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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

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

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or…

Machine Learning · Computer Science 2024-03-06 Darshil Doshi , Aritra Das , Tianyu He , Andrey Gromov

Machine unlearning is rapidly becoming a practical requirement, driven by privacy regulations, data errors, and the need to remove harmful or corrupted training samples. Despite this, most existing methods tackle the problem purely from a…

Machine Learning · Computer Science 2026-04-03 Sonia Laguna , Jorge da Silva Goncalves , Moritz Vandenhirtz , Alain Ryser , Irene Cannistraci , Julia E. Vogt

We investigate the phenomenon of grokking -- delayed generalization accompanied by non-monotonic test loss behavior -- in a simple binary logistic classification task, for which "memorizing" and "generalizing" solutions can be strictly…

Machine Learning · Statistics 2025-07-22 Alon Beck , Noam Levi , Yohai Bar-Sinai

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

Machine unlearning, a process enabling pre-trained models to remove the influence of specific training samples, has attracted significant attention in recent years. Although extensive research has focused on developing efficient machine…

Machine Learning · Computer Science 2026-01-13 Heng Xu , Tianqing Zhu , Dayong Ye , Lefeng Zhang , Le Wang , Wanlei Zhou

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

The pretrain-finetune paradigm usually improves downstream performance over training a model from scratch on the same task, becoming commonplace across many areas of machine learning. While pretraining is empirically observed to be…

Computer Vision and Pattern Recognition · Computer Science 2023-07-13 Gabriele Merlin , Vedant Nanda , Ruchit Rawal , Mariya Toneva

We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase. This view is supported by the shared temporal structure of three phenomena:…

High Energy Physics - Theory · Physics 2025-07-28 Robert de Mello Koch , Animik Ghosh

Machine unlearning is the process of efficiently removing specific information from a trained machine learning model without retraining from scratch. Existing unlearning methods, which often provide provable guarantees, typically involve…

Machine Learning · Computer Science 2026-02-04 Somnath Basu Roy Chowdhury , Rahul Kidambi , Avinava Dubey , David Wang , Gokhan Mergen , Amr Ahmed , Aranyak Mehta

Machine unlearning aims to remove the influence of specific data from trained models while preserving general utility. Existing approximate unlearning methods often rely on performance-degradation heuristics, such as loss maximization or…

Machine Learning · Computer Science 2026-03-13 Jonas Mirlach , Sonia Laguna , Julia E. Vogt

In this paper, we investigate the phenomenon of grokking, where models exhibit delayed generalization following overfitting on training data. We focus on data-scarce regimes where the number of training samples falls below the critical…

Machine Learning · Computer Science 2025-11-10 Vaibhav Singh , Eugene Belilovsky , Rahaf Aljundi

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 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

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

We explore the critical data size in language models, a threshold that marks a fundamental shift from quick memorization to slow generalization. We formalize the phase transition under the grokking configuration into the Data Efficiency…

Computation and Language · Computer Science 2024-05-24 Xuekai Zhu , Yao Fu , Bowen Zhou , Zhouhan Lin

Machine unlearning is the process through which a deployed machine learning model is made to forget about some of its training data points. While naively retraining the model from scratch is an option, it is almost always associated with…

Machine Learning · Computer Science 2022-03-03 Anvith Thudi , Gabriel Deza , Varun Chandrasekaran , Nicolas Papernot

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

Machine unlearning is the task of updating a trained model to forget specific training data without retraining from scratch. In this paper, we investigate how unlearning of deep neural networks (DNNs) is affected by the model…

Machine Learning · Computer Science 2026-05-20 Gal Alon , Yehuda Dar