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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…

Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…

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…

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…

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…

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…

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…

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…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

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…

Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic…

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…

This paper focuses on predicting the occurrence of grokking in neural networks, a phenomenon in which perfect generalization emerges long after signs of overfitting or memorization are observed. It has been reported that grokking can only…

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…

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…

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…

Machine learning (ML) has recently facilitated many advances in solving problems related to many-body physical systems. Given the intrinsic quantum nature of these problems, it is natural to speculate that quantum-enhanced machine learning…

Recently, an interesting phenomenon called grokking has gained much attention, where generalization occurs long after the models have initially overfitted the training data. We try to understand this seemingly strange phenomenon through the…

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…

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel…