# Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking

arXiv: https://arxiv.org/abs/2510.04930 · HTML: https://mlsanity.com/paper/2510.04930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 34)

- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Old Optimizer, New Norm: An Anthology](https://mlsanity.com/paper/2409.20325/) (2024)
- [Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limit](https://mlsanity.com/paper/2207.08799/) (2022)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Omnigrok: Grokking Beyond Algorithmic Data](https://mlsanity.com/paper/2210.01117/) (2022)
- [Explaining grokking through circuit efficiency](https://mlsanity.com/paper/2309.02390/) (2023)
- [Grokking as the Transition from Lazy to Rich Training Dynamics](https://mlsanity.com/paper/2310.06110/) (2023)
- [The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon](https://mlsanity.com/paper/2206.04817/) (2022)
- [Grokking modular arithmetic](https://mlsanity.com/paper/2301.02679/) (2023)
- [A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks](https://mlsanity.com/paper/2303.11873/) (2023)
- [Grokking of Hierarchical Structure in Vanilla Transformers](https://mlsanity.com/paper/2305.18741/) (2023)
- [Unifying Grokking and Double Descent](https://mlsanity.com/paper/2303.06173/) (2023)
- [Grokking at the Edge of Numerical Stability](https://mlsanity.com/paper/2501.04697/) (2025)
- [Grokfast: Accelerated Grokking by Amplifying Slow Gradients](https://mlsanity.com/paper/2405.20233/) (2024)
- [Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition](https://mlsanity.com/paper/2407.12332/) (2024)
- [Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grok](https://mlsanity.com/paper/2306.13253/) (2023)
- [Grokking in Linear Estimators -- A Solvable Model that Groks without Understanding](https://mlsanity.com/paper/2310.16441/) (2023)
- [Critical Data Size of Language Models from a Grokking Perspective](https://mlsanity.com/paper/2401.10463/) (2024)
- [Data-Dependence of Plateau Phenomenon in Learning with Neural Network --- Statistical Mechanical Analysis](https://mlsanity.com/paper/2001.03371/) (2020)
- [Unified View of Grokking, Double Descent and Emergent Abilities: A Perspective from Circuits Competition](https://mlsanity.com/paper/2402.15175/) (2024)
- [Stable Gradients for Stable Learning at Scale in Deep Reinforcement Learning](https://mlsanity.com/paper/2506.15544/) (2025)
- [Grokking Modular Polynomials](https://mlsanity.com/paper/2406.03495/) (2024)

## Built on by (most cited first, 2 of 2)

- [Tuning the Implicit Regularizer of Masked Diffusion Language Models: Enhancing Generalization via Insights from k-Parity](https://mlsanity.com/paper/2601.22450/) (2026)
- [Statistical Vignettes on the Grokking Phenomenon](https://mlsanity.com/paper/2610.18811/) (2026)

## Abstract (arXiv)

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 to perfect levels. In practice, it is desirable to reduce the length of such plateaus, that is to make the learning process "grok" faster. In this work, we provide new insights into grokking. First, we show both empirically and theoretically that grokking can be induced by asymmetric speeds of (stochastic) gradient descent, along different principal (i.e singular directions) of the gradients. We then propose a simple modification that normalizes the gradients so that dynamics along all the principal directions evolves at exactly the same speed. Then, we establish that this modified method, which we call egalitarian gradient descent (EGD) and can be seen as a carefully modified form of natural gradient descent, groks much faster. In fact, in some cases the stagnation is completely removed. Finally, we empirically show that on classical arithmetic problems such as modular addition and sparse parity problem which this stagnation has been widely observed and intensively studied, that our proposed method eliminates the plateaus.