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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

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

This paper focuses on predicting the occurrence of grokking in neural networks, a phenomenon in which perfect generalization emerges long after signs of overfitting or memorization are observed. It has been reported that grokking can only…

Machine Learning · Computer Science 2023-10-02 Pascal Jr. Tikeng Notsawo , Hattie Zhou , Mohammad Pezeshki , Irina Rish , Guillaume Dumas

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…

Machine Learning · Statistics 2017-10-11 Madhu S. Advani , Andrew M. Saxe

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

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

Machine Learning · Computer Science 2020-11-11 Frithjof Gressmann , Zach Eaton-Rosen , Carlo Luschi

Critical-data-size accounts of grokking suggest a natural post-threshold intuition: once training data is sufficient to identify the underlying rule, additional data should accelerate validation convergence. We show that this intuition can…

Machine Learning · Computer Science 2026-05-15 Shin So , Kyelim Lee , Albert No

Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…

Machine Learning · Computer Science 2026-04-24 Shreel Golwala

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

The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…

Machine Learning · Computer Science 2026-02-03 Chiwun Yang

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

We study the approximation capabilities, convergence speeds and on-convergence behaviors of transformers trained on in-context recall tasks -- which requires to recognize the \emph{positional} association between a pair of tokens from…

Machine Learning · Computer Science 2025-10-22 Quan Nguyen , Thanh Nguyen-Tang

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

Neural collapse, i.e., the emergence of highly symmetric, class-wise clustered representations, is frequently observed in deep networks and is often assumed to reflect or enable generalization. In parallel, flatness of the loss landscape…

Machine Learning · Computer Science 2026-02-05 Ting Han , Linara Adilova , Henning Petzka , Jens Kleesiek , Michael Kamp

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons…

Machine Learning · Computer Science 2025-05-20 Lucas Prieto , Melih Barsbey , Pedro A. M. Mediano , Tolga Birdal

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

Adaptation and Self-Organizing Systems · Physics 2024-10-04 S. Barland , L. Gil

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

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and…

Machine Learning · Statistics 2026-04-15 Abdessamed Qchohi , Simone Rossi

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine…

Machine Learning · Computer Science 2024-06-06 Jaerin Lee , Bong Gyun Kang , Kihoon Kim , Kyoung Mu Lee

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