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The Necessity of Extended Training in Grokking Algorithms

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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?

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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?

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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

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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

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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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Understanding Why Adversarial Examples Exploit Sharp Minima

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Introduction to Adversarial Examples Adversarial examples represent a crucial phenomenon in the realm of machine learning, particularly within the field of neural networks. These are input data points that have been deliberately modified in a subtle way to mislead a machine learning model into making incorrect predictions or classifications. Although these alterations are often undetectable

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Can Flatter Minima Resist Distribution Shifts?

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Introduction to Distribution Shifts In the realm of machine learning and statistical modeling, the term “distribution shift” refers to a situation where the statistical properties of the input data change between the training and deployment phases of a model. Essentially, it signifies a divergence in the data distribution from the time the model was trained

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Understanding Flat-Minima Hypothesis and Its Role in Generalization

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Introduction to Flat-Minima Hypothesis The Flat-Minima Hypothesis is a concept that has garnered attention in the field of machine learning, particularly concerning model optimization and generalization capabilities. At its core, the hypothesis posits that models which attain flat minima in the loss landscape tend to exhibit better generalization performance compared to those that reach sharp

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How Group Normalization Helps with Small-Batch Training

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Introduction to Group Normalization Group normalization is a technique introduced to address the limitations of batch normalization, particularly in scenarios involving small batch sizes. Traditional batch normalization works by normalizing the inputs across the entire batch, which can lead to issues when the batch size is small. This is because the statistics calculated from a

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Understanding the Causes of Gradient Vanishing in Plain Networks

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Introduction to Gradient Vanishing Gradient vanishing is a phenomenon that significantly affects the training of neural networks, particularly during the backpropagation process. This issue occurs when the gradients of the loss function diminish to near zero as they are propagated back through the layers of the network. Consequently, the lower layers receive very small updates,

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