0 # correct cells

cl

c2

c3

c4

c5

T4

2 W

Q current slot

filled (next state) slot

em pty slot

Figure 3.5: T h e search table is p artially filled w ith th e cu rren t state and th e resu ltin g possible next states. See te x t for detail.

D uring th e second tim e step th e changes in th e num ber of active correct an d spurious cells are calculated for each ta b le en try w ith a tim e stam p equal to one (c u rre n t s ta te ). Note th a t th e tim e stam p clearly labels th e set of tab le entries th a t are possible at th e prior tim e step. If a th resh o ld applied a t th e n th step re su lts in a num ber of correct and spurious cells th a t is already in th e ta b le th e n th e tab le entry is not changed.

In th e th ir d tim e step, exactly th e same process is carried out except th a t th e c u rre n t sta te s are th e ones th a t have th e tim e stam p of two and th e newly calcu lated s ta te s have tim e stam p three, and so on.

rions cells w ith tim e stam p t. Among possible values of th e threshold, four th resh o ld s T 1 . . A p roduced th e next expected states th a t have n o t yet been arrived a t previously. T h e four states, [ ( c l,0), (c 2 ,s l), (c4,s4), (c5,s5)], are filled w ith relevant inform ation described in tab le 3.1. They all have th e same tim e stam p , namely, t + 1 and are linked to th e cu rren t sta te using correct

an d spurious a ttrib u te s of th e entry. T his process is carried out u n til fifteenth tim e step.

T h e optim al th resh o ld sequence is found by identifying th e tab le en try th a t has th e highest q uality value. T he associated th resh o ld sequence can be o b tain ed by back-tracking th e correct an d spurious value in th e tab le entries (th e technique is explained in chapter 2). In order to sh orten th is search process we did no t evaluate threshold sequences th a t are guaranteed to resu lt in lower q u ality recall. More specifically, w ith each num ber of spurious cells (row) in th e tab le we only evaluated th e th resh o ld s for th e e n try which had th e largest num ber of correct cells, or equivalently we evaluated a t m ost one sta rtin g p o in t p e r row of th e table.

3.4

R esu lts

T h e tab le search algorithm is im plem ented for th e netw ork as described in ch ap te r 2. T h e storage space required to m a in ta in th e search tab le is IV x

2 W X s i z e o f {entry) bytes. T he size of each e n try in th e tab le is 20 bytes,

w hen each a ttrib u te occupies 4 bytes. T he num b er of active cells in each sto red p a tte rn {W) of th e tested netw ork is 200. Therefore, th e to ta l am ount of storage occupied by th e search table is 1.6 M bytes, which is m anagable.

Figure 3.6 com pares th e expected value of recall perform ance using th e th resh o ld in g stra teg y proposed by G ardner-M edw in w ith th a t found using

rho=0.2 T nJ 3 O 0.8 - 0.6 - 0.4 0.2 Modified_Present rho=0.3 T

g

0 0.2 0.4 0.6 0.8 Initial seed size (wo/W)

Figure 3.6: A nalysis of th e expected value of recall perform ance (figure 3.2) is superim posed w ith th e optim al thresholds identified by tab le search algorithm (P resen t). T h e plot shows th a t th ere is a sequence of thresholds th a t results in far higher recall quality. In order to make a d irect com parison, th e exhaustive search is re stric ted to contain no spurious cells in th e final stage of recall.

th e thresh o ld s from th e table search m eth o d. T his figure shows th a t th e table based search resu lts in higher recall quality th a n G ardner-M edw in’s th resh o ld ­ ing stra te g y (G ardner-M edw in 1976), suggesting th a t th e re are b e tte r th re sh ­ old sequences. T he recall perform ance p red icted by th e tab le based search is consistently higher th a n G ardner-M edw in’s thresh o ldin g strategy, b u t th is is p a rtic u la rly tru e if th e recall is in itia te d using a seed th a t is a sm all fraction of th e sto red p a tte rn .

In order to te st th e perform ance p red icted by th e p resen t model, we searched th ro u g h th resh o ld sequences w ith a sim u lated netw ork. It is of course im pos­ sible to evaluate all threshold sequences w ith a full sim ulation of th e network. In stead , a t each step in the recall process w ith a sim ulated netw ork th e five th re sh o ld settin gs w ith highest quality are rem em bered. All possible threshold

rho=0.2 rho=0.3 03 3 o 1 0.8 0.6 0.4 theory --- thecry-ns --- simulation ... simuiation-ns ... 0.2 0 0.2 0.4 0.6 0.8 1 0

Initial seed size (wo/W)

CO 3 o 1 0.8 0.6 0.4 theory --- theory-ns --- simulation ... simulation-ns ... 0.2 0 0 0.2 0.4 0.6 0.8 1

Initial seed size (wo/W)

Figure 3.7: C om parison betw een expected p erform ance an d sim ulation results.

N = 5000,72 = 500,VF = 200. In th is grap h th e resu lts of th e search for optim al th resh o ld sequence, based on theory, are com pared w ith sim ulation resu lts. In one case (theory-ns and sim ulation-ns) th e com parison is betw een recall sequences which end w ith no spurious cells active, an d in th e o th er case

(th eo ry and sim ulation) the end p o in t w ith b e st final qu ality is selected.

settin g s are te sted for each of these five can d id ates, an d th e b est five a t th e next step are retain ed . The num ber of progressive recall steps evaluated is also lim ited to five, resulting in Zli=o possible end p oints. T h e re su lt of th is sim ulation m atches well w ith th e theoretical p rediction. It is shown, com pared to th e th eo retical prediction, in Figure 3.7.

3.5

C on clu d in g rem arks and su m m a ry

In th is stu d y , it is shown th a t th e prior th eo ry overestim ated th e perform ance of th e p rio r progressive recall strategy. Also, it is shown, w ith b o th an ex­ tension to th e theory and by com puter sim ulation of netw orks, th a t a b e tte r th resh o ld sequence exists. In b o th cases, th e optim al thresho ld in g strateg y included several steps w ith m any active spurious cells.

M ethods to identify optim al th resh o ld sequences have been proposed and im plem ented in th is chapter and th e previous ch ap ter.

C h a p ter 4

E v a lu a tio n o f th e lin ear