Summary of Position Coupling: Improving Length Generalization Of Arithmetic Transformers Using Task Structure, by Hanseul Cho et al.
Position Coupling: Improving Length Generalization of Arithmetic Transformers Using Task Structure
by Hanseul Cho, Jaeyoung Cha, Pranjal Awasthi, Srinadh Bhojanapalli, Anupam Gupta, Chulhee Yun
First submitted to arxiv on: 31 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); 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 presents a method called position coupling to improve the generalizability of Transformers on sequence-to-sequence tasks, particularly for arithmetic operations like integer addition. The approach assigns the same positional encoding to tokens that are relevant to each other, allowing the model to better capture task structure. Experimentally, the proposed method enables models trained on shorter sequences (up to 30 digits) to generalize to longer sequences (up to 200 digits), a significant improvement over vanilla Transformers. On a theoretical level, the authors prove that a 1-layer Transformer with position coupling can solve addition tasks involving exponentially many digits, whereas without positional information, the model cannot fully solve it. Additionally, the method is shown to be applicable to other algorithmic tasks, such as Nx2 multiplication and two-dimensional problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you’re trying to teach a computer to do math problems that get really long, like adding up hundreds of numbers. The problem is that most computers aren’t very good at doing this kind of math when the numbers get too big. This paper introduces a new way to make computers better at this type of math by giving them hints about how the numbers are related. By using these hints, the computer can do really long math problems much more accurately than before. The authors also show that their method works not just for simple addition but also for other types of math problems. This could be useful in all sorts of situations where computers need to do complex calculations. |
Keywords
» Artificial intelligence » Positional encoding » Transformer
