Bernal S D_2010.pdf - University of Plymouth

3.4. EXISTING MODELS
the node encoded by the LINC. In a final step, the output message is normalized via a normaliza­
tion circuit where Ihe different values are recurrently inhibiting each other This is achieved by
connecling Ihe excitatory population of all sunimalion units to a central inhibitory population.
A schematic representation of a neuronal LINC node is shown in Figure 3.11.
The model was tested using two sets of graphs, one wilh 12 hidden binary variables and one
with 6 hidden ternary variables. In each case 100 different random conliguralions of the node
weights and evidence values were tested and compared with the original analytical methods.
Results showed ihc neuronal circuit was able to effectively approximate the marginal distri­
butions, although Ihe accuracy decreased when using temaiy variables as compared to binary
variables. The inaccuracy of the model was shown to arise not only from the sub-circuit's ap­
proximations (sum, max and normalization), but from inherent network phenomena such as the
evolving desynchronization in subpopulalions.
With regard to the scalability, the model can map any arbitrary graph structure and discrete
variables with any number of stales, with a linear relation between the number of neurons and
the number of nodes. However, for large-scale networks and variables with many slates, the
number of neurons might be prohibitive (6 hidden variables each wilh 3 stales require over
16.000 neurons). The speed of the computation provides a biologically reahslic inference time
{^ 400 ms) due to the highly dislributed implementation. The model also attempts to map the
different algorithm operations onto the conical laminar circuits, as described in Section 3,4,3.
A comparison between the most significant feaiures of the previous two models is depicted in
Table 3.1, including a summary of the main advantages and drawbacks of each model,
3.4.1.4 Kleclronic implementation of networks of .spiking neurons
An emerging and rapidly growing field of research is dedicated to the implementation of real­
istic spiking neural circuits in hybrid analog/digital very large scale integration (VLSI) devices.
Recent advances have allowed the implementation of winner-iake-all networks in the VLSI de­
vices, which has lead to the development of simple state-dependent systems (Neftci el ;il. 2010).
Simple graphical models, such as factor graphs and belief propagation, can be approximated us­
ing winner-take-a 11 networks wilh state-dependent processing. Lxamplcs of graphical models,
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