Neuroscience, evolution, and culture
Tag Archives: mathematical model
2015/01/02Posted by on
A few weeks ago I had the good news that our paper on the comparator model of associative learning had been accepted in Psychological Review. This is my first published paper co-authored with by an undergraduate student, Ismet Ibadullaiev, which makes me even happier. The paper (I put up an unofficial copy on my Papers page) deals with a very interesting model of associative learning in which most of the interesting phenomena are generated as memories are retrieved, rather than when memory are stored as assumed by most mainstream theories of associative learning (e.g., the Rescorla-Wagner model and its derivatives).
Our conclusion, unfortunately, is that the theory makes a number of paradoxical predictions that are hard to reconcile with empirical data on learning. For example, it predicts that, in many cases, animals would not distinguish which of two stimuli is most associated with a reward (they do distinguish, of course), or that they should learn equally about faint and intense stimuli (in reality, animals learn preferentially about intense rather than faint stimuli).
These problems have been hard to recognize because the theory had been studied exclusively by intuition and computer simulation. Both are fine tools, but they do run into trouble. The predictions of comparator, as it turns out, vary greatly depending on the value of a few parameters, and our intuition is not well equipped to reason about the non-linear effects that abound in the theory. Simulations give us correct results, but only for the parameter combinations we simulate. We have been fortunate enough to realize that one could write down a formal mathematical solution to the theory. With this solution it became much easier to see the big picture and actually prove what the theory can or cannot do.
I enjoyed working with comparator theory because of its distinct flavor – as hinted above, it’s rather different from other learning models – and because of the many surprises we had while exploring its predictions. Although we found what appear to be serious flaws in the theory, these might be more in its mathematical implementation than in its core concepts. The ideas that memory retrieval is an important factor in associative learning, and that stimulus-stimulus associations are more important than other models acknowledge, may well be worth pursuing. But the formulae that translate these ideas into a testable model will surely need to be revised.