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Related papers: A Systematic Empirical Study of Grokking: Depth, A…

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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

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

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

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

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

Why does a Transformer that has memorized its training set wait thousands of steps before it generalizes? Existing accounts locate this delay in norm minimization, feature emergence, or the late discovery of sparse subnetworks. These…

Machine Learning · Computer Science 2026-05-18 Kai Hidajat , Solden Stoll , Joseph An

This paper presents the first study of grokking in practical LLM pretraining. Specifically, we investigate when an LLM memorizes the training data, when its generalization on downstream tasks starts to improve, and what happens if there is…

Machine Learning · Computer Science 2026-02-04 Ziyue Li , Chenrui Fan , Tianyi Zhou

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

This paper investigates the grokking phenomenon, which refers to the sudden transition from a long memorization to generalization observed during neural networks training, in the context of learning multiplication in finite-dimensional…

Machine Learning · Computer Science 2026-05-15 Pascal Jr Tikeng Notsawo , Guillaume Dumas , Guillaume Rabusseau

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 - the delayed transition from memorisation to generalisation in neural networks - remains poorly understood. We study this phenomenon through the geometry of learned representations and identify a consistent empirical signature…

Machine Learning · Computer Science 2026-05-13 Truong Xuan Khanh , Truong Quynh Hoa , Luu Duc Trung , Phan Thanh Duc

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which…

Machine Learning · Computer Science 2025-12-03 Yuandong Tian

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

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a…

Machine Learning · Statistics 2024-02-06 Noam Levi , Alon Beck , Yohai Bar-Sinai

Grokking, referring to the abrupt improvement in test accuracy after extended overfitting, offers valuable insights into the mechanisms of model generalization. Existing researches based on progress measures imply that grokking relies on…

Machine Learning · Computer Science 2025-04-15 Zihan Gu , Ruoyu Chen , Hua Zhang , Yue Hu , Xiaochun Cao

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

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

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

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

Grokking in modular arithmetic has established itself as the quintessential fruit fly experiment, serving as a critical domain for investigating the mechanistic origins of model generalization. Despite its significance, existing research…

Artificial Intelligence · Computer Science 2026-04-01 Junjie Zhang , Zhen Shen , Gang Xiong , Xisong Dong