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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…

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…

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…

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…

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…

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…

Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a…

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…

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…

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…

Grokking, the phenomenon of delayed generalization, is often attributed to the depth and compositional structure of deep neural networks. We study grokking in one of the simplest possible settings: the learning of a linear model with…

The phenomenon of grokking in over-parameterized neural networks has garnered significant interest. It involves the neural network initially memorizing the training set with zero training error and near-random test error. Subsequent…

Grokking, a delayed generalization in neural networks after perfect training performance, has been observed in Transformers and MLPs, but the components driving it remain underexplored. We show that embeddings are central to grokking:…

''Grokking'' is a phenomenon where a neural network first memorizes training data and generalizes poorly, but then suddenly transitions to near-perfect generalization after prolonged training. While intriguing, this delayed generalization…

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…

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…

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…

Grokking typically achieves similar loss to ordinary, "steady", learning. We ask whether these different learning paths - grokking versus ordinary training - lead to fundamental differences in the learned models. To do so we compare the…

Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and…

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,…