# Misalignment of Low-Loss Regions Causes Grokking

arXiv: https://arxiv.org/abs/2610.00620 · HTML: https://mlsanity.com/paper/2610.00620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [Explaining grokking through circuit efficiency](https://mlsanity.com/paper/2309.02390/) (2023)
- [The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon](https://mlsanity.com/paper/2206.04817/) (2022)
- [Loss Surface Simplexes for Mode Connecting Volumes and Fast Ensembling](https://mlsanity.com/paper/2102.13042/) (2021)
- [Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity](https://mlsanity.com/paper/2307.08286/) (2023)
- [Deep Learning is Singular, and That's Good](https://mlsanity.com/paper/2010.11560/) (2020)
- [Grokking at the Edge of Numerical Stability](https://mlsanity.com/paper/2501.04697/) (2025)
- [On the training dynamics of deep networks with L2 regularization](https://mlsanity.com/paper/2006.08643/) (2020)
- [Overfitting Mechanism and Avoidance in Deep Neural Networks](https://mlsanity.com/paper/1901.06566/) (2019)
- [Critical Data Size of Language Models from a Grokking Perspective](https://mlsanity.com/paper/2401.10463/) (2024)
- [A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective](https://mlsanity.com/paper/2509.16499/) (2025)
- [Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers](https://mlsanity.com/paper/2504.20752/) (2025)
- [Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory](https://mlsanity.com/paper/2404.12367/) (2024)
- [To Grok Grokking: Provable Grokking in Ridge Regression](https://mlsanity.com/paper/2601.19791/) (2026)
- [How Good is a Single Basin?](https://mlsanity.com/paper/2402.03187/) (2024)
- [Connecting Independently Trained Modes via Layer-Wise Connectivity](https://mlsanity.com/paper/2505.02604/) (2025)

## Abstract (arXiv)

Grokking refers to the delayed emergence of validation-set generalization after a model has already overfit the training set. Although first observed in small algorithmic tasks trained with transformers, its underlying mechanism remains unsettled. In this work, we develop an analysis framework based on mode connectivity and the geometry of low-loss regions. The framework predicts that the standard modular-arithmetic setting does not always produce grokking: under a symmetry-preserving train/validation split, we observe a stable anti-grokking case in which validation performance does not recover. This counterexample challenges several existing correlational explanations of grokking. More broadly, our analysis framework and results further suggest that grokking arises when the low-loss regions induced by the training and validation partitions are misaligned. Once these regions become well aligned, training hyperparameters alone cannot produce grokking and the observed dynamics collapse to either trainable or non-trainable behavior.