Hypothetical response patterns

In each discrimination learning stage of the set-shifting task, only one stimulus (e.g., a specific odour or medium) is associated with the food reward. A rat must learn to find the association between this stimulus and the food reward based on the feedback (i.e., either found food or not found food) from its choice of bowl on each trial. However, before the rats have learned the correct stimulus, there is no reason to believe that their choice of bowl is random. Rather, a rat might use various response patterns based on the stimulus configuration. There are at least two classes of external information about the bowls that the rat might use: spatial and perceptual. If a rat chooses a bowl based on the spatial locations of bowls rather than the stimuli in the bowls, then the rat would be using a spatial response pattern for bowl choice. Instead, if the rat chooses a bowl based on the stimuli (e.g., digging medium or odour) in the bowls, the rat would be using a perceptual response pattern for bowl choice. The plausible spatial and perceptual response patterns for bowl choice in the 7-stage task are listed below.

Spatial response patterns:

 Spatial alternation: if choosing the left (or right) side at the last trial,

choose the right (or left) side for the current trial.

 Spatial perseveration: return to the same location as the previous trial, no

matter whether the location is on the left or on the right. This would capture a side bias (left or right).

 Win-stay: if rewarded at the last trial, choose the same location for the

current trial; otherwise choose the alternative location.

 Win-shift: if rewarded at the last trial, choose the alternative location for

the current trial; otherwise, choose the same location.

Perceptual response patterns: there are four different stimuli combined across the two bowls, assuming no other perceptual characteristics are used given that the bowls are standardised: two odours (O1 and O2) and two media (M1 and M2). A

rat may choose a bowl based on one of the following perceptual response patterns:

 M1: choose the bowl which contains M1.  M2: choose the bowl which contains M2.  O1: choose the bowl which contains O1.  O2: choose the bowl which contains O2.

Note that different perceptual stimuli may be used in different stages; therefore perceptual response patterns will be specific to particular stages. In comparison, the above four spatial response patterns may appear in any stage. Also note that here, only the simple response patterns were considered. More complex response patterns (e.g., the combination of O1 and M2) were not included, although they could be added if necessary. In addition, while the literature used the term rules to describe the above

response patterns, we believe that response pattern is a more appropriate term, because (1) we can never know for sure what rules rats used, (2) even whether rats actually used any rules during learning, and (3) rats might make a selection to exclude a possibility even though they had a tentative rule in mind (e.g., a rat chose cumin maybe because it wanted to confirm it was incorrect rather than thinking cumin was correct).

Because we cannot know for sure which response pattern was actually used at each trial for each rat, we can only estimate the probability that the rat’s choices match a given response pattern. More formally, we apply Bayes’ rule to estimate the posterior probability of the following eight hypotheses regarding the possible response patterns at each trial:

 Hypothesis 1 (h₁), or spatial alternation hypothesis: the rat uses spatial alternation response pattern to choose bowls.

 Hypothesis 2 (h₂), or spatial perseveration hypothesis: the rat uses spatial perseveration response pattern to choose bowls.

 Hypothesis 3 (h₃), or spatial win-stay hypothesis: the rat uses spatial win- stay response pattern to choose bowls.

 Hypothesis 4 (h₄), or spatial win-shift hypothesis: the rat uses spatial win- shift response pattern to choose bowls.

 Hypothesis 5 (h₅), or M1 hypothesis: the rat uses perceptual M1 response pattern to choose bowls.

 Hypothesis 6 (h₆), or M2 hypothesis: the rat uses perceptual M2 response pattern to choose bowls.

 Hypothesis 7 (h₇), or O1 hypothesis: the rat uses perceptual O1 response pattern to choose bowls.

 Hypothesis 8 (h₈), or O2 hypothesis: the rat uses perceptual O2 response pattern to choose bowls.

Note that in the SD stage, only two (rather than four) stimuli appear in the bowls. Therefore, for the SD stage, there are in total only six hypotheses. On the other hand, more hypotheses would be generated if more complex response patterns were considered. However, Bayesian estimate of these eight hypotheses already provides much richer information compared to the hypothesis testing approach, which evaluates only one hypothesis linked to the random responding associated with the null hypothesis. Also, the eight hypotheses are used as a proof of concept to establish the utility of Bayesian analysis applied to learning. Other hypotheses could be added to the Bayesian analysis with limited effort if necessary. In addition, we assume that the eight hypotheses are disjointed (mutually exclusive of each other).This assumption is reasonable because the rat cannot simultaneously use two or more response patterns to make choice in a trial. In other words, considering one hypothesis being true would be exclusive of all the other seven hypotheses being true. I would like to clarify that such independence assumption describes relationship between the hypotheses in the same trial. Such assumption does not exclude the potential

relationships between hypotheses across trials. For example, if rats would try spatial response patterns first and then stimulus-based response patterns, the priors of stimulus-based hypotheses at current trial might be affected by how likely the rat tries both the stimulus-based response pattern and spatial response patterns from the previous trial. We did not explore this possibility because (1) we were exploring to begin with and this add yet another free variable to the analysis and (2) Occam’s razor – until we have concrete data that suggests this on balance we should assume a simpler mechanism. From the observation of Bayesian analysis results on multiple rats’ data, we found no evidence for such spatial-stimulus circle of patterns. Note as well that there are other potential dependences between the hypotheses across trials, for instance the rats always went with odour first and then medium. All such potential cross-trial dependence relationship does not contradict with the within-trial independence relationship between hypotheses.