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Related papers: Measuring Sharpness in Grokking

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Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

Machine Learning · Statistics 2022-05-26 Vincent Szolnoky , Viktor Andersson , Balazs Kulcsar , Rebecka Jörnsten

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

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

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

\emph{Memorization} in neural networks lacks a precise operational definition and is often inferred from the grokking regime, where training accuracy saturates while test accuracy remains very low. We identify a previously unreported third…

Machine Learning · Computer Science 2026-02-04 Hari K Prakash , Charles H Martin

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

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

We examine the pre-training dynamics of language models, focusing on their ability to copy text from preceding context--a fundamental skill for various LLM applications, including in-context learning (ICL) and retrieval-augmented generation…

Computation and Language · Computer Science 2025-02-07 Ang Lv , Ruobing Xie , Xingwu Sun , Zhanhui Kang , Rui Yan

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing…

Machine Learning · Computer Science 2022-10-17 Ziming Liu , Ouail Kitouni , Niklas Nolte , Eric J. Michaud , Max Tegmark , Mike Williams

We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various…

Machine Learning · Computer Science 2023-01-10 Andrey Gromov

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

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'' 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

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

For humans, language production and comprehension is sensitive to the hierarchical structure of sentences. In natural language processing, past work has questioned how effectively neural sequence models like transformers capture this…

Computation and Language · Computer Science 2023-05-31 Shikhar Murty , Pratyusha Sharma , Jacob Andreas , Christopher D. Manning

In continual learning problems, it is often necessary to overwrite components of a neural network's learned representation in response to changes in the data stream; however, neural networks often exhibit \primacy bias, whereby early…

Machine Learning · Computer Science 2025-07-29 Clare Lyle , Gharda Sokar , Razvan Pascanu , Andras Gyorgy

We attribute grokking, the phenomenon where generalization is much delayed after memorization, to compression. To do so, we define linear mapping number (LMN) to measure network complexity, which is a generalized version of linear region…

Machine Learning · Computer Science 2023-10-10 Ziming Liu , Ziqian Zhong , Max Tegmark

Grokking-delayed generalization that emerges well after a model has fit the training data-has been linked to robustness and representation quality. We ask whether this training regime also helps with machine unlearning, i.e., removing the…

Machine Learning · Computer Science 2025-12-04 Yuanbang Liang , Yang Li

Grokking the delayed transition from memorization to generalization in neural networks remains poorly understood, in part because prior empirical studies confound the roles of architecture, optimization, and regularization. We present a…

Machine Learning · Computer Science 2026-03-27 Shalima Binta Manir , Anamika Paul Rupa

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…