Bernal S D_2010.pdf - University of Plymouth

3.4. EXISTING MODELS
attenlmn.
The main contribution of this model is that it managed lo implement Bayesian inference us­
ing equations representing a recurrently connected network of spiking neurons. However, the
main limitation of the model is that it does not offer a general solution lo implementing belief
propagation with spiking neurons, but rather very specific and simple examples with heuristic
implementations. The main model consists of just a single layer containing 30 neurons, which
does not capture the complexities of belief propagation, nor its many benefits, such as a local
and distributed implementation; furthermore, it does not capture the complexities inherent in
visual processing. Additionally, the implementation in the log domain requires the use of an
approximation lo the conditional probability weighl.s, which has not been proven to provide
accurate results when the system is scaled up.
3.4.1.2 Liquid state machine model
A more recent model of belief propagation in networks of spiking neurons was provided by
Steimer et al. (2009). The model approximates belief propagation in Forney factor graphs, a
type of graphical model that is considered more general than Bayesiun network.s, and therefore
can capture all of ils properties. The model makes use of liquid stute machines composed of
liquid pools of spiking neurons lo represent the function nodes in the factor graph, similar to the
conditional probability functions in Bayesian networks. The internal dynamics of each pool of
neurons aUows it lo combine Ihe incoming messages from Ihe corresponding input nixies. Mes­
sages from one node to another are transmitted using iradouT populations of neurons which
extract the output information from the liquid pools. The readout populations need to be cali­
brated and trained to map the input synaptic current with desired output message (probability
from 0 to 1). encoded using an average population rate. Figure 3.10 shows the neural imple­
mentation of belief propagation in a factor graph using the liquid and readout populations of a
liquid stale machine.
The model was evaluated using two simple examples: a classical inference problem dealing
wiih ihe transmission of binary infomiation in an unreliable channel, and a more biologically-
grounded example dealing with the integration of psychophysical information to elucidate the
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