Causal Expression in Probabilistic Generation: Selection Dynamics and Residual Alternatives

This research note proposes a structural explanation of causal expressions in large language model generation. Large language models generate sequences by sampling from conditional probability distributions P(y|x). Although these systems do not explicitly encode causal mechanisms, they frequently produce causal expressions such as “because”, “therefore”, or “as a result”. This note argues that causal language can emerge from the dynamics of probabilistic generation. At each step multiple alternative continuations exist, a single continuation is selected, and the resulting sequence forms a trajectory through a conditional probability field. Under this view, causal expressions can be interpreted as linearized descriptions of dominant generative trajectories, while unselected continuations remain as residual alternatives surrounding the realized path. Parts of this manuscript were prepared with the assistance of AI-based language models.The author reviewed and edited the final text.