{"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/deconstructing-the-goldilocks-zone-of-neural","title":"Deconstructing the Goldilocks Zone of Neural Network Initialization","arxiv_id":"2402.03579","date":"2024-02-05","proceeding":null,"authors":["Artem Vysogorets","Anna Dawid","Julia Kempe"],"abstract":"The second-order properties of the training loss have a massive impact on the optimization dynamics of deep learning models. Fort & Scherlis (2019) discovered that a large excess of positive curvature and local convexity of the loss Hessian is associated with highly trainable initial points located in a region coined the \"Goldilocks zone\". Only a handful of subsequent studies touched upon this relationship, so it remains largely unexplained. In this paper, we present a rigorous and comprehensive analysis of the Goldilocks zone for homogeneous neural networks. In particular, we derive the fundamental condition resulting in excess of positive curvature of the loss, explaining and refining its conventionally accepted connection to the initialization norm. Further, we relate the excess of positive curvature to model confidence, low initial loss, and a previously unknown type of vanishing cross-entropy loss gradient. To understand the importance of excessive positive curvature for trainability of deep networks, we optimize fully-connected and convolutional architectures outside the Goldilocks zone and analyze the emergent behaviors. We find that strong model performance is not perfectly aligned with the Goldilocks zone, calling for further research into this relationship.","url_abs":"https://arxiv.org/abs/2402.03579v2","url_pdf":"https://arxiv.org/pdf/2402.03579v2.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":"deconstructing-the-goldilocks-zone-of-neural","repo_url":"https://github.com/avysogorets/goldilocks-zone","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2402.03579","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.03579"}},"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/avysogorets/goldilocks-zone","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":6,"unverified":1},"by_repo_kind":{"official":{"samples":7,"ran":6,"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":"df3b40ccd6bffb42","entry":"cos_vec_vec","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"linalg.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/linalg.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"df3b40ccd6bffb42"}},{"code_sha256_prefix":"9bdf27d1a2e41c3a","entry":"get_fileid","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"trainability.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/trainability.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9bdf27d1a2e41c3a"}},{"code_sha256_prefix":"378e0b433d171101","entry":"get_prior","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"misc.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/misc.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"378e0b433d171101"}},{"code_sha256_prefix":"7480feec9903d9ca","entry":"get_random_ortho_matrix","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"linalg.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/linalg.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7480feec9903d9ca"}},{"code_sha256_prefix":"b00e10d874879a60","entry":"random_prior","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"misc.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/misc.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b00e10d874879a60"}},{"code_sha256_prefix":"e2ac4e81ffca1cea","entry":"sparse_vector","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"linalg.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/linalg.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e2ac4e81ffca1cea"}},{"code_sha256_prefix":"9eff295d9a4ac8eb","entry":"WCA","repo":"avysogorets/goldilocks-zone","repo_kind":"official","path":"misc.py","file_url":"https://github.com/avysogorets/goldilocks-zone/blob/HEAD/misc.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":"9eff295d9a4ac8eb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}