# Markov Chain Estimation with In-Context Learning

arXiv: https://arxiv.org/abs/2508.03934 · HTML: https://mlsanity.com/paper/2508.03934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 19 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [LTX-Video: Realtime Video Latent Diffusion](https://mlsanity.com/paper/2501.00103/) (2024)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [YourTTS: Towards Zero-Shot Multi-Speaker TTS and Zero-Shot Voice Conversion for everyone](https://mlsanity.com/paper/2112.02418/) (2021)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [Revisiting Neural Scaling Laws in Language and Vision](https://mlsanity.com/paper/2209.06640/) (2022)
- [The Evolution of Statistical Induction Heads: In-Context Learning Markov Chains](https://mlsanity.com/paper/2402.11004/) (2024)
- [In-Context Language Learning: Architectures and Algorithms](https://mlsanity.com/paper/2401.12973/) (2024)
- [What Makes Multimodal In-Context Learning Work?](https://mlsanity.com/paper/2404.15736/) (2024)

## Abstract (arXiv)

We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the next token. Matrices used during training and test are different and we show that there is a threshold in transformer size and in training set size above which the model is able to learn to estimate the transition probabilities from its context instead of memorizing the training patterns. Additionally, we show that more involved encoding of the states enables more robust prediction for Markov chains with structures different than those seen during training.