Predictive Geometry in Language Models

For a given token, a language model's prediction may be more or less robust to changes in the preceding context. We ask how training exposure changes this context robustness. To capture that change, we trace the full next-token distribution as the preceding context grows. We apply Fisher-Rao geometry to this path of predictive distributions, viewing context growth as motion on a statistical manifold. We develop a theory of these paths that measures the total predictive change and decomposes it into the part associated with the observed token's probability and the remaining change in the distribution over alternative tokens. Across four model-data settings, we show that the theoretical decomposition captures systematic effects of repeated exposure: both components of the predictive change increase with exposure. We then use the theory in two ways. For privacy auditing, we use Fisher-Rao context paths to distinguish documents presented during continued training from those omitted from it. For context-scoped editing, we use the geometry to strengthen a continuation after a short context while keeping longer-context predictions near their pre-edit values. It rises from $0.002$% to $6$-$9$%, while prediction changes on held-out longer extensions are $41$-$58\times$ smaller than without protection. Together, these results show that training exposure leaves a measurable geometric signature in context-dependent predictions that can be used both to detect exposure and to control where its effects appear.