout. The mean field theory shows that the existence of depth scales that limit the maximum depth of signal propagation and gradient backpropagation. However, the gradient backpropagation is derived under the gradient independence assumption that weights used during feed forward are drawn independently from the ones used in backpropagation. This is not how neural networks are trained in a real setting. Instead, the same weights used in a feed-forward step needs to be carried over to its corresponding backpropagation. Using this realistic condition, we perform theoretical computation on linear dropout networks and a series of experiments on dropout networks. Our empirical results show an interesting phenomenon that the length gradients can backpropagate for a single input and a pair of inputs are governed by the same depth scale. Besides, we study the relationship between variance and mean of statistical metrics of the gradient and shown an emergence of universality. Finally, we investigate the maximum trainable length for deep dropout networks through a series of experiments using MNIST and CIFAR10 and provide a more precise empirical formula that describes the trainable length than original work.","url_abs":"https://arxiv.org/abs/1912.09132v3","url_pdf":"https://arxiv.org/pdf/1912.09132v3.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":"mean-field-theory-for-deep-dropout-networks","repo_url":"https://github.com/WeiHuang05/Mean-field-theory-for-deep-dropout-networks","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[{"method_slug":"dropout","method_name":"Dropout"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1912.09132","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1912.09132"}},"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/WeiHuang05/Mean-field-theory-for-deep-dropout-networks","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"listed":{"samples":1,"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":1,"samples":[{"code_sha256_prefix":"2597cb5ead43e1d8","entry":"randomize_weight","repo":"WeiHuang05/Mean-field-theory-for-deep-dropout-networks","repo_kind":"listed","path":"network/net.py","file_url":"https://github.com/WeiHuang05/Mean-field-theory-for-deep-dropout-networks/blob/HEAD/network/net.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"2597cb5ead43e1d8"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}