Bernal S D_2010.pdf - University of Plymouth

4.4. FEEDFORWARD PROCESSING
(he simultaneous coincidence of the features in the afferent nodes, as proposed by George and
Hawkins (2009). Finally, the weight matrix for each S2 prototype is approximated by the CPT
p{a\s2).
S2b>n^n^szJ'si=^^V {-P - ||C1{6„.„,.,1 - n«||^)
fc,j,,.V, k,
where the indices are given by Equations (4.3) to (4.5),
Similarly, the invariance operation in HMAX i.s approximated u.sing belief propagation as shown
in liquation 4.9. The approximation to ihe max operation is emiwdded in the ^i(52) output
messages to S2 generated using the weights in the CPT P{C\\S2), which sum over the CI
features of the same group. In order to make this possible, the most common SI states and
locations have previously been combined in the CI node states through the CPT /^(Sl|Cl) (see
r'igures 4.7 and 4.9). In this sense it can be argued that both the selectivity operation and
the invariance operation are actually implemenled using the weights in P{C\\S2), whereas the
weights in P(i'l |C1) implement a necessary pre-processing step.
4.4.2 Dealing with large-scale Bayeslan networks
Due to the large fan-in in the network and the large number of stales, calculating the A function
of a node requires multiplying a high number of polL'ntially very low probability values. For
example, a CI node in band 8 receives input from 96S (22 x 22 locations x 2 bands) SI nodes,
meaning that it is necessary to obtain the product of 968 probability disiribuiions. The result
172
(4.9)