Probability Learning by Perceptrons and People
In 2008, Comparative Cognition & Behavior Reviews was kind enough to publish a monograph that explored the relationship between simple artificial neural networks called perceptrons and models of associative learning (Dawson, 2008). That work attempted to use perceptrons as a medium in which associative learning could be examined from the perspective of cognitive science. To do so, it presented a number of formal analyses as well as the results of a number of computer simulations of associative learning. It made the interesting discovery that two systems (i.e., perceptrons and the Rescorla-Wagner model) could be formally equivalent and at the same time produce different behavioral results. This “perceptron paradox” was dealt with by arguing that the equivalence between the two systems was at what cognitive scientists call the computational level of analysis, but differences between formally equivalent systems could still exist when their formal theories were brought to life at a different level, the algorithmic level of analysis.
One consequence of that monograph was my involvement in a research project with Marcia Spetch, Debbie Kelly, and my student Brian Dupuis that attempted to use perceptrons to model the behavior of biological agents in the reorientation task (Dawson, Kelly, Spetch, & Dupuis, 2008, 2010; Dupuis & Dawson, 2013a, 2013b). During this work, I (too slowly) realized that what the perceptrons were really doing was learning about the probability of reward associated with signals carried by cues. This led to some early explorations of the behavior of perceptrons in simple contingency experiments (Dawson & Dupuis, 2012; Dawson, Dupuis, Spetch, & Kelly, 2009). Eventually I started to explore the behavior of perceptrons when they learned about uncertain environments—environments in which an input stimulus does not signal an outcome with certainty but only signals the outcome with a certain degree of probability. The current monograph describes the results of this exploration.
The current monograph is a sequel to Dawson (2008). It presents computational and algorithmic treatments of how perceptrons adapt to uncertainty. It reports formal analyses that relate perceptron structures to Bayesian probability and logistic regression. It describes the results of experiments that investigate what perceptrons learn when there is not a one-to-one relationship between stimuli and responses. It also details the results of a study that explores human probability learning in a variety of conditions and relates human performance to that of perceptrons. All of these results suggest that both perceptrons and people behave as if they are naive Bayesians, at least in the basic kind of task studied here. The current monograph also serves as a case study in synthetic psychology, an approach that involves building simple systems and then studying their behavior in a variety of interesting environments. I have long viewed artificial neural networks as a medium in which this synthetic approach can be pursued (Dawson, 2004). The various approaches described in the chapters that follow are attempts to demonstrate the utility of the synthetic approach for the study of probability learning. Finally, the current monograph relates a specific topic (how associative systems adapt to uncertainty) to a variety of other literature related in one way or another to the evolution of cognitivism in psychology. These include cybernetics, information theory, probability theory, systems theory, statistical inference, decision theory, and the cognitive psychology of category learning. Some of the core ideas in these theories appear repeatedly as one studies the cognitive science of associative learning. I hope that the current monograph illustrates the rich interrelationships between the psychology of associative learning and these other fields.