Related papers: Mechanistic Insights into Grokking from the Embedd…

Grokking is the phenomenon whereby, unlike the training performance, which peaks early in the training process, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close…

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…

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training…

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…

We examine the pre-training dynamics of language models, focusing on their ability to copy text from preceding context--a fundamental skill for various LLM applications, including in-context learning (ICL) and retrieval-augmented generation…

In some settings neural networks exhibit a phenomenon known as \textit{grokking}, where they achieve perfect or near-perfect accuracy on the validation set long after the same performance has been achieved on the training set. In this…

Grokking, the abrupt transition from memorization to generalisation after extended training, suggests the presence of competing solution basins with distinct statistical properties. We study this phenomenon through the lens of Singular…

\emph{Memorization} in neural networks lacks a precise operational definition and is often inferred from the grokking regime, where training accuracy saturates while test accuracy remains very low. We identify a previously unreported third…

Grokking is the phenomenon where neural networks NNs initially fit the training data and later generalize to the test data during training. In this paper, we empirically provide a frequency perspective to explain the emergence of this…

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…

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…

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…

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the…

Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level,…

We study whether transformers can learn to implicitly reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we…

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 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…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…

We demonstrate the existence of a complexity phase transition in neural networks by studying the grokking phenomenon, where networks suddenly transition from memorization to generalization long after overfitting their training data. To…

Neural collapse, i.e., the emergence of highly symmetric, class-wise clustered representations, is frequently observed in deep networks and is often assumed to reflect or enable generalization. In parallel, flatness of the loss landscape…