Summary of Pre-trained Large Language Models Use Fourier Features to Compute Addition, by Tianyi Zhou et al.
Pre-trained Large Language Models Use Fourier Features to Compute Addition
by Tianyi Zhou, Deqing Fu, Vatsal Sharan, Robin Jia
First submitted to arxiv on: 5 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computation and Language (cs.CL)
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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 how pre-trained large language models (LLMs) perform basic arithmetic operations like addition. The study reveals that these models use a mechanism called Fourier features, which represent numbers in the hidden state as dimensions sparse in the frequency domain. The model’s MLP and attention layers utilize these features in distinct ways: MLP layers primarily estimate the magnitude of the answer using low-frequency features, while attention layers perform modular addition (e.g., determining whether the answer is even or odd) using high-frequency features. Pre-training plays a crucial role in this mechanism, as models trained from scratch only exploit low-frequency features and achieve lower accuracy. Introducing pre-trained token embeddings to a randomly initialized model improves its performance. The analysis shows that appropriate pre-trained representations can unlock Transformers’ ability to learn precise mechanisms for algorithmic tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper looks at how big language models do math, specifically addition. It found out that these models use a special way of representing numbers called Fourier features. These features are like a code that helps the model do addition by looking at different parts of the number. The study also showed that if the model is not pre-trained, it won’t be very good at adding numbers. But when you add pre-trained information to the model, it gets much better! Overall, this research shows that big language models can learn new ways of doing math if they have the right starting point. |
Keywords
» Artificial intelligence » Attention » Token
