Predicting upcoming events is critical to our ability to effectively interact with ourenvironment and conspecifics. In natural language processing, transformer models,which are trained on next-word prediction, appear to construct a general-purposerepresentation of language that can support diverse downstream tasks. However, westill lack an understanding of how a predictive objective shapes such representations.Inspired by recent work in vision neuroscience Hénaff et al. (2019), here we test ahypothesis about predictive representations of autoregressive transformer models.In particular, we test whether the neural trajectory of a sequence of words in asentence becomes progressively more straight as it passes through the layers of thenetwork. The key insight behind this hypothesis is that straighter trajectories shouldfacilitate prediction via linear extrapolation. We quantify straightness using a 1-dimensional curvature metric, and present four findings in support of the trajectorystraightening hypothesis: i) In trained models, the curvature progressively decreasesfrom the first to the middle layers of the network. ii) Models that perform better onthe next-word prediction objective, including larger models and models trained onlarger datasets, exhibit greater decreases in curvature, suggesting that this improvedability to straighten sentence neural trajectories may be the underlying driver ofbetter language modeling performance. iii) Given the same linguistic context, thesequences that are generated by the model have lower curvature than the groundtruth (the actual continuations observed in a language corpus), suggesting thatthe model favors straighter trajectories for making predictions. iv) A consistentrelationship holds between the average curvature and the average surprisal ofsentences in the middle layers of models, such that sentences with straighter neuraltrajectories also have lower surprisal. Importantly, untrained models don’t exhibitthese behaviors. In tandem, these results support the trajectory straighteninghypothesis and provide a possible mechanism for how the geometry of the internalrepresentations of autoregressive models supports next word prediction.