Rational eye movements in reading combining uncertainty about previous words with contextual probability

Rational eye movements in reading combining uncertainty about previous words with contextual probability Klinton Bicknell & Roger Levy {kbicknell, rlevy}@ling.ucsd. edu UC San Diego Department of Linguistics 9500 Gilman Drive #108, La Jolla, CA 92093-0108 USA Abstract While there exist a range of sophisticated models of eye move- ments in reading, it remains an open question to what ex- tent human eye movement behavior during reading is adaptive given the demands of the task. In this paper, we help to an- swer this question by presenting a model of reading that cor- rects two problems with a rational model of the task, Mr. Chips (Legge, Klitz, & Tjan, 1997). We show that the resulting model is closer to human performance across two measures, support- ing the idea that many components of eye movement behavior in reading can be well understood as a rational response to the demands of the task. Keywords: computational modeling; rational analysis; eye movements; reading Introduction Choosing when and where to move one’s eyes during reading is one of the most complicated skilled tasks humans perform. While there are a number of computational models achiev- ing good numerical fits on eye movement data from read- ing (e.g., Reichle, Pollatsek, & Rayner, 2006; Engbert, Nuth- mann, Richter, & Kliegl, 2005), it is still unclear to what ex- tent the complex behaviors observed are rational responses to the demands of the problem itself and to what extent they arise from the idiosyncrasies and restrictions of human cog- nition. Legge, Klitz, and Tjan (1997) started to answer this question with Mr. Chips, a model which predicts eye move- ments that approximate an optimal solution to one formaliza- tion of the task of reading. Legge et al. pointed out that their model’s behavior exhibits a number of patterns also found in human reading, providing evidence for understanding those behaviors as rational responses to the task. Despite its suc- cess, however, the Mr. Chips model oversimplifies two im- portant aspects of the problem of reading, and also has empir- ical problems accounting for human reading behavior in two domains. In this paper, we propose a model extending Mr. Chips that removes these two oversimplifications to make the model’s task more similar to that faced by humans. We show that the resulting model also remedies the two empirical defi- ciencies in Mr. Chips, further supporting the notion that many aspects of human reading behavior can be explained as ratio- nal responses to the demands of reading. The essentials of the problem of making eye movements in reading are determining how long to leave the eyes in a given spot and – when a reader decides to move them – where to go. These decisions are made sequentially to pro- duce the alternating sequence of fixations (relatively stable periods) and saccades (movements) that characterizes the eye movement record. The past 30 years have seen a prolifera- tion of experimental studies investigating this topic, which have answered a number of low-level questions such as the nature of the perceptual span and constraints on saccade la- tency as well as questions concerning the relationship be- tween eye movements and higher-level cognitive processes such as the effect of word frequency and predictability (see Rayner, 1998 for an overview). Sophisticated computational models have been developed based on these findings, the most well-known of which are E-Z Reader (Reichle, Pollat- sek, Fisher, & Rayner, 1998; Reichle et al., 2006) and SWIFT (Engbert et al., 2005). Both E-Z Reader and SWIFT assume that lexical processing (or word recognition) is the primary driver for eye-movements in reading, and both have enjoyed considerable success, in large part because they achieve very good fits to eye movement data from reading in a number of contexts, using a relatively small number of parameters. De- spite their empirical strength, they fail to illuminate the rea- son why human reading behavior looks the way it does in one crucial respect – the extent to which it resembles a rational response to the problem posed by reading. One leading approach for answering such questions is that of rational analysis (Anderson, 1990), a paradigm in which one formalizes the goals and cognitive and physical con- straints relevant to a problem and develops a model of optimal behavior under those condition. To the extent that the behav- ior of the model is similar to that of humans, this provides a new way of understanding the reason why human behavior looks the way it does – it is the best way to solve the problem. The relationship between rational models and models such as E-Z Reader and SWIFT is well understood in terms of Marr’s (1982) levels of analysis. Marr distinguishes three levels of mutually-constraining analyses that can be performed on cog- nitive processes: the computational level, which specifies the nature of the computation being performed, the information relevant to solving it, and the way to combine that information to solve it; the algorithmic level, which specifies the represen- tation for the input and output and the algorithm by which the agent goes about solving it; and the implementational level, which specifies how the representations and algorithm are re- alized neurally. In these terms, rational models generally pro- vide answers at the computational level of analysis. Models such as E-Z Reader and SWIFT help us to understand the al- gorithmic level, but cannot answer questions about the extent to which human reading is rational. Legge et al. (1997) presented a computational level analy-