{"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/memorization-dilation-modeling-neural","title":"Memorization-Dilation: Modeling Neural Collapse Under Label Noise","arxiv_id":"2206.05530","date":"2022-06-11","proceeding":null,"authors":["Duc Anh Nguyen","Ron Levie","Julian Lienen","Gitta Kutyniok","Eyke Hüllermeier"],"abstract":"The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of all examples of the same class tend to collapse to a single representation, and the features of different classes tend to separate as much as possible. Neural collapse is often studied through a simplified model, called the unconstrained feature representation, in which the model is assumed to have \"infinite expressivity\" and can map each data point to any arbitrary representation. In this work, we propose a more realistic variant of the unconstrained feature representation that takes the limited expressivity of the network into account. Empirical evidence suggests that the memorization of noisy data points leads to a degradation (dilation) of the neural collapse. Using a model of the memorization-dilation (M-D) phenomenon, we show one mechanism by which different losses lead to different performances of the trained network on noisy data. Our proofs reveal why label smoothing, a modification of cross-entropy empirically observed to produce a regularization effect, leads to improved generalization in classification tasks.","url_abs":"https://arxiv.org/abs/2206.05530v3","url_pdf":"https://arxiv.org/pdf/2206.05530v3.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":"memorization-dilation-modeling-neural","repo_url":"https://github.com/julilien/memorizationdilation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"memorization","task_name":"Memorization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.05530","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.05530"}},"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/julilien/memorizationdilation","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"official":{"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":0,"samples":[{"code_sha256_prefix":"ca5f233eb44392be","entry":"assess_loss","repo":"julilien/memorizationdilation","repo_kind":"official","path":"train_simple_model.py","file_url":"https://github.com/julilien/memorizationdilation/blob/HEAD/train_simple_model.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"ca5f233eb44392be"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}