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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

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

The current trend of scaling language models involves increasing both parameter count and training dataset size. Extrapolating this trend suggests that training dataset size may soon be limited by the amount of text data available on the…

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 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

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

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These…

Computation and Language · Computer Science 2022-11-15 Cem Anil , Yuhuai Wu , Anders Andreassen , Aitor Lewkowycz , Vedant Misra , Vinay Ramasesh , Ambrose Slone , Guy Gur-Ari , Ethan Dyer , Behnam Neyshabur

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

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

A principled understanding of generalization in deep learning may require unifying disparate observations under a single conceptual framework. Previous work has studied \emph{grokking}, a training dynamic in which a sustained period of…

Machine Learning · Computer Science 2023-03-14 Xander Davies , Lauro Langosco , David Krueger

Several studies have investigated the reasons behind the effectiveness of fine-tuning, usually through the lens of probing. However, these studies often neglect the role of the size of the dataset on which the model is fine-tuned. In this…

Computation and Language · Computer Science 2022-03-21 Houman Mehrafarin , Sara Rajaee , Mohammad Taher Pilehvar

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a…

Machine Learning · Statistics 2024-05-07 Noa Rubin , Inbar Seroussi , Zohar Ringel

The web-scale of pretraining data has created an important evaluation challenge: to disentangle linguistic competence on cases well-represented in pretraining data from generalization to out-of-domain language, specifically the dynamic,…

Computation and Language · Computer Science 2025-08-14 Wesley Scivetti , Melissa Torgbi , Austin Blodgett , Mollie Shichman , Taylor Hudson , Claire Bonial , Harish Tayyar Madabushi

Grokking, the abrupt transition from memorization to generalisation after extended training, suggests the presence of competing solution basins with distinct statistical properties. We study this phenomenon through the lens of Singular…

Machine Learning · Statistics 2026-05-08 Ben Cullen , Sergio Estan-Ruiz , Riya Danait , Jiayi Li

Systematic generalization remains challenging for current language models, which are known to be both sensitive to semantically similar permutations of the input and to struggle with known concepts presented in novel contexts. Although…

Computation and Language · Computer Science 2025-05-28 Sondre Wold , Lucas Georges Gabriel Charpentier , Étienne Simon

Mechanistic interpretability typically relies on post-hoc analysis of trained networks. We instead adopt an interventional approach: testing hypotheses a priori by modifying architectural topology to observe training dynamics. We study…

Machine Learning · Computer Science 2026-05-05 Alper Yıldırım

Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…

Computation and Language · Computer Science 2024-06-05 Henry Conklin , Kenny Smith

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the…

Machine Learning · Computer Science 2022-06-14 Vimal Thilak , Etai Littwin , Shuangfei Zhai , Omid Saremi , Roni Paiss , Joshua Susskind

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

Traditionally, large language models have been either trained on general web crawls or domain-specific data. However, recent successes of generative large language models, have shed light on the benefits of cross-domain datasets. To examine…