On the blessing of abstraction.

The "blessing of abstraction" refers to the observation that acquiring abstract knowledge sometimes proceeds more quickly than acquiring more specific knowledge. This observation can be formalized and reproduced by hierarchical Bayesian models. The key notion is that more abstract layers of the hierarchy have a larger "effective" sample size, because they combine information across multiple specific instances lower in the hierarchy. This notion relies on specific variables being relatively concentrated around the abstract "overhypothesis". If the variables are highly dispersed, then the effective sample size for the abstract layers will not be appreciably larger than for the specific layers. Moreover, the blessing of abstraction is counterbalanced by the fact that data are more informative about lower levels of the hierarchy, because there is necessarily less stochasticity intervening between specific variables and the data. Thus, in certain cases abstract knowledge will be acquired more slowly than specific knowledge. This paper reports an experiment that shows how manipulating dispersion can produce both fast and slow acquisition of abstract knowledge in the same paradigm.