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The Impact of Batch Size on Grokking Dynamics

Understanding Grokking Dynamics The term “grokking dynamics” refers to the profound level of understanding that machine learning and deep learning models achieve when they effectively grasp complex concepts. To “grok” in this context means that a model not only learns to recognize patterns in data but also internalizes and comprehends the intricacies of those patterns. […]

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Understanding the Rarity of Grokking in Natural Language Data

Introduction to Grokking The term “grokking” is derived from Robert A. Heinlein’s science fiction novel, Stranger in a Strange Land, published in 1961. In the book, grokking signifies a profound level of understanding that transcends superficial knowledge. It encapsulates the ability to fully absorb and resonate with information, resulting in an instinctive grasp of its

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Can Weight Decay Speed Grokking Convergence?

Introduction to Weight Decay and Grokking In the realm of deep learning, two essential concepts that warrant discussion are weight decay and grokking. Weight decay is a regularization technique employed in the training of neural networks. Its primary objective is to prevent overfitting, a scenario where the model learns noise and patterns that are not

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Understanding Phase Transitions in Grokking: Triggers and Mechanisms

Introduction to Grokking and Phase Transitions The term grokking is derived from the science fiction novel “Stranger in a Strange Land” by Robert A. Heinlein, where it describes a deep, intuitive understanding of a subject or concept. In the context of cognitive science and learning, grokking signifies the moment when an individual engages with complex

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How Curriculum Learning Accelerates Grokking

Introduction to Curriculum Learning and Grokking Curriculum learning represents a pivotal approach in the field of machine learning, characterized by a structured methodology that enhances the educational process for models. This paradigm can be likened to traditional educational practices where learners progress through increasingly complex material, thereby consolidating foundational knowledge before tackling advanced topics. By

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The Necessity of Extended Training in Grokking Algorithms

Introduction to Grokking and Algorithms Grokking, a term popularized by science fiction author Robert A. Heinlein, refers to a deep, intuitive understanding of a concept. In the context of learning algorithms, grokking signifies not merely the surface comprehension of algorithmic principles but an intrinsic grasp that enables one to apply these principles proficiently in various

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Why Do Wide Nets Show Weaker Double Descent?

Introduction to Double Descent Double descent is a concept in machine learning that addresses the relationship between model complexity, training error, and generalization error. Traditionally, the bias-variance tradeoff has served as a foundation for understanding this relationship, suggesting that an increase in model complexity leads to a decrease in bias but an increase in variance,

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Can NTK Predict Double Descent in Transformers?

Introduction to Neural Tangent Kernel (NTK) The Neural Tangent Kernel (NTK) has emerged as a pivotal concept in understanding the dynamics of neural networks, especially during the training phase. This mathematical framework provides a means to analyze the behavior of neural networks through the lens of a linear approximation around their initialization. As neural networks

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Understanding Feature Learning in Relation to Late Descent

Introduction to Feature Learning Feature learning is a crucial aspect of machine learning and artificial intelligence that focuses on automatically discovering representations from raw data. By leveraging algorithms, feature learning enables models to identify patterns, relationships, and structures within vast datasets without the need for explicit programming. This process is particularly significant because it allows

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Understanding the Drop in Test Error After Interpolation

Introduction to Interpolation Interpolation is a fundamental concept in both machine learning and statistics, serving as a method for estimating unknown values that lie within the range of a discrete set of known data points. The process involves constructing new data points based on the existing dataset, which can significantly enhance the predictive capabilities of

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