Summary of Understanding Scaling Laws with Statistical and Approximation Theory For Transformer Neural Networks on Intrinsically Low-dimensional Data, by Alex Havrilla et al.
Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data
by Alex Havrilla, Wenjing Liao
First submitted to arxiv on: 11 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); 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 The abstract proposes a novel understanding of why transformer-based large language models follow power scaling laws, despite their massive size. The authors establish statistical estimation and mathematical approximation theories for transformers when input data is concentrated on a low-dimensional manifold. They find that the generalization error scales with both the training data size and network size, with a power dependent on the intrinsic dimension of the data. Notably, the constructed model architecture is shallow and requires only logarithmic depth in the intrinsic dimension. The theory is tested by training large language models on natural language datasets, which closely agree with the predicted scaling laws. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Transformers are special kinds of artificial intelligence that can understand and process human language. Sometimes, these transformers get really big and powerful, but they don’t always work well when we try to use them for new tasks. Researchers want to know why this happens. One idea is that the data they’re trained on might be too simple or not complex enough. To test this idea, scientists developed a new way of understanding how these transformers work based on the structure of the data they learn from. They found that when the data is organized in a special way, called a low-dimensional manifold, the transformer’s performance improves significantly. This means that we can build more powerful and useful language models by organizing our data in this special way. |
Keywords
* Artificial intelligence * Generalization * Scaling laws * Transformer
