<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Haeusler</style></author><author><style face="normal" font="default" size="100%">Markram, H.</style></author><author><style face="normal" font="default" size="100%">W. Maass</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Perspectives of the high dimensional dynamics of neural microcircuits from the point of view of low dimensional readouts</style></title><secondary-title><style face="normal" font="default" size="100%">Complexity (Special Issue on Complex Adaptive Systems)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><number><style face="normal" font="default" size="100%">4</style></number><volume><style face="normal" font="default" size="100%">8</style></volume><pages><style face="normal" font="default" size="100%">39-50</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We investigate generic models for cortical microcircuits, i.e. recurrent circuits of&lt;br /&gt;
integrate-and fire neurons with dynamic synapses. These complex dynamic systems&lt;br /&gt;
subserve the amazing information processing capabilities of the cortex, but are at the&lt;br /&gt;
present time very little understood. We analyze the transient dynamics of models for&lt;br /&gt;
neural microcircuits from the point of view of one or two readout neurons that collapse&lt;br /&gt;
the high dimensional transient dynamics of a neural circuit into a 1- or 2--dimensional&lt;br /&gt;
output stream. This stream may for example represent the information that is projected&lt;br /&gt;
from such circuit to some particular other brain area or actuators. It is shown that simple&lt;br /&gt;
local learning rules enable a readout neuron to extract from the high dimensional&lt;br /&gt;
transient dynamics of a recurrent neural circuit quite different low-dimensional&lt;br /&gt;
projections, that even may contain &amp;quot;virtual attractors&amp;quot; which are not apparent in the high&lt;br /&gt;
dimensional dynamics of the circuit itself. Furthermore it is demonstrated that the&lt;br /&gt;
information extraction capabilities of linear readout neurons are boosted by the&lt;br /&gt;
computational opertions of a sufficiently large preceding neural microcircuit. Hence a&lt;br /&gt;
generic neural microcircuit may play a similar role for information processing as a kernel&lt;br /&gt;
for support vector machines in machine learning. We demonstrate that the projection of&lt;br /&gt;
time-varying inputs into a large recurrent neural circuit enables a linear readout neuron to&lt;br /&gt;
classify the time-varying circuit inputs with the same power as a complex nonlinear&lt;br /&gt;
classifiers, such as for example a pool of perceptrons trained by the p-delta-rule, or a&lt;br /&gt;
feedforward sigmoidal neural net trained by backprop, provided that the size of the&lt;br /&gt;
2&lt;br /&gt;
recurrent circuit is sufficiently large. At the same time such readout neuron can exploit&lt;br /&gt;
the stability and speed of learning rules for linear classifiers, thereby overcoming the&lt;br /&gt;
problems caused by local minima in the error function of nonlinear classifiers. In addition&lt;br /&gt;
it is demonstrated that pairs of readout neurons can transform the complex trajectory of&lt;br /&gt;
transient states of a large neural circuit into a simple and clearly structured 2-dimensional&lt;br /&gt;
trajectory. This 2-dimensional projection of the high-dimensional trajectory can even&lt;br /&gt;
exhibit convergence to virtual attractors which are not apparent in the high dimensional&lt;br /&gt;
trajectory.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;</style></abstract></record></records></xml>