This week saw a big change of direction for the project. With the higher capacity working memory model completely debugged, I expected the beginning of this week to be data analysis, before moving on to a bigger, better model. But the results we saw made us reconsider our entire approach to the problem of serial recall phenomena.
The working memory content never surpassed two items, even with the theoretical capacity of four. How did this happen? It was due to the probability of spontaneously forgetting any stimulus. Consider the following situation:
At state s, the working memory content consists of [stimulus 2, stimulus 3]. Stimulus 1 is presented, and the agent decides to replace the third item of working memory. To unpack the situation, we can take a look at the possible outcomes and their respective probabilities.
So what are the possible outcomes? Well, any one of the 6 stimuli might be presented next, and there are three possible working memory states: the agent might not forget anything in which case the working memory would contain [stimulus 2, stimulus 3, stimulus 1], or either of the original memories might be forgotten, in which case the working memory would consist of either [stimulus 3, stimulus 1] or [stimulus 2, stimulus 1]. That’s a total of 18 possible outcomes. But, let’s say the probability of the same stimulus being presented twice in a row is 0. Now, we have 15 possible outcomes. The model assumes that each of these scenarios has an equal probability. In this case, the possible outcomes all have a probability of 1/15. This gives a ⅔ chance of having two items in working memory in the next state.
The fact that only two items are ever stored in working memory made it clear that it was time to reevaluate our initial assumptions about memory loss. Especially given the fact that evidence as to whether working memories decay temporally is mixed (Peterson and Peterson 1959; Oberauer, 2008). It could be that memory loss in such tasks is primarily due to replacement. Additionally, as the model is now, you are more likely to forget a given stimulus the longer it is stored in working memory, because of the cumulative effect of forgetting probability at each time step. This is not necessarily reflective of actual properties of working memory. We needed to rethink forgetting probabilities.
Paul and I arranged a meeting to discuss exactly this. Aside from designing forgetting probabilities to generate the primacy and recency effects, there was no clear way to find logical values. Furthermore, serial recall may not be a fruitful area to apply optimal control theory because the concept of optimizing performance is not meaningful in this context. Success in this task is independent of which memories are retained, because as long as the agent fills its working memory, performance will be the same. It makes more sense, on the other hand, that working memory might be optimized to natural human behaviors like language processing. Phenomena like primacy and recency could be byproducts of an optimal solution to a different task. We were left with two options: moving to a dual store model of working memory, or ditching serial recall tasks and using a more behaviorally relevant task as a model.