Optimal Processing Times in Reading: A Formal Model and Empirical Investigation

Optimal Processing Times in Reading: a Formal Model and Empirical Investigation Nathaniel J. Smith (njs@pobox.com) Department of Cognitive Science, 9500 Gilman Drive #515 La Jolla, CA 92093-0515 USA Roger Levy (rlevy@ling.ucsd.edu) Department of Linguistics, 9500 Gilman Drive #108 La Jolla, CA 92093-0108 USA Abstract noisy samples from which to (Bayes-optimally) average out the noise and extract the signal; if we are optimal perceptual discriminators then the number of samples we must gather (and thus how long we must wait) depends on the form of the signal, of the noise, and of our prior beliefs. (For one exam- ple of this approach in the context of word recognition, see Norris, 2006.) It seems unlikely, however, that the sensory system is to blame for all response delays; we are reminded every time we start up our computers that computation qua computation takes time. Furthermore, while such models seem plausible for visual perception, it is unclear how they might apply to, for instance, audition. We have reasonable control over how long we look at a scene, but very little control over how long we listen to an utterance. Yet, tasks using single auditorily presented words as stimuli find systematic variation in reaction time — and, in fact, these variations are similar to those observed in cor- responding visual presentation paradigms (Goldinger, 1996). This is one reason that we believe language to be a fruitful area in which to investigate alternative approaches to model- ing processing time as an optimal behavior. While language can be presented in the written modality, which is very con- venient for experimentation, the bulk of our exposure is to spoken language, and the spoken modality has primacy both evolutionarily and developmentally. To the extent, then, that sensory sampling approaches couched in the framework of optimal perceptual discrimination are implausible for spoken language comprehension, these approaches are unlikely to provide the full story for general language processing. On the other hand, language processing is highly practiced and very efficient, which suggests that some other kind of optimality approach would still be valuable. In this paper, we present a new model of optimal response time couched in a framework of optimal preparation that we believe may be more appropriate to domains such lan- guage processing in which we cannot always control time of sensory exposure. This model is motivated by the well- established fact that processing times in language compre- hension are probability-sensitive: in a given context, words which are more predictable are also read more quickly (e.g. Ehrlich & Rayner, 1981). This is intuitively sensible — cer- tainly we would prefer it to the reverse! — but it is, as yet, inadequately theorized. Our model explains this result as op- timal behavior under a cost function which trades off prepa- ration costs versus processing time; one would like to pro- It is widely known that humans can respond to events they ex- pect more quickly than to unexpected events, but we still have a poor understanding of why. Models exist that derive a relation between subjective probability and response time on the basis of optimal perceptual discrimination, but these models rely on the ability of the responder control over perceptual sampling of the environment, rendering them problematic for some do- mains, such as auditory language processing, in which there are nevertheless clear dependencies between probability and response time. We present a new model deriving the relation- ship between probability and reaction time as a consequence of optimal preparation. This model is valid under very gen- eral conditions, requiring only that the results of optimization are invariant across scale of input stimulus granularity. The model makes the strong prediction that response times should scale linearly with the negative conditional log-probability of the stimulus. We present evidence for this prediction in an analysis of an existing database of eye movements in the read- ing of naturalistic texts. Keywords: Optimal behavior; Language; Response time mod- eling; Surprisal; Sentence comprehension; Eye movements; Reading Introduction It takes time to perform computation using a physical device, and the human brain is such a device. While obvious, this point is worth revisiting in light of the recent surge of interest in rational models of optimal behavior (Chater et al., 2006; Todorov, 2004). Such models have provided elegant explana- tions for many aspects of behavior, but processing time pro- vides a particular challenge for this approach. In general, hu- mans respond to different stimuli within any given class with different speeds, and response times are a large part of the stock and trade of experimental cognitive psychology. From an optimality perspective, the difficulty is that it is unclear why the time to spend on performing a computation should ever be larger than the physical minimum. Yet, from a theo- retical point of view, response times seem like the perfect can- didate for an optimality approach, because they are so clearly relevant to evolutionary fitness. We are all real-time organ- isms who must react quickly and correctly in a wide variety of circumstances. So why are we still so much slower than we could be? The primary approach to these problems deployed within the Bayes-optimal framework has been to ascribe reaction times and other such delays to the sensory system. The argu- ment is that we require accurate information about the world to act, but our sensory system is noisy. Therefore, to ac- quire accurate information, we must wait and gather multiple