Summary of Why Do You Grok? a Theoretical Analysis Of Grokking Modular Addition, by Mohamad Amin Mohamadi et al.
Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition
by Mohamad Amin Mohamadi, Zhiyuan Li, Lei Wu, Danica J. Sutherland
First submitted to arxiv on: 17 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed paper provides a theoretical explanation for the “grokking” phenomenon, where models generalize well long after overfitting. The study focuses on modular addition and shows that early in gradient descent, no permutation-equivariant model can achieve small population error without seeing at least a constant fraction of all possible data points. However, as the model escapes the kernel regime, it is shown to generalize well with substantially fewer training points using two-layer quadratic networks that achieve zero training loss with bounded _{} norm. The paper also provides empirical evidence supporting the case for grokking as a consequence of the transition from kernel-like behavior to limiting behavior of gradient descent on deep networks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The proposed study helps us understand how models can generalize well even after they’ve overfitting. It looks at how models perform on modular addition and shows that early on, no model can do well unless it sees most of the possible data points. Later, though, models that do this thing called “grokking” are shown to be good at generalizing even with fewer training points. The study also shows that simple Transformers and other networks can leave this “kernel regime” only after initially overfitting. |
Keywords
» Artificial intelligence » Gradient descent » Overfitting
