Markov Source

Markov sources are probabilistic models generating sequential data where the next element depends only on a fixed number of preceding elements. Current research focuses on understanding how powerful models like transformers learn to represent and predict from these sources, investigating the interplay between model architecture (e.g., depth, attention mechanisms), data characteristics (e.g., order of the Markov process), and model performance. This research is crucial for improving our understanding of sequence modeling in general, with implications for areas like natural language processing and efficient communication systems where optimal resource allocation based on semantic importance is critical. Furthermore, analyzing the performance of these models through the lens of Markov chains provides a rigorous framework for evaluating and improving their predictive capabilities.