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Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we…

In some settings neural networks exhibit a phenomenon known as \textit{grokking}, where they achieve perfect or near-perfect accuracy on the validation set long after the same performance has been achieved on the training set. In this…

Machine Learning · Computer Science 2024-04-02 Jack Miller , Charles O'Neill , Thang Bui

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

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 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

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

Recent research on the grokking phenomenon has illuminated the intricacies of neural networks' training dynamics and their generalization behaviors. Grokking refers to a sharp rise of the network's generalization accuracy on the test set,…

Machine Learning · Computer Science 2024-05-31 Simin Fan , Razvan Pascanu , Martin Jaggi

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

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

This paper studies emergent phenomena in neural networks by focusing on grokking where models suddenly generalize after delayed memorization. To understand this phase transition, we utilize higher-order mutual information to analyze the…

Machine Learning · Computer Science 2024-08-20 Kenzo Clauw , Sebastiano Stramaglia , Daniele Marinazzo

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking…

Machine Learning · Computer Science 2023-09-06 Vikrant Varma , Rohin Shah , Zachary Kenton , János Kramár , Ramana Kumar

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

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 unusual phenomenon for algorithmic datasets where generalization happens long after overfitting the training data, has remained elusive. We aim to understand grokking by analyzing the loss landscapes of neural networks,…

Machine Learning · Computer Science 2023-03-24 Ziming Liu , Eric J. Michaud , Max Tegmark

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, the phenomenon of delayed generalization, is often attributed to the depth and compositional structure of deep neural networks. We study grokking in one of the simplest possible settings: the learning of a linear model with…

Machine Learning · Computer Science 2026-02-10 Nataraj Das , Atreya Vedantam , Chandrashekar Lakshminarayanan

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'' 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

Neural networks sometimes exhibit grokking, a phenomenon where perfect or near-perfect performance is achieved on a validation set well after the same performance has been obtained on the corresponding training set. In this workshop paper,…

Machine Learning · Computer Science 2024-02-15 Jack Miller , Patrick Gleeson , Charles O'Neill , Thang Bui , Noam Levi

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
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