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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

Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure…

Machine Learning · Computer Science 2023-03-22 William Merrill , Nikolaos Tsilivis , Aman Shukla

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

Grokking is the phenomenon where neural networks NNs initially fit the training data and later generalize to the test data during training. In this paper, we empirically provide a frequency perspective to explain the emergence of this…

Machine Learning · Computer Science 2024-05-29 Zhangchen Zhou , Yaoyu Zhang , Zhi-Qin John Xu

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To…

Machine Learning · Statistics 2024-04-12 Tanishq Kumar , Blake Bordelon , Samuel J. Gershman , Cengiz Pehlevan

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons…

Machine Learning · Computer Science 2025-05-20 Lucas Prieto , Melih Barsbey , Pedro A. M. Mediano , Tolga Birdal

Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example…

Grokking -- the delayed onset of generalization after early memorization -- is often described with phase-transition language, but that claim has lacked falsifiable finite-size inputs. Here we supply those inputs by treating the group order…

Machine Learning · Computer Science 2026-03-27 Yuda Bi , Chenyu Zhang , Qiheng Wang , Vince D Calhoun

Grokking has been actively explored to reveal the mystery of delayed generalization and identifying interpretable representations and algorithms inside the grokked models is a suggestive hint to understanding its mechanism. Grokking on…

Machine Learning · Computer Science 2024-12-31 Hiroki Furuta , Gouki Minegishi , Yusuke Iwasawa , Yutaka Matsuo

We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking…

Machine Learning · Computer Science 2024-05-28 Yeachan Park , Minseok Kim , Yeoneung Kim

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…

Machine Learning · Computer Science 2026-04-21 Joon Hyeok Kim , Yong-Hyun Park , Mattis Dalsætra Østby , Jiatao Gu

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

Adaptation and Self-Organizing Systems · Physics 2024-10-04 S. Barland , L. Gil

A principled understanding of generalization in deep learning may require unifying disparate observations under a single conceptual framework. Previous work has studied \emph{grokking}, a training dynamic in which a sustained period of…

Machine Learning · Computer Science 2023-03-14 Xander Davies , Lauro Langosco , David Krueger

Grokking - the delayed transition from memorisation to generalisation in neural networks - remains poorly understood. We study this phenomenon through the geometry of learned representations and identify a consistent empirical signature…

Machine Learning · Computer Science 2026-05-13 Truong Xuan Khanh , Truong Quynh Hoa , Luu Duc Trung , Phan Thanh Duc

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

Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular arithmetic. Whether this mechanism extends beyond arithmetic…

Machine Learning · Computer Science 2026-04-06 Yongzhong Xu

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance…

Machine Learning · Computer Science 2026-05-29 Chi-Ning Chou , Oscar Uzdelewicz , Neng-Chun Chiu , Yao-Yuan Yang , SueYeon Chung

Grokking, the abrupt transition from memorization to generalisation after extended training, suggests the presence of competing solution basins with distinct statistical properties. We study this phenomenon through the lens of Singular…

Machine Learning · Statistics 2026-05-08 Ben Cullen , Sergio Estan-Ruiz , Riya Danait , Jiayi Li

Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance. To examine the structure of when and where memorization occurs in a deep network, we use a recently developed…

Machine Learning · Computer Science 2021-06-01 Cory Stephenson , Suchismita Padhy , Abhinav Ganesh , Yue Hui , Hanlin Tang , SueYeon Chung

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