https://arxiv.org/abs/2410.04489 Skip to main content Cornell University We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate arxiv logo > stat > arXiv:2410.04489 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Statistics > Machine Learning arXiv:2410.04489 (stat) [Submitted on 6 Oct 2024] Title:Grokking at the Edge of Linear Separability Authors:Alon Beck, Noam Levi, Yohai Bar-Sinai View a PDF of the paper titled Grokking at the Edge of Linear Separability, by Alon Beck and 2 other authors View PDF HTML (experimental) Abstract:We study the generalization properties of binary logistic classification in a simplified setting, for which a "memorizing" and "generalizing" solution can always be strictly defined, and elucidate empirically and analytically the mechanism underlying Grokking in its dynamics. We analyze the asymptotic long-time dynamics of logistic classification on a random feature model with a constant label and show that it exhibits Grokking, in the sense of delayed generalization and non-monotonic test loss. We find that Grokking is amplified when classification is applied to training sets which are on the verge of linear separability. Even though a perfect generalizing solution always exists, we prove the implicit bias of the logisitc loss will cause the model to overfit if the training data is linearly separable from the origin. For training sets that are not separable from the origin, the model will always generalize perfectly asymptotically, but overfitting may occur at early stages of training. Importantly, in the vicinity of the transition, that is, for training sets that are almost separable from the origin, the model may overfit for arbitrarily long times before generalizing. We gain more insights by examining a tractable one-dimensional toy model that quantitatively captures the key features of the full model. Finally, we highlight intriguing common properties of our findings with recent literature, suggesting that grokking generally occurs in proximity to the interpolation threshold, reminiscent of critical phenomena often observed in physical systems. Comments: 24 pages, 13 figures Machine Learning (stat.ML); Disordered Systems and Neural Subjects: Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Mathematical Physics (math-ph) Cite as: arXiv:2410.04489 [stat.ML] (or arXiv:2410.04489v1 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2410.04489 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alon Beck [view email] [v1] Sun, 6 Oct 2024 14:08:42 UTC (805 KB) Full-text links: Access Paper: View a PDF of the paper titled Grokking at the Edge of Linear Separability, by Alon Beck and 2 other authors * View PDF * HTML (experimental) * TeX Source * Other Formats view license Current browse context: stat.ML < prev | next > new | recent | 2024-10 Change to browse by: cond-mat cond-mat.dis-nn cs cs.LG math math-ph math.MP stat References & Citations * NASA ADS * Google Scholar * Semantic Scholar a export BibTeX citation Loading... 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