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Neural network grokking -- the abrupt memorization-to-generalization transition -- challenges our understanding of learning dynamics. Through finite-size scaling of gradient avalanche dynamics across eight model scales, we find that…

Machine Learning · Computer Science 2026-04-07 Ping Wang

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine…

Machine Learning · Computer Science 2024-06-06 Jaerin Lee , Bong Gyun Kang , Kihoon Kim , Kyoung Mu Lee

We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and…

Statistical Mechanics · Physics 2022-10-28 Bojan Žunkovič , Enej Ilievski

This paper investigates the grokking phenomenon, which refers to the sudden transition from a long memorization to generalization observed during neural networks training, in the context of learning multiplication in finite-dimensional…

Machine Learning · Computer Science 2026-05-15 Pascal Jr Tikeng Notsawo , Guillaume Dumas , Guillaume Rabusseau

Grokking, a delayed generalization in neural networks after perfect training performance, has been observed in Transformers and MLPs, but the components driving it remain underexplored. We show that embeddings are central to grokking:…

Machine Learning · Computer Science 2025-05-22 H. V. AlquBoj , Hilal AlQuabeh , Velibor Bojkovic , Munachiso Nwadike , Kentaro Inui

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled…

Machine Learning · Computer Science 2024-06-10 Ahmed Imtiaz Humayun , Randall Balestriero , Richard Baraniuk

Grokking refers to delayed generalization in which the increase in test accuracy of a neural network occurs appreciably after the improvement in training accuracy This paper introduces several practical metrics including variance under…

Machine Learning · Computer Science 2025-07-17 Ahmed Salah , David Yevick

We investigate the phenomenon of grokking -- delayed generalization accompanied by non-monotonic test loss behavior -- in a simple binary logistic classification task, for which "memorizing" and "generalizing" solutions can be strictly…

Machine Learning · Statistics 2025-07-22 Alon Beck , Noam Levi , Yohai Bar-Sinai

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the…

Machine Learning · Computer Science 2022-06-14 Vimal Thilak , Etai Littwin , Shuangfei Zhai , Omid Saremi , Roni Paiss , Joshua Susskind

Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data. Previous research has linked this delayed generalization to…

Machine Learning · Computer Science 2026-01-12 Tiberiu Musat

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great…

Machine Learning · Computer Science 2022-01-07 Alethea Power , Yuri Burda , Harri Edwards , Igor Babuschkin , Vedant Misra

Grokking is an intriguing phenomenon of delayed generalization, where neural networks initially memorize training data with perfect accuracy but exhibit poor generalization, subsequently transitioning to a generalizing solution with…

Machine Learning · Computer Science 2025-05-12 Gouki Minegishi , Yusuke Iwasawa , Yutaka Matsuo

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after…

Machine Learning · Computer Science 2024-04-03 Kaifeng Lyu , Jikai Jin , Zhiyuan Li , Simon S. Du , Jason D. Lee , Wei Hu

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel…

Machine Learning · Computer Science 2024-07-18 Mohamad Amin Mohamadi , Zhiyuan Li , Lei Wu , Danica J. Sutherland

This paper focuses on predicting the occurrence of grokking in neural networks, a phenomenon in which perfect generalization emerges long after signs of overfitting or memorization are observed. It has been reported that grokking can only…

Machine Learning · Computer Science 2023-10-02 Pascal Jr. Tikeng Notsawo , Hattie Zhou , Mohammad Pezeshki , Irina Rish , Guillaume Dumas

Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or…

Machine Learning · Computer Science 2025-07-14 Pascal Jr Tikeng Notsawo , Guillaume Dumas , Guillaume Rabusseau

Grokking is proposed and widely studied as an intricate phenomenon in which generalization is achieved after a long-lasting period of overfitting. In this work, we propose NeuralGrok, a novel gradient-based approach that learns an optimal…

Machine Learning · Computer Science 2025-04-28 Xinyu Zhou , Simin Fan , Martin Jaggi , Jie Fu

Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level,…

Machine Learning · Computer Science 2026-01-06 Xiaotian Zhang , Yue Shang , Entao Yang , Ge Zhang

Grokking-the phenomenon where validation accuracy of neural networks on modular addition of two integers rises long after training data has been memorized-has been characterized in previous works as producing sinusoidal input weight…

Machine Learning · Computer Science 2026-03-26 Anand Swaroop

Recently, an interesting phenomenon called grokking has gained much attention, where generalization occurs long after the models have initially overfitted the training data. We try to understand this seemingly strange phenomenon through the…

Machine Learning · Computer Science 2024-02-05 Zhiquan Tan , Weiran Huang