Computational Models of Learning and Beyond: Symmetries of Associative Learning

Computational Models of Learning and Beyond: Symmetries of Associative Learning

Eduardo Alonso (City University London, UK) and Esther Mondragón (Centre for Computational and Animal Learning Research, UK)
DOI: 10.4018/978-1-60960-021-1.ch013
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The authors propose in this chapter to use abstract algebra to unify different models of theories of associative learning -- as complementary to current psychological, mathematical and computational models of associative learning phenomena and data. The idea is to compare recent research in associative learning to identify the symmetries of behaviour. This approach, a common practice in Physics and Biology, would help us understand the structure of conditioning as opposed to the study of specific linguistic (either natural or formal) expressions that are inherently incomplete and often contradictory.
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2. Psychological Models Of Associative Learning

The study of associative learning in Psychology has specialized in two sub-fields: Classical (Pavlovian) conditioning focuses on how “mental” representations of stimuli are linked whereas instrumental conditioning deals with response-outcome associations. It is agreed though that, at the most general level, their associative structures are isomorphic (Hall, 2002). In both procedures, changes in behavior are considered the result of an association between two concurrent events and explained in terms of operations of a (conceptual) system that consists of nodes among which links can be formed. Since research in associative learning has predominantly focused on classical conditioning, we will use it as our leading example.

At the risk of over-simplification, we can identify the main trends in classical conditioning according to two dimensions, namely, the mechanisms of the learning process and the way in which the stimuli are represented by the learning system. The former fuels the debate between stimulus-processing theories vs. connectionist models, exemplified in the competitive model of (Rescorla & Wagner, 1972) and the Standard Operating Procedures (SOP) theory (Wagner, 1981) respectively; the latter illustrates the distinction between elemental models (for instance, both Rescorla and Wagner’s and SOP) and configural approaches (e.g., Pearce, 1987).

Rescorla and Wagner’s model rests on a sum error term. The idea that all stimuli present in a trial compete for associative strength is at the heart of the model. It is precisely this characterizing feature that differentiates it from earlier models such as Hull’s (Hull, 1943). This assumption allows the model to explain phenomena such as blocking and conditioned inhibition, that is, phenomena that result from the interaction among different stimuli. Other assumptions of the model are path-independence (i.e., that the associative strength of a stimulus does not depend on its previous learning history), monotonicity (i.e., that learning and behavior are one and the same thing), that acquisition and extinction are opposite processes, and that the associability of the conditioned stimulus (CS) is fixed.

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