English
Related papers

Related papers: Grokking Explained: A Statistical Phenomenon

200 papers

Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we…

Machine Learning · Computer Science 2026-04-16 Laura Gomezjurado Gonzalez

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

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

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

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

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

Machine Learning · Computer Science 2026-03-05 Jerome Garnier-Brun , Luca Biggio , Davide Beltrame , Marc Mézard , Luca Saglietti

We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the…

Machine Learning · Computer Science 2025-11-06 Etienne Boursier , Scott Pesme , Radu-Alexandru Dragomir

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

Machine Learning · Computer Science 2022-06-07 Satrajit Chatterjee , Piotr Zielinski

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

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

Spectral bias, the tendency of neural networks to learn low frequencies first, can be both a blessing and a curse. While it enhances the generalization capabilities by suppressing high-frequency noise, it can be a limitation in scientific…

Machine Learning · Computer Science 2026-05-08 Shuai Jiang , Alexey Voronin , Eric Cyr , Ben Southworth

Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular arithmetic. Whether this mechanism extends beyond arithmetic…

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

Grokking, the sudden transition from memorization to generalization, is characterized by the emergence of low-dimensional representations, yet the mechanism underlying this organization remains elusive. We propose that intrinsic task…

Machine Learning · Computer Science 2026-03-03 Hyeonbin Hwang , Yeachan Park

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 is proposed and widely studied as an intricate phenomenon in which generalization is achieved after a long-lasting period of overfitting. In this work, we propose NeuralGrok, a novel gradient-based approach that learns an optimal…

Machine Learning · Computer Science 2025-04-28 Xinyu Zhou , Simin Fan , Martin Jaggi , Jie Fu

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

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

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

Standard optimization theories struggle to explain grokking, where generalization occurs long after training convergence. While geometric studies attribute this to slow drift, they often overlook the interaction between the optimizer's…

Machine Learning · Computer Science 2026-03-17 Pratyush Acharya , Habish Dhakal

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of…

Machine Learning · Computer Science 2024-11-04 Alan Jeffares , Alicia Curth , Mihaela van der Schaar