www.gfai.de/~heinz www.gfai.de/~heinz How Network Topology Defines its How Network Topology Defines its Behavior - Behavior - Serial Code Detection with Spiking Serial Code Detection with Spiking Networks Networks Dr. Gerd Heinz Dr. Gerd Heinz Gesellschaft zur Förderung Gesellschaft zur Förderung angewandter Informatik e.V angewandter Informatik e.V Berlin-Adlershof Berlin-Adlershof Workshop „Autonomous Workshop „Autonomous Systems” Systems” Herwig Unger & Wolfgang Herwig Unger & Wolfgang Halang Halang Hotel Sabina Playa, Cala Hotel Sabina Playa, Cala Millor Millor Sensor- und Motor- Sensor- und Motor- Homunculus. Homunculus. Natural History Museum, London Natural History Museum, London
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Www.gfai.de/~heinz How Network Topology Defines its Behavior - Serial Code Detection with Spiking Networks Dr. Gerd Heinz Gesellschaft zur Förderung angewandter.
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How Network Topology Defines its Behavior How Network Topology Defines its Behavior --Serial Code Detection with Spiking Serial Code Detection with Spiking NetworksNetworks
Dr. Gerd Heinz Dr. Gerd Heinz
Gesellschaft zur Förderung Gesellschaft zur Förderung angewandter Informatik e.Vangewandter Informatik e.V
Herwig Unger & Wolfgang HalangHerwig Unger & Wolfgang Halang
Hotel Sabina Playa, Cala Millor Hotel Sabina Playa, Cala Millor
Mallorca, 13-17 Oct. 2013Mallorca, 13-17 Oct. 2013 Sensor- und Motor- Sensor- und Motor- Homunculus. Homunculus.
Natural History Museum, Natural History Museum, London London
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Contents
Abstract Convolution A Small Interference Network Construction of Transfer Functions Applying a Convolution Spike Output Frequency Analysis Unipolar or Bipolar Signal Levels? Interpreting Bursts Examples
function [H] = trans(T,W,fs); if length(T) == length(W) then T = T * fs; // apply sample rate of H T = round(T); // T becomes index: integer H = 1:max(T); H = H * 0; // create an empty H for i = 1:length(T), // for all T(i), W(i) j = T(i), // delay becomes the H-index j H(j) = H(j) + W(i), // add the weight to H end // for else // if printf('\n\nerror: T and W have different size\n'); end // if endfunction;
We interprete a burst as transfer function H (seen as pulse response) and reproduce the delays T and weights W of the network behind:function [T,W] = net(H,fs); // returns T and W j=1; // W-index j for i=1:length(H) // H-index i if H(i) == 0 then ; // do nothing else // write the value to W, the index to T W(j) = H(i); // value to W T(j) = i; // index to T j = j+1; // increment j end; // endif end; // endfor T = T ./ fs; // multiply with sample duration T = T - min(T); // scale to min: reduced T-vectorendfunction;
To characterize time- and frequency domain, we transform delays and weights of a simplest interference network into a LTI transfer response
A procedure [H] = trans(T,W,fs) calculates the (time-discrete) transfer function H (pulse response) of the net from delay vector T (delay mask) and weight vector W
The FFT shows learning problems for unipolar signals and unipolar H because of highest DC-value
A mixture between unipolar signals and bipolar transfer function (weights) acts as good alternative (nerve nets)
Interpreting bursts as transfer functions (pulse responses), we design an inverse procedure [T,W] = net(H,fs) that reconstructs the net structure [T,W] from transfer function H
Find Scilab sources and the paper on the webwww.gfai.de/~heinz/publications/papers/2013_autosys.pdfwww.gfai.de/~heinz/techdocs/index.htm#conv
The transfer function or pulse response H is responsible for all sequential properties of a network: for code and sound generation or detection
The lecture shows, that smallest delays and delay differences change the pulse response H of the network
Remembering the "Neural Networks" (NN, ANN) approach with layers clocked by clock cycles we find, that the NN-approach destroyes the sequential structure of each network complete
In no case ANN or NN are candidates to understand the function of nerve like structures
Thinking about nerves we need interferential approches that does not destroy the delay structure of the net.
Erfolgreiche Google-Suchterme: Erfolgreiche Google-Suchterme: "Interferenznetze", "Mathematik des "Interferenznetze", "Mathematik des Nervensystems", "Heinz", Nervensystems", "Heinz", "Akustische Kamera""Akustische Kamera"
Und der Herr sprach: "So führte ich Und der Herr sprach: "So führte ich euch auf den Weg der Erkenntnis. euch auf den Weg der Erkenntnis. Gehet nun, und traget die Botschaft in Gehet nun, und traget die Botschaft in die Welt hinaus!"die Welt hinaus!"