Bernal S D_2010.pdf - University of Plymouth

4.5. FEEDBACK PROCESSING
is proportional lo V^i„.
4.5 Feedback processing
Section 4.4 describes how for the feedforward object recognition simulations the network was
assumed lo he singly-connected and tree-structured during the initial boitom-up propagation of
evidence. This wa-s done in order to simplify the computations and facilitate the approximation
to the HMAX selectivity and invariance operations.
For the feedback simulations the network is not restricted by this assumption, and is thu.s al­
lowed lo maintain its multiply connected structure (multiple parents with loops). Evidence
propagates simultaneously in both directions (up and down), at all layers of the network. The
combination of parent mes.sages is approximated using the weighted sum of compatible parental
coijfifjuralions method. To deal with loops, belief propagalion becomes lotipy belief propaga­
tion, which provides an approximation to the exact beliefs after several iterations. Further
details of the feedback implementation and the approximations required due lo the large dimen­
sions of the network are included in this section.
4.5.1 Approximating n messages as beliefs
As shown in Fquaiion 3.31, the outward it message generated at each node can be obtained as
a function of its belief. The only difference is that the message from node X lo Cj, i.e. Ttc^lA')
includes ail incoming messages to X, except the one arriving from the destination node. i.e.
Ac (X). This is done in order to avoid the circulation of duplicate information in the network.
However, for the purpose of simplification and increased computational performance, and only
when the number of incoming messages is high, the outgoing ^:j{X) message can be approx­
imated by the belief, Hel{X). This approximation implies Jk-,{X) also includes the evidence
contained in h:^{X). However, ntj(-X) is calculated by combining messages from a total of
N -j- M nodes (all parent and children nodes), so the overall effect of one single message on
the final message is proportional to I /(A' -I- M). This justifies the approximation in the present
model where the values of N and M are in the order of hundreds or thousands. The same ap­
proximation is employed by other similar belief propagation mcxiels (Litvak and Ullman 2{X)9.
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