{"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/spectral-gap-regularization-of-neural","title":"Spectral Gap Regularization of Neural Networks","arxiv_id":"2304.03096","date":"2023-04-06","proceeding":null,"authors":["Edric Tam","David Dunson"],"abstract":"We introduce Fiedler regularization, a novel approach for regularizing neural networks that utilizes spectral/graphical information. Existing regularization methods often focus on penalizing weights in a global/uniform manner that ignores the connectivity structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization. We provide theoretical motivation for this approach via spectral graph theory. We demonstrate several useful properties of the Fiedler value that make it useful as a regularization tool. We provide an approximate, variational approach for faster computation during training. We provide an alternative formulation of this framework in the form of a structurally weighted $\\text{L}_1$ penalty, thus linking our approach to sparsity induction. We provide uniform generalization error bounds for Fiedler regularization via a Rademacher complexity analysis. We performed experiments on datasets that compare Fiedler regularization with classical regularization methods such as dropout and weight decay. Results demonstrate the efficacy of Fiedler regularization. This is a journal extension of the conference paper by Tam and Dunson (2020).","url_abs":"https://arxiv.org/abs/2304.03096v1","url_pdf":"https://arxiv.org/pdf/2304.03096v1.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":[],"tasks":[],"methods":[{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"tam","method_name":"TAM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2304.03096","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2304.03096"}},"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":"deterministic:regex_extraction","url":"https://github.com/edrictam/FiedlerRegularization","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"found_in_text":{"samples":1,"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":1,"samples":[{"code_sha256_prefix":"a96ef395934e1285","entry":"NeuralNetFiedler","repo":"edrictam/FiedlerRegularization","repo_kind":"found_in_text","path":"models.py","file_url":"https://github.com/edrictam/FiedlerRegularization/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":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a96ef395934e1285"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}