Bernal S D_2010.pdf - University of Plymouth

.1.4. EXISTING MODELS
Figure J. 10: Neural implemcnlalion of belief propagalion in a hbrney faclor firaph using ihe
liquid and readoui neuronal pupulaiions of a liquid slate machine. Left) lllusiralion
of a homey faclor graph where the nodes represent faclors/i, .-,/) (conditional
probabiliiy funciions). ;ind the edges represent variables Jfj X7. Arrows
represeni ihe messages exchanged during belief propagalion. Hifihi) Neural implementation
of ihe Fmey factor graph and belief propagalion shown in the lefl.
The liquid pools (L) represeni Ihe fueiors of ihe graph and eombino input messages
from neighbouring nodes. The messages (and, itnpliciily, the variables)
are encoded by the population rate of readout pls (R) and are injected to the
corresponding liquid pools via ihe synaptic connections (Sieimer et al. 2tX)9).
shape and illumination of an object. The population rales of Ihe readout pools, resulting from
Ihe network dynamics, were in agreement wilh the direct numerical evaluation of belief propa­
gation.
Although both networks consisted of a very small number of binary variables (9 and 4 respec­
tively), ihe authors claim the model can be generalized to more large-scale and complex sce­
narios. Nonetheless, the number of neurons required to do ihis, both for ihe liquid and readout
populaUons, would be extremely high and thus very expensive from the computalional perspec­
tive. According to the audiors, a current line of research aims at increasing the ctxiing efficiency
of the neuron pools by making use of a place-coding scheme. A further limitation of scaling
up is related lo ihe accuracy of Ihe results in networks wilh several hierarchical levels. It was
shown that messages deep in the network were less correlated to the exact numerical values,
than those near the input layer.
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