Eye-movements in reading exhibit frequency spillover effects: fixation durations on a word are affected by the frequency of the previous word. We explore the idea that this effect may be an emergent property of a computationally rational eye-movement strategy that is navigating a tradeoff between processing immediate perceptual input, and continued processing of past input based on memory. We present an adaptive eye-movement control model with a minimal capacity for such processing, based on a composition of thresholded sequential samplers that integrate information from noisy perception and noisy memory. The model is applied to the List Lexical Decision Task and shown to yield frequency spillover-a robust property of human eye-movements in this task, even with parafoveal masking. We show that spillover in the model emerges in approximately optimal control policies that sometimes process memory rather than perception. We compare this model with one that is able to give priority to perception over memory, and show that the perception-priority policies in such a model do not perform as well in a range of plausible noise settings. We explain how the frequency spillover arises from a counter-intuitive but fundamental property of sequenced thresholded samplers.
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