Summary of Transformers on Markov Data: Constant Depth Suffices, by Nived Rajaraman et al.
Transformers on Markov Data: Constant Depth Suffices
by Nived Rajaraman, Marco Bondaschi, Kannan Ramchandran, Michael Gastpar, Ashok Vardhan Makkuva
First submitted to arxiv on: 25 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computation and Language (cs.CL); Information Theory (cs.IT); 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 Transformers have excelled at modeling generative processes across various domains and modalities. This paper investigates the performance of attention-based transformers on data drawn from k-th Markov processes. Surprisingly, empirical results show that a transformer with a fixed depth and one head per layer can achieve low test loss on sequences from k-th Markov sources as k grows. Theoretically, our main result demonstrates that a single-head, three-layer transformer can represent the in-context conditional empirical distribution for k-th Markov sources, consistent with empirical findings. We also prove that attention-only transformers with O(log2(k)) layers can represent the in-context conditional empirical distribution by composing induction heads to track previous symbols in the sequence. These results provide insight into how transformers capture context, understanding their behavior on Markov sources. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies a type of artificial intelligence model called a transformer. Transformers are good at generating patterns we see in data. The researchers looked at how well transformers work when the patterns follow certain rules. They found that transformers can do surprisingly well even when these rules get more complicated. This helps us understand how transformers learn to recognize patterns, which is important for many applications. |
Keywords
* Artificial intelligence * Attention * Transformer
