Summary of Grokking Modular Polynomials, by Darshil Doshi et al.
Grokking Modular Polynomials
by Darshil Doshi, Tianyu He, Aritra Das, Andrey Gromov
First submitted to arxiv on: 5 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Disordered Systems and Neural Networks (cond-mat.dis-nn); High Energy Physics – Theory (hep-th); Number Theory (math.NT); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates the limitations of neural networks in learning modular arithmetic tasks, such as addition and multiplication with multiple terms. While MLP architectures can generalize to some extent, they fail to learn most tasks. The authors demonstrate that analytical solutions for MLP weights exist for specific tasks, including modular addition and multiplication. They extend these solutions to include arbitrary modular polynomials and show that real networks trained on these datasets learn similar patterns. The paper also explores the classification of modular polynomials into learnable and non-learnable via neural network training, providing experimental evidence to support this hypothesis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study looks at how well artificial intelligence models called neural networks can perform math problems involving modular arithmetic, like addition and multiplication with many terms. Researchers found that these models are good at some tasks but struggle with others. They discovered a special solution for certain math problems that helps the models learn better. The team also shows that if they combine these solutions, the models can solve more complicated math problems. Finally, they tested how well the models do on different types of math problems and found that some are easier to learn than others. |
Keywords
» Artificial intelligence » Classification » Neural network
