How stable and general is behavior once reached maximum learning? To answer this question and understand post-acquisition behavior and its related individual differences, we explore analytic models of Pavlovian conditioning extending the basic associative model of Hull (i.e., the Rescorla-Wagner model with just one cue) and propose three new models valid for individual data, which we argue to be quite natural. The first two are descriptive settings: (  i) a framework of dynamical models inspired by the classical mechanics of a particle in a given potential, which comprises Hull model and also a specific model encoding resistance to learning in the first few sessions followed by an over-optimal response peak ; (ii) the most direct stochastic extension of Hull model, characterized by the presence of stochastic noise; (iii) a theory where response fluctuations are described by quantum mechanics and based on the general framework of dynamical models (i) explaining the noise met in (ii) and giving characteristic predictions . We ran an unusually long experiment with 32 rats over 3960 trials, where we excluded habituation and other well-known phenomena as sources of variability in the subjects' performance. The best nonlinear regression to averaged data and 60\% of individual data is Hull's model, while for the remaining 40\% of the subjects the dynamical model (i) provides a better fit . The noise encountered in all individual responses is white, thus confirming the simplest version of model ( ii ) but standing in contrast with the colored-noise findings in human performance. Finally, data are compatible with theory (iii ), although experimental uncertainties dominate the result. On the other hand, data do not favor models with  a long-memory effect or  where response variability is solely described by a random fractal.
How stable and general is behavior once reached maximum learning? To answer this question and understand post-acquisition behavior and its related individual differences, we propose a psychological principle that naturally extends the basic associative single-cue Rescorla-Wagner model ( which may also be called Hull model) of Pavlovian conditioning to ( i) a framework of dynamical models predicting resistance to learning in the first few sessions followed by an over-optimal response peak . In turn, (ii) the theory can be further extended to describe response fluctuations by the laws of quantum mechanics. (iii) We also introduce an independent model characterized by the presence of a stochastic noise of cognitive origin . We ran an unusually long experiment with 32 rats over 3960 trials, where we excluded habituation and other well-known phenomena as sources of variability in the subjects' performance. There is weak to positive evidence that Hull model is the best nonlinear regression to averaged data only for a minority of the subjects , while its dynamical extension (i) can explain the totality of data . The noise encountered in all individual responses is white, thus confirming the simplest version of model ( iii ) but standing in contrast with the colored-noise findings in human performance. Finally, data are compatible with the quantum extension (ii ), although experimental uncertainties dominate the result. On the other hand, data do not favor models with (iv) a long-memory effect or (v) where response variability is solely described by a random fractal.
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