# Grokking Explained: A Statistical Phenomenon

arXiv: https://arxiv.org/abs/2502.01774 · HTML: https://mlsanity.com/paper/2502.01774/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 10 of 10)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Grokking as the Transition from Lazy to Rich Training Dynamics](https://mlsanity.com/paper/2310.06110/) (2023)
- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Grokking in Linear Estimators -- A Solvable Model that Groks without Understanding](https://mlsanity.com/paper/2310.16441/) (2023)

## Built on by (most cited first, 1 of 1)

- [Topological Signatures of Grokking](https://mlsanity.com/paper/2605.06352/) (2026)

## Abstract (arXiv)

Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in deep learning networks. In this paper, we formalize and investigate grokking, highlighting that a key factor in its emergence is a distribution shift between training and test data. We introduce two synthetic datasets specifically designed to analyze grokking. One dataset examines the impact of limited sampling, and the other investigates transfer learning's role in grokking. By inducing distribution shifts through controlled imbalanced sampling of sub-categories, we systematically reproduce the phenomenon, demonstrating that while small-sampling is strongly associated with grokking, it is not its cause. Instead, small-sampling serves as a convenient mechanism for achieving the necessary distribution shift. We also show that when classes form an equivariant map, grokking can be explained by the model's ability to learn from similar classes or sub-categories. Unlike earlier work suggesting that grokking primarily arises from high regularization and sparse data, we demonstrate that it can also occur with dense data and minimal hyper-parameter tuning. Our findings deepen the understanding of grokking and pave the way for developing better stopping criteria in future training processes.