Computational Models for Generic Cortical Microcircuits - Computational Neuroscience: A Comprehensive Approach - page 593

and features

- projection of the input into a very high dimensional space

In machine learning both preprocessing steps are carried out simultaneously by
a so-called kernel, that uses a mathematical trick to avoid explicit computations in
high-dimensional spaces. In contrast, in our model for computation in neural mi-
crocircuits both operations of a kernel are physically implemented (by the microcir-
cuit). The high-dimensional space into which the input is projected is the state space
of the neural microcircuit (a typical column consists of roughly 100 000 neurons).
This implementation makes use of the fact that the precise mathematical formulas
by which these nonlinear combinations and high-dimensional projections are com-
puted are less relevant. Hence these operations can be carried out by found neural
circuits that have not been constructed for a particular task. The fact that the generic
neural microcircuit models in our simulations automatically compute an abundance
of nonlinear combinations of input fragments can be seen from the fact that the target
output values for the tasks considered in Figures 18.2 , 18.4, 18.6, 18.8 are nonlinear
in the input, but are nevertheless approximated quite well by linear readouts from
the current state of the neural microcircuit.
The capability of neural microcircuits to boost the power of linear readouts by
projecting the input into higher dimensional spaces is further underlined by joint
work with Stefan Hausler [6]. There the task to recover the number of the template
spike pattern used to generate the second-to-last segment of the input spike train*
was carried out by generic neural microcircuit models of different sizes, ranging from
12 to 784 neurons.In each case a perceptron was trained by the E-rule to classify
at time 0 the template that had been used to generate the input in the time segment
[-500, -250 ms]. The results of the computer simulations reported in Figure 18.13
show that the performance of such (thresholded) linear readout improves drastically
with the size of the microcircuit into which the spike train is injected, and therefore
with the dimension of the liquid state that is presented to the readout.

18.7 Software for evaluating the computational

capabilities of neural microcircuit models

New software for the creation, fast simulation and computational evaluation of neural
microcircuit models has recently been written by Thomas Natschlager (with contri-
butions by Christian Naeger), see [21]. This software, which has been made avail-
able for free use on WWW.LSM.TUGRAZ.AT, uses an efficient C ++ kernel for the

*This is exactly the task of the second readout in the spike pattern classification task discussed in Fig-
ures 18.11 and 18.12.