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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

Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by…

Machine Learning · Statistics 2014-10-22 Saahil Ognawala , Justin Bayer

''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, 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-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, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled…

Machine Learning · Computer Science 2024-06-10 Ahmed Imtiaz Humayun , Randall Balestriero , Richard Baraniuk

While Large Language Models (LLMs) excel at factual retrieval, they often struggle with the "curse of two-hop reasoning" in compositional tasks. Recent research suggests that parameter-sharing transformers can bridge this gap by forming a…

Computation and Language · Computer Science 2026-01-15 Kaiyu He , Zhang Mian , Peilin Wu , Xinya Du , Zhiyu Chen

\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

Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using…

Machine Learning · Computer Science 2026-05-19 Linyu Liu , Pinyan Lu

Recently deep neural networks have shown their capacity to memorize training data, even with noisy labels, which hurts generalization performance. To mitigate this issue, we provide a simple but effective baseline method that is robust to…

Machine Learning · Computer Science 2019-09-30 Yucen Luo , Jun Zhu , Tomas Pfister

Deep neural networks are over-parameterized and easily overfit the datasets they train on. In the extreme case, it has been shown that these networks can memorize a training set with fully randomized labels. We propose using the curvature…

Machine Learning · Computer Science 2023-10-03 Isha Garg , Deepak Ravikumar , Kaushik Roy

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

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

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 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

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 roles played by learning and memorization represent an important topic in deep learning research. Recent work on this subject has shown that the optimization behavior of DNNs trained on shuffled labels is qualitatively different from…

Machine Learning · Statistics 2018-02-22 Elias Chaibub Neto

Despite the empirical advances of deep learning across a variety of learning tasks, our theoretical understanding of its success is still very restricted. One of the key challenges is the overparametrized nature of modern models, enabling…

Machine Learning · Computer Science 2023-02-24 Sotiris Anagnostidis , Gregor Bachmann , Lorenzo Noci , Thomas Hofmann

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

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