The Mechanics of Associative Change

The Mechanics of Associative Change M.E. Le Pelley (mel22@hermes.cam.ac.uk) I.P.L. McLaren (iplm2@cus.cam.ac.uk) Department of Experimental Psychology; Downing Site Cambridge CB2 3EB, England Abstract Rescorla (in press) investigated the change in associative strength undergone by cues A and B as a result of rein- forcement or nonreinforcement of an AB compound. Many leading theories of associative learning predict that if A and B are equally salient then the associative change expe- rienced by each should be the same regardless of their asso- ciative strength preceding AB trials. Rescorla explored this prediction for a compound composed of an excitatory A and an inhibitory B, using rats and pigeons as subjects. We repeated Rescorla’s experiment using human subjects and a causal judgment task, and obtained diametrically op- posite results to those of Rescorla’s earlier study. The im- plications of this finding are discussed with reference to a number of influential theories of associative learning. Introduction It has long been recognised that stimuli presented in com- pound can, and will, interact and compete for associative strength. This is powerfully demonstrated in the phenome- non of blocking (Kamin, 1969). This refers to the finding that the gain in excitatory strength accruing to a conditioned stimulus (CS), B, following reinforcement (+) of an AB compound is much reduced if cue A has previously been trained as being a good predictor of that outcome (uncondi- tioned stimulus, US). Learning does not simply progress with each cue independently. Instead the two cues seem to compete for a limited amount of associative strength. Such demonstrations of cue competition provided the motivation for the development of models that can deal with the issue of predictive redundancy in associative learning (e.g. Rescorla & Wagner, 1972; Mackintosh, 1975; Pearce, 1987). A common feature of these models is the idea that the magnitude of associative change depends in some way on the discrepancy (or error) between the current associative strength of the presented cues and the strength which the outcome (unconditioned stimulus, US) following these cues can support. Consider, for instance, the Rescorla-Wagner (1972) model (R-W), perhaps the most influential of all of these “error-correcting” theories: ∆ V A = α A β U S ( λ US − Σ V ) where ∆V A is the change in associative strength of cue A, α A and β US are rate parameters relating to the salience of cue A and the US respectively, λ US is the asymptote of condi- tioning supportable by that US, and ΣV is the summed as- sociative strength of all cues present on a trial. Hence R-W states that the error governing associative change for any cue on a trial is based on the combined associative strength of all cues present on that trial. This is essential to R-W’s ex- planation of blocking. On A+ trials, V A will increase, with A coming to predict the US. On AB+ trials, the error term for cue B (and also for A) will be (λ-{V A +V B }). But of course as a result of A+ training V A will already be high, and so the error term will be correspondingly small, such that any increase in V B will be only very small. Thus the R-W explanation of blocking crucially hinges on the idea that, when determining the associative change undergone by B, the associative strength of other cues present on the trial (A) is also considered. This use of a common error term governing associative change for all stimuli on a trial has important consequences. Rescorla (in press) noted that, in the absence of additional assumptions, it predicts that equally salient stimuli pre- sented together on a trial will undergo equal associative changes. This prediction holds true regardless of the associa- tive history of the cues in question. In a recent series of experiments, Rescorla (in press) in- vestigated this prediction in rats and pigeons (using maga- zine approach conditioning and autoshaping procedures re- spectively). He looked at the particular instance of an AB compound composed of an excitatory A and an inhibitory B. Specifically, he was interested in the associative change un- dergone by A and B as a result of either reinforcement or nonreinforcement of the AB compound. If we assume that A and B are of equal salience (ensured by counterbalancing) then, as a result of using a common error term, R-W is con- strained to predict that both A and B will show equal asso- ciative change following either AB+ or AB- trials. Consider, for example, the AB+ condition. If A and B are equally sali- ent, then α A =α B . Since both are presented with the same US, β will also be equal when calculating ∆V A and ∆V B according to equation (1). And finally, the error term for both A and B will be (λ-{V A +V B }). Hence, given that all the terms in the calculation for ∆V A and ∆V B are identical, Rescorla-Wagner must predict that on AB+ trials, ∆V A =∆V B . This prediction of equal associative change holds true despite the fact that A (an excitor) and B (an in- hibitor) begin these trials with very different associative strengths (V A > 0, V B < 0). The problem with investigations such as this is one of how to assess the magnitude of associative change for two stimuli that differ in their “baseline” associative strength. It would be unwise to make any strong assumptions with re- gard to mappings between associative strength and measur- able performance, and yet without such mappings we cannot be sure that two equal-sized changes in performance at differ- ent points on the performance scale represent equal-sized changes in associative strength.