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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

Delayed generalization, termed grokking, in a machine learning calculation occurs when the increase in test accuracy is delayed relative to the training accuracy. This paper examines grokking in the context of a dense neural network trained…

Disordered Systems and Neural Networks · Physics 2026-02-06 Karolina Hutchison , David Yevick

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous…

Machine Learning · Computer Science 2023-10-23 Neel Nanda , Lawrence Chan , Tom Lieberum , Jess Smith , Jacob Steinhardt

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

The phenomenon of grokking in over-parameterized neural networks has garnered significant interest. It involves the neural network initially memorizing the training set with zero training error and near-random test error. Subsequent…

Machine Learning · Computer Science 2024-12-17 Hu Qiye , Zhou Hao , Yu RuoXi

We demonstrate the existence of a complexity phase transition in neural networks by studying the grokking phenomenon, where networks suddenly transition from memorization to generalization long after overfitting their training data. To…

Machine Learning · Computer Science 2025-08-22 Branton DeMoss , Silvia Sapora , Jakob Foerster , Nick Hawes , Ingmar Posner

Grokking, a phenomenon where machine learning models generalize long after overfitting, has been primarily observed and studied in algorithmic tasks. This paper explores grokking in real-world datasets using deep neural networks for…

Machine Learning · Computer Science 2024-06-21 Satvik Golechha

Grokking is a intriguing phenomenon in machine learning where a neural network, after many training iterations with negligible improvement in generalization, suddenly achieves high accuracy on unseen data. By working in the quantum-inspired…

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'' is a phenomenon where a neural network first memorizes training data and generalizes poorly, but then suddenly transitions to near-perfect generalization after prolonged training. While intriguing, this delayed generalization…

Machine Learning · Computer Science 2025-04-21 Zhiwei Xu , Zhiyu Ni , Yixin Wang , Wei Hu

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a…

Machine Learning · Statistics 2024-02-06 Noam Levi , Alon Beck , Yohai Bar-Sinai

Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in…

Machine Learning · Computer Science 2025-02-05 Breno W. Carvalho , Artur S. d'Avila Garcez , Luís C. Lamb , Emílio Vital Brazil

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

The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the…

Machine Learning · Computer Science 2026-01-28 Keitaro Sakamoto , Issei Sato

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, referring to the abrupt improvement in test accuracy after extended overfitting, offers valuable insights into the mechanisms of model generalization. Existing researches based on progress measures imply that grokking relies on…

Machine Learning · Computer Science 2025-04-15 Zihan Gu , Ruoyu Chen , Hua Zhang , Yue Hu , Xiaochun Cao

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

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

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

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a…

Machine Learning · Statistics 2024-05-07 Noa Rubin , Inbar Seroussi , Zohar Ringel
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