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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 -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a…

Artificial Intelligence · Computer Science 2026-05-05 Truong Xuan Khanh , Truong Quynh Hoa , Luu Duc Trung , Phan Thanh Duc

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

Existing accounts of grokking explain the phenomena in terms of mechanistic frameworks such as circuit efficiency or lazy-to-rich transitions. However, despite a known dependence between grokking and model size, how model capacity shapes…

Machine Learning · Computer Science 2026-05-12 Yiding Song , Hanming Ye

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great…

Machine Learning · Computer Science 2022-01-07 Alethea Power , Yuri Burda , Harri Edwards , Igor Babuschkin , Vedant Misra

This paper demonstrates that grokking behavior in modular arithmetic with a modulus P in a neural network can be controlled by modifying the profile of the activation function as well as the depth and width of the model. Plotting the even…

Machine Learning · Computer Science 2024-11-11 Ahmed Salah , David Yevick

Training Neural Networks (NNs) without overfitting is difficult; detecting that overfitting is difficult as well. We present a novel Random Matrix Theory method that detects the onset of overfitting in deep learning models without access to…

Machine Learning · Computer Science 2026-05-15 Hari K. Prakash , Charles H Martin

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance…

Machine Learning · Computer Science 2026-05-29 Chi-Ning Chou , Oscar Uzdelewicz , Neng-Chun Chiu , Yao-Yuan Yang , SueYeon Chung

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

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…

Machine Learning · Computer Science 2026-04-21 Joon Hyeok Kim , Yong-Hyun Park , Mattis Dalsætra Østby , Jiatao Gu

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

Recent studies have uncovered intriguing phenomena in deep learning, such as grokking, double descent, and emergent abilities in large language models, which challenge human intuition and are crucial for a deeper understanding of neural…

Machine Learning · Computer Science 2024-02-27 Yufei Huang , Shengding Hu , Xu Han , Zhiyuan Liu , Maosong Sun

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

Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dynamics in transformers trained on modular arithmetic. PCA of…

Machine Learning · Computer Science 2026-04-06 Yongzhong Xu

We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking…

Machine Learning · Computer Science 2024-05-28 Yeachan Park , Minseok Kim , Yeoneung Kim

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

What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained…

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 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

We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the…

Machine Learning · Computer Science 2026-02-09 Jaisidh Singh , Diganta Misra , Antonio Orvieto