Information-Theoretic Analysis of Next-Token Prediction under Markovian Data

Masoud Kavian, Abdellatif Zaidi, Milad Sefidgaran

We develop an information-theoretic framework for generalization in next-token prediction under temporally dependent data. We consider independent trajectories generated by finite-memory Markov processes and distinguish algorithmic dependence, quantified by mutual information, from temporal dependence, characterized by mixing. For cross-entropy loss, we derive an expected generalization bound using the Donsker--Varadhan variational representation and a McDiarmid-type concentration inequality for Markov chains. A refinement captures the joint effect of context length and temporal mixing through the mixing properties of the history-state process. We then extend the bound through a rate--distortion formulation, replacing mutual information with the minimum information rate required to represent the learned model within a prescribed distortion in the generalization gap, yielding informative guarantees for deterministic algorithms over continuous hypothesis spaces. For margin-based prediction, we derive explicit bounds for linear and self-attention next-token predictors via noisy low-dimensional compression, revealing the roles of context length, model complexity, sample size, margin,…