It is well known that real-time human language processing is highly incremental and context-driven, and that the strength of a comprehender's expectation for each word encountered is a key determinant of the difficulty of integrating that word into the preceding context. In reading, this differential difficulty is largely manifested in the amount of time taken to read each word. While numerous studies over the past thirty years have shown expectation-based effects on reading times driven by lexical, syntactic, semantic, pragmatic, and other information sources, there has been little progress in establishing the quantitative relationship between expectation (or prediction) and reading times. Here, by combining a state-of-the-art computational language model, two large behavioral data-sets, and non-parametric statistical techniques, we establish for the first time the quantitative form of this relationship, finding that it is logarithmic over six orders of magnitude in estimated predictability. This result is problematic for a number of established models of eye movement control in reading, but lends partial support to an optimal perceptual discrimination account of word recognition. We also present a novel model in which language processing is highly incremental well below the level of the individual word, and show that it predicts both the shape and time-course of this effect. At a more general level, this result provides challenges for both anticipatory processing and semantic integration accounts of lexical predictability effects. And finally, this result provides evidence that comprehenders are highly sensitive to relative differences in predictability - even for differences between highly unpredictable words - and thus helps bring theoretical unity to our understanding of the role of prediction at multiple levels of linguistic structure in real-time language comprehension.
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