# Attention with Markov: A Framework for Principled Analysis of Transformers via Markov Chains

**Authors:** Ashok Vardhan Makkuva, Marco Bondaschi, Adway Girish, Alliot Nagle, Martin Jaggi, Hyeji Kim, Michael Gastpar  
**arXiv:** [2402.04161](https://arxiv.org/abs/2402.04161)  
**Date:** 2024-02-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2402.04161v1/

## Key points

- Attention-based transformers are powerful tools in various fields, especially in natural language processing.
- Transformers achieve success through generative pretraining on large text corpora in an auto-regressive manner.
- A new framework leveraging Markov chains has been proposed to explore transformers' sequential modeling abilities inspired by natural language's Markovianity.
- The framework allows for a systematic study of the relationship between data-distributional properties, transformer architecture, learned distribution, and overall model performance.
- Theoretical analysis shows the existence of global minima and bad local minima based on specific data characteristics and transformer architecture.
- Empirical experiments validate theoretical findings, demonstrating alignment between theory and practice.
- Investigation extends to higher order Markov chains and deeper architectures to explore additional complexities within model performance.

## Summary

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In recent years, attention-based transformers have emerged as a powerful tool in various fields, particularly in natural language processing. These models have achieved great success due to their generative pretraining procedure, where they are trained on large text corpora in an auto-regressive manner. To further explore the capabilities of transformers and understand their sequential modeling abilities, a new framework has been proposed that leverages Markov chains. This framework is inspired by the inherent Markovianity of natural languages and allows for a systematic study of the relationship between data-distributional properties, transformer architecture, learned distribution, and overall model performance. By modeling the data as a Markovian source, researchers have been able to theoretically characterize the loss landscape of single-layer transformers. Through theoretical analysis, it has been shown that global minima and bad local minima exist based on specific data characteristics and transformer architecture. Empirical experiments have further validated these theoretical findings, demonstrating alignment between theory and practice. The investigation extends to higher order Markov chains and deeper architectures to explore additional complexities and nuances within the model performance. Open problems in this area are outlined for future research directions. This study was conducted by Ashok Vardhan Makkuva, Marco Bondaschi, Adway Girish, Alliot Nagle, Martin Jaggi, Hyeji Kim, and Michael Gastpar. The detailed analysis and findings can be accessed through the provided code repository at \url{https://github.com/Bond1995/Markov}.