In Asa H (Trans. Kansas Acad. Sci., vol. 109, pg 159, 2006) a similarity measure (usually a vector dot product) is used to decide if an input vector, IN, falls into some category, Ini. If the dot product of IN with Ini > ThA (some threshold value) then IN is a member of category i.
One can add a second threshold, ThB < ThA and if IN dot Ini < ThB then IN is not a member of category i.
If, however, ThB < IN dot Ini < ThA then we can look more closely at the degree of match between IN and Ini. For instance, we can tune the time warping or spatial transformations like scaling, shifting, rotating, etc. to see if a better match is possible (>ThA).
*Various sorts of attention have been employed in Asa H. As the input comes in as a function of time we may stay with the currently active case/category, i , so long as the match remains strong enough (similarity measure exceeds some threshold TH). We can avoid search until the match drops below TH. This is a sort of attention (to category i) present in Asa H 2.0 lite (see my blog of 10 Feb. 2011)