Copyright 2007 by the American Psychological Association 0097-7403/07/$12.00 DOI: 10.1037/0097-7403.33.3.191
Learning About Environmental Geometry: An Associative Model
Noam Y. Miller and Sara J. Shettleworth
University of Toronto
K. Cheng (1986) suggested that learning the geometry of enclosing surfaces takes place in a geometric module blind to other spatial information. Failures to find blocking or overshadowing of geometry learning by features near a goal seem consistent with this view. The authors present an operant model in which learning spatial features competes with geometry learning, as in the Rescorla–Wagner model. Relative total associative strength of cues at a location determines choice of that location and thus the frequencies of reward paired with each cue. The model shows how competitive learning of local features and geometry can appear to result in potentiation, blocking, or independence, depending on enclosure shape and kind of features. The model reproduces numerous findings from dry arenas and water mazes. Keywords: spatial learning, geometric module, Rescorla–Wagner model, associative learning, water maze
Cheng (1986) was the first to show that animals can use the geometry of an enclosure to locate a hidden goal. In a working memory task, he found that distinctive corner panels did not prevent rats from learning about the shape of a rectangular enclosure and that rats sometimes ignored the panels and searched for a hidden reward at the diagonally opposite, geometrically identical, corner of the enclosure, dubbed the rotational corner (see Figure 1). Cheng concluded that shape parameters of the enclosure are learned separately from featural information in a specialized geometric module. Later studies have shown that, in a reference memory version of Cheng’s task, features are also eventually learned (e.g., Cheng, 1986, Experiments 2 and 3; Wall, Botly, Black, & Shettleworth, 2004). Many other species, including fish, birds, monkeys, and human children, learn geometry in a similar way (see review in Cheng & Newcombe, 2005). Studies of geometry learning raise two essentially separate issues. One is, what is encoded in geometry learning? This debate has centered on whether animals extract some global parameter of a space, such as its principal axis, or use local geometric features, such as sizes of angles and sides (see Cheng & Gallistel, 2005). Here we focus on the other fundamental issue in the area: How does learning based on the hypothesized geometric module interact with learning based on other spatial cues? In the most recent version of the geometric module hypothesis, Cheng and Newcombe (2005; see also Cheng, 2005b) suggested several interpretations for the modularity of geometric information. Rather than
Noam Y. Miller and Sara J. Shettleworth, Department of Psychology, University of Toronto, Toronto, Ontario, Canada. This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada to Sara J. Shettleworth. It formed part of a master’s thesis submitted to the Department of Psychology, University of Toronto. We thank Ken Cheng and Robert Rescorla for comments on an earlier version of the article and John Pearce for his helpful comments. Correspondence concerning this article should be addressed to Noam Y. Miller, Department of Psychology, University of Toronto, 100 St. George Street, Room 4020, Toronto, Ontario, M5S 3G3 Canada. E-mail: firstname.lastname@example.org 191
being entirely separate from processing of features, geometry could combine with featural information in memory or in determining performance. Pearce, Ward-Robinson, Good, Fussell, and Aydin (2001) were apparently the first to point out that reliance on geometric cues for learning the location of a goal, even in the presence of more informative features, implies that geometry and...