Next-token prediction (NTP) has become the go-to training paradigm for modern language models, yet its optimization principles are not well-understood. To bridge this gap, we initiate a study of the structural properties of the solutions selected by gradient-based optimizers among the many possible minimizers of the NTP objective. By framing NTP as cross-entropy minimization across \emph{distinct} contexts, each tied with a \emph{sparse} conditional probability distribution across a finite vocabulary of tokens, we introduce ``NTP-separability conditions'' that enable reaching the data-entropy lower bound. With this setup, our focus then shifts to linear models, for which we characterize the optimization bias of gradient descent (GD): Within a data subspace defined by the sparsity patterns of distinct contexts, GD selects parameters that equate the logits' differences of in-support tokens to their log-odds. In the orthogonal subspace, the GD parameters diverge in norm and select the direction that maximizes a margin specific to NTP. These findings extend previous research on implicit bias in one-hot classification to the NTP setting, highlighting key differences and prompting further research into the optimization and generalization properties of NTP.