Summary of Positional Attention: Expressivity and Learnability Of Algorithmic Computation, by Artur Back De Luca et al.
Positional Attention: Expressivity and Learnability of Algorithmic Computation
by Artur Back de Luca, George Giapitzakis, Shenghao Yang, Petar Veličković, Kimon Fountoulakis
First submitted to arxiv on: 2 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Data Structures and Algorithms (cs.DS)
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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 research explores the role of attention in transformers for executing algorithmic tasks, such as arithmetic, statistics, and sorting. The study investigates how transformers can execute algorithms using positional attention, which depends exclusively on positional encodings. The authors prove that transformers with positional attention (positional transformers) maintain the same expressivity as parallel computational models, while incurring a logarithmic depth cost relative to input length. The analysis shows that positional transformers introduce a learning trade-off between theoretical dependence on parameter norms and sample complexity. Empirical results demonstrate good out-of-distribution performance for tasks relying on positional information. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research looks at how artificial intelligence networks called transformers can do mathematical tasks, like adding numbers or finding averages. The study wants to know if the way these networks pay attention to certain parts of the data helps them do these tasks better. They found that a special kind of transformer, called a positional transformer, is really good at doing tasks where it needs to look at the position of the data. This new type of transformer can even learn from experience and get better at certain tasks over time. |
Keywords
* Artificial intelligence * Attention * Transformer
