<?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%">Lars Buesing</style></author><author><style face="normal" font="default" size="100%">Benjamin Schrauwen</style></author><author><style face="normal" font="default" size="100%">Robert Legenstein</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Connectivity, Dynamics and Memory in Reservoir Computing with Binary and Analog Neurons</style></title><secondary-title><style face="normal" font="default" size="100%">Neural Computation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">In Press</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.igi.tugraz.at/lars/papers/NECO-01-09-947-PDF.pdf</style></url></web-urls></urls><abstract><style face="normal" font="default" size="100%">&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Reservoir Computing (RC) systems are powerful models for online computations&amp;nbsp;on input sequences. They consist of a memoryless readout neuron which is&amp;nbsp;trained on top of a randomly connected recurrent neural network. RC systems are commonly&amp;nbsp;used in two flavors: with analog or binary (spiking) neurons in the recurrent&amp;nbsp;circuits. Previous work indicated a fundamental difference in the behavior of these two&amp;nbsp;implementations of the RC idea. The performance of a RC system built from binary&amp;nbsp;neurons seems to depend strongly on the network connectivity structure. In networks&amp;nbsp;of analog neurons such clear dependency has not been observed. In this article we address&amp;nbsp;this apparent dichotomy by investigating the influence of the network connectivity&amp;nbsp;(parametrized by the neuron in-degree) on a family of network models that interpolates&amp;nbsp;between analog and binary networks. Our analyses are based on a novel estimation of&amp;nbsp;the Lyapunov exponent of the network dynamics with the help of branching process&amp;nbsp;theory, rank measures which estimate the kernel-quality and generalization capabilities&amp;nbsp;of recurrent networks, and a novel mean-field predictor for computational performance.&amp;nbsp;These analyses reveal that the phase transition between ordered and chaotic network&amp;nbsp;behavior of binary circuits qualitatively differs from the one in analog circuits, leading&amp;nbsp;to differences in the integration of information over short and long time scales. This&amp;nbsp;explains the decreased computational performance observed in binary circuits that are&amp;nbsp;densely connected. The mean-field predictor is also used to bound the memory function&amp;nbsp;of recurrent circuits of binary neurons.&lt;/p&gt;
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