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We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and…

Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we…

Grokking, a phenomenon where machine learning models generalize long after overfitting, has been primarily observed and studied in algorithmic tasks. This paper explores grokking in real-world datasets using deep neural networks for…

Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training…

Training dynamics during grokking concentrate along a small number of dominant update directions -- the spectral edge -- which reliably distinguishes grokking from non-grokking regimes. We show that standard mechanistic interpretability…

Grokking is a intriguing phenomenon in machine learning where a neural network, after many training iterations with negligible improvement in generalization, suddenly achieves high accuracy on unseen data. By working in the quantum-inspired…

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…

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…

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…

Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after…

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective,…

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…

Self-referential learning -- training a model on data it generated itself -- promises boundless scalability but chronically suffers from model collapse: language models degenerate into repetitive text, GANs drop modes, and…

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…

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…

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…

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…

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:…

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse -- a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior…