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Related papers: Deep Networks Always Grok and Here is Why

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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

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

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

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

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

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work…

Machine Learning · Computer Science 2025-08-01 Thomas Walker , Ahmed Imtiaz Humayun , Randall Balestriero , Richard Baraniuk

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

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

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

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

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

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'' 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

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, 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 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

We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight…

Machine Learning · Computer Science 2026-02-09 Mingyue Xu , Gal Vardi , Itay Safran

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

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
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