From Markov to Laplace: How Mamba In-Context Learns Markov Chains

The paper presents insights into the Mamba (S6) and Mamba-2 models, which are structured state space sequence models offering significant inference speed-ups over transformer architectures while maintaining competitive performance in language modeling tasks. It demonstrates that a single-layer Mamba model can effectively learn the in-context Laplacian smoothing estimator, achieving Bayes and minimax optimality, and provides a theoretical framework to understand Mamba's representation capacity through convolution. This research highlights the potential of Mamba models in efficient statistical learning, suggesting new avenues for enhancing AI model training and performance.