T able-based search

It is now possible to evaluate th e expected num bers of nex t active correct cell and spurious cell, given the current sta te of th e netw ork. Moreover, using th e form alism defined in th e previous section, it is possible to calculate th e expected s ta te of th e netw ork a t tim e t, if th e in itial in p u t to th e netw ork and th e th re sh o ld sequence are given. A table-based search algorithm is developed to look for optim al netw ork perform ance from th e th eo retical calculations of expected perform ances.

T h e search is carried out by constructing a two dim ensional ta b le (the search ta b le ) th a t stores th e sh o rtest sequence of thresholds required to arrive at a p a rtic u la r num ber of correct and spurious cells. T he num ber of rows and colum ns in th e search table are set by th e range of possible num bers of correct and spurious cells. T he num ber of correct cells ranges from zero to W an d th e range of spurious cells is from zero to 2 W (See figure 3.4). A larger num ber of spurious cells is likely to lead to unsuccessful recall.

T h e table-based search algorithm reads an d w rites d a ta from th e table. E n tries of th e tab le are indexed by cor and spur, corresponding to th e num ber of correct cells and th e num ber of spurious cells, respectively. For conve-

0 1 c/3

S 2

0

# correct cells

1 2

3

4

W

2W

F igure 3.4: A schem atic diagram of th e search space in table-based search. For each n u m b er of correct cells and spurious cells, th e re is an en tity (slot) to hold a ttrib u te s listed in table 3.1 Each e n tity in th e ta b le is initialised to zero (d ash ed ro u n d ed box). Hence there is no link w ith th e e n tity at th e s ta rt of th e algorithm .

correct T he num ber of correct cells in th e previous tim e step. T his value is used as an index to po in t to th e previous en try in th e table.

spurious T he num ber of spurious cells in th e previous tim e step. This value is used as an index to p o in t to th e previous e n try in th e table.

threshold T hreshold value applied in th e previous tim e step to o b tain the current configuration (i.e. cor an d spur).

stage T he tim e step (integer value) a t which th e e n try was m ade into th e table.

X Given th e previous configuration, x is th e p ro b ab ility th a t a correct cell fires w ith th e specified threshold.

y Given th e previous configuration, y is th e p ro b ab ility th a t a spurious cell fires w ith th e specified threshold.

Table 3.1: tab le caption

nience, th e en try w ith cor correct cells and spur spurious cells is represented as (cor,spur). Each en try of th e tab le contains th e d a ta shown in ta b le 3.1.

T h e essential aim of th e algorithm is to identify th e sh o rtest p a th betw een a s ta te (goal state) an d th e in itial state. T his is accom plished by linking th e e n try in th e search tab le th a t corresponds to th e sta te an d th e in itia l state via th e entries th a t represents th e in term ed iate recall states of th e netw ork. S ta rtin g from th e in itial state, tab le entries are com pleted for th e expected resu lts of applicable thresholds. T he details are as follows.

Each ta b le en try is initialised to zero (figure 3.4). A t th e first tim e step each possible threshold value and th e resu ltin g (expected) netw ork s ta tu s are co m p u ted an d stored in the tab le w ith a tim e stam p of one. O nly integer th re sh o ld values are tested since the n et in p u t to a neuron is necessarily an integer. If two thresholds result in th e sam e num ber of active correct and spurious cells th en th e first threshold value is kept in th e table.

0