Mind, Body, World- Foundations of Cognitive Science, 2013a

theories have proposed that a geometric module guides reorienting behaviour
(Cheng, 1986; Gallistel, 1990).
The existence of a geometric module has been proposed because different kinds
of results indicate that the processing of geometric cues is mandatory. First, in some
cases agents continue to make rotational errors (i.e., the agent does not go to the
goal location, but goes instead to an incorrect location that is geometrically identical
to the goal location) even when a feature disambiguates the correct corner
(Cheng, 1986; Hermer & Spelke, 1994). Second, when features are removed following
training, agents typically revert to choosing both of the geometrically correct
locations (Kelly et al., 1998; Sovrano et al., 2003). Third, when features are moved,
agents generate behaviours that indicate that both types of cues were processed
(Brown, Spetch, & Hurd, 2007; Kelly, Spetch, & Heth, 1998).
Recently, some researchers have begun to question the existence of geometric
modules. One reason for this is that the most compelling evidence for claims
of modularity comes from neuroscience (Dawson, 1998; Fodor, 1983), but such
evidence about the modularity of geometry in the reorientation task is admittedly
sparse (Cheng & Newcombe, 2005). This has led some researchers to propose
alternative notions of modularity when explaining reorientation task regularities
(Cheng, 2005, 2008; Cheng & Newcombe, 2005).
Still other researchers have explored how to abandon the notion of the geometric
module altogether. They have proceeded by creating models that produce the
main findings from the reorientation task, but they do so without using a geometric
module. A modern perceptron that uses the logistic activation function has been
shown to provide just such a model (Dawson et al., 2010).
The perceptrons used by Dawson et al. (2010) used a single output unit that,
when the perceptron was “placed” in the original arena, was trained to turn on to
the goal location and turn off to all of the other locations. A set of input units was
used to represent the various cues—featural and geometric—available at each location.
Both feature cues and geometric cues were treated in an identical fashion by
the network; no geometric module was built into it.
After training, the perceptron was “placed” into a new arena; this approach
was used to simulate the standard variations of the reorientation task in which geometric
cues and feature cues could be placed in conflict. In the new arena, the perceptron
was “shown” all of the possible goal locations by activating its input units
with the features available at each location. The resulting output unit activity was
interpreted as representing the likelihood that there was a reward at any of the locations
in the new arena.
The results of the Dawson et al. (2010) simulations replicated the standard reorientation
task findings that have been used to argue for the existence of a geometric
module. However, this was accomplished without using such a module. These
194 Chapter 4