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Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the weights in late stages of learning. At the end of learning, we obtain back a single model by taking a spatial average in weight space. To avoid incurring increased computational costs, we investigate a family of low-dimensional late-phase weight models which interact multiplicatively with the remaining parameters. Our results show that augmenting standard models with late-phase weights improves generalization in established benchmarks such as CIFAR-10/100, ImageNet and enwik8. These findings are complemented with a theoretical analysis of a noisy quadratic problem which provides a simplified picture of the late phases of neural network learning.","url_abs":"https://arxiv.org/abs/2007.12927v4","url_pdf":"https://arxiv.org/pdf/2007.12927v4.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":"economical-ensembles-with-hypernetworks","repo_url":"https://github.com/google/uncertainty-baselines","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"economical-ensembles-with-hypernetworks","repo_url":"https://github.com/seijin-kobayashi/late-phase-weights","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"}],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-classification-on-cifar-10","task":"Image Classification","dataset":"CIFAR-10","model":"WRN 28-14","rank_in_archive_order":82,"of":265,"metrics":{"Percentage correct":"97.45"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-cifar-10","task":"Image Classification","dataset":"CIFAR-10","model":"WRN 28-10","rank_in_archive_order":98,"of":265,"metrics":{"Percentage correct":"96.81"},"uses_additional_data":false},{"leaderboard":"/sota/image-classification-on-cifar-100","task":"Image Classification","dataset":"CIFAR-100","model":"WRN 28-14","rank_in_archive_order":70,"of":211,"metrics":{"Percentage correct":"85.00"},"uses_additional_data":true},{"leaderboard":"/sota/image-classification-on-cifar-100","task":"Image Classification","dataset":"CIFAR-100","model":"WRN 28-10","rank_in_archive_order":92,"of":211,"metrics":{"Percentage correct":"83.06"},"uses_additional_data":true}],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2007.12927","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2007.12927"}},"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. 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