Biomedical Engineering Reference
In-Depth Information
18.3 The generic neural microcircuit model
We used a randomly connected circuit consisting of leaky integrate-and-fire (I&F)
neurons, 20% of which were randomly chosen to be inhibitory, as generic neural mi-
crocircuit model. Best performance was achieved if the connection probability was
higher for neurons with a shorter distance between their somata (see
Figure 18.3)
.
Random circuits were constructed with sparse, primarily local connectivity (see Fig-
ure 18.3), both to fit anatomical data and to avoid chaotic effects.
The
liquid state x
of the recurrent circuit consisting of
n
neurons was modeled
by an
n
-dimensional vector consisting of the current firing activity of these
n
neurons.
To reflect the membrane time constant of the readout neurons a low pass filter with a
time constant of 30 ms was applied to the spike trains generated by the neurons in the
recurrent microcircuit. The output of this low pass filter applied separately to each
of the
n
neurons, defines the liquid state
x
(
t
)
. Such low pass filtering of the
n
spike
trains is necessary for the relatively small circuits that we simulate, since at many
time points
t
no or just very few neurons in the circuit fire (see top of
Figure 18.5)
.
As readout units we used simply linear neurons, trained by linear regression (unless
stated otherwise).
(
t
)
18.4 Towards a non-Turing theory for real-time neu-
ral computation
Whereas the famous results of Turing have shown that one can construct Turing ma-
chines that are universal for digital sequential offline computing, we propose here
an alternative computational theory that is more adequate for parallel real-time com-
puting on analog input streams. Furthermore we present a theoretical result which
implies that within this framework the computational units of a powerful compu-
tational system can be quite arbitrary, provided that sufficiently diverse units are
available (see the separation property and approximation property discussed below).
It also is not necessary to
construct
circuits to achieve substantial computational
power.
Instead sufficiently large and complex
found
circuits (such as the generic
nA) was chosen to be 30 (EE), 60 (EI), -19 (IE), -19 (II). In the case of input synapses the parameter
A
had
a value of 18 nA if projecting onto a excitatory neuron and 9 nA if projecting onto an inhibitory neuron.
The SD of the
A
parameter was chosen to be 100% of its mean and was drawn from a gamma distribution.
The postsynaptic current was modeled as an exponential decay exp
(
−
t
/
u
s
)
with u
s
=
3ms(u
s
=
6ms)for
excitatory (inhibitory) synapses. The transmission delays between liquid neurons were chosen uniformly
to be 1.5 ms (
EE
), and 0.8 ms for the other connections. We have shown in [16] that without synaptic dy-
namics the computational power of these microcircuit models decays significantly. For each simulation,
the initial conditions of each I&F neuron, i.e., the membrane voltage at time
t
=
0, were drawn randomly
(uniform distribution) from the interval [13.5 mV, 15.0 mV].
Search WWH ::
Custom Search