Summary of On Rank-dependent Generalisation Error Bounds For Transformers, by Lan V. Truong
On Rank-Dependent Generalisation Error Bounds for Transformers
by Lan V. Truong
First submitted to arxiv on: 15 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Functional Analysis (math.FA)
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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 paper introduces novel covering number bounds for linear function classes, dependent on input and matrix norms, with constraints on rank. These bounds are applied to derive generalization errors for single-layer transformers. The results improve existing literature bounds, showcasing benefits of low-rank matrices in transformer design. Specifically, the achieved bound decays as O(1/√n) and O(log rw), where n is sample length and rw is the rank of query and key matrices. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores ways to make transformers more efficient by using lower-ranked matrices. It does this by developing new mathematical tools that help us understand how well a transformer will generalize (work on new, unseen data). The results show that using lower-ranked matrices can lead to better generalization performance. This is important because it could be used in real-world applications where speed and efficiency are crucial. |
Keywords
» Artificial intelligence » Generalization » Transformer
