Heinz, G.:

Wave Interference Networks State of Research

    Historical Remarks Time codes Space Integral Transformations Application Acoustic Camera  Interference Projections & I.-Integrals  Properties: – Self-I. (Zoom, Movement, Somato-t. Maps) – Cross-I. (Spatio-Temporal Maps) – Holomorphic Maps (Lashleys Rats, I. Overflow)… Modelling the Brains Labyrinth, Fodele Beach Crete, 23.-27.9.2006

www.gfai.de/~heinz [email protected]

Motivation

        Human brain has about 10 10 - 10 11 neurons Any neuron is typically connected with 1,000 to 10,000 others Unthinkable amount of connectivity Neurons communicate using time functions – small pulses with geometrical wavelength in the range between 50µm and 12mm* Dependent of thickness, time functions flow slowly: µm/s … m/s Excitements appear, where lots of pulses meet To analyze a net, we have to ask only for possible places of interference of pulses (ionic, electric, molecular) Time functions can mathematically be expressed as waves -> Wave interference network research on inhomogeneous nets 26/09/06 *see www.gfai.de/~heinz/publications/papers/1994_IWK.pdf

© G. Heinz, www.gfai.de/~heinz 2

Great Interference Ideas

26/09/06 © G. Heinz, www.gfai.de/~heinz 3

Great Ideas …

Interference Projection

Vorlage

Primary field

 Optical lense systems, Sonar  Beamformíng with delay elements

Interference Reconstruction

Vorlage non-mirrored  Fink "Time Reversal Mirrors"  Heinz "Acoustic Camera" 26/09/06

lense maximum delay Secondary field

Mirrored projection dT dT dT   Projection : continuous time interference integral appears mirrored   Reconstruction : inverse time Interference integral appears non-mirrored © G. Heinz, www.gfai.de/~heinz 4

Supersonic Arrays

  A, B, M – Methods Beam forming (ABF) 26/09/06 © G. Heinz, www.gfai.de/~heinz 5

GPS

The ultimative space time solution 26/09/06 © G. Heinz, www.gfai.de/~heinz 6

Radio Telescopes

 Two directions: – Superimposition of I² (images) - VLA – Superimposition of time functions - SKA Very Large Array (VLA) Superimposition of I² (images) to minimize noise © G. Heinz, www.gfai.de/~heinz 26/09/06 7

Square Kilometer Array (SKA)

26/09/06 © G. Heinz, www.gfai.de/~heinz Superimposition of time functions 8

WLAN-Transceiver

   Digital filters Timing Signal-Processing 26/09/06 © G. Heinz, www.gfai.de/~heinz 9

Historical Remarks: First Interference Systems

  Outstanding ideas about interference, beyond: – Lloyd A. Jeffress 1947 Place theory of sound localization – David Bohm/Karl Pribram 1973 ff Holomorphic memory – – – – Shun Ichi Amari 1977 Mosche Abeles 1988 Wolf Singer 1988 Mark Konishi 1993 Cognition networks Synfire chains Syncrozization in cats cortex Place theory of sound localization (2) – Andrew Packard 1995 Waves on Squids The alternative: State machines f(t-1), f(t-2),…f(t-n) – – – Boole 1854, Augusta Ada 1858 McCulloch/Pitts 1943 (!) Neural (Pattern-) Networks – – Medwedjev, Moore, Mealy 1955 Fairchild TTL 1968, Intel 4004 1971 © G. Heinz, www.gfai.de/~heinz 26/09/06 10

The Idea: Time codes Space

   Well known relations between f(x) and f(t) about velocity Timing defines interference location Different timing -> different interference location

intensity f(x) Timing f(t-T) location x

© G. Heinz, www.gfai.de/~heinz 26/09/06 11

Time Function or Wave?

f(t) f(t-

t

)

Delay distance t (Fig.: constant velocity)   Identity: time function is a wave Independent of any circuit structur (local coupled): only delay defines location(!)  Global models allowed, but do not model eating waves (nonlinear superimposition) © G. Heinz, www.gfai.de/~heinz 12 26/09/06

Weights or Delays?

Nerve Net

Hebbs rule interpreted by patterns and weights Jeffress rule interpreted by weights and delays -> Interference networks Non-mirrored maps Difference: Mirrored maps © G. Heinz, www.gfai.de/~heinz 26/09/06 13

Waves Generate Images

time-integration over a location in a wavefield produces the Interference Integral (I²) – called "image" Vorlage Zeitfunktionen Bild

demo

26/09/06 © G. Heinz, www.gfai.de/~heinz 14

Second Remark: Intellectual Power of Mankind

  26/09/06 Signal theory is built on interference of two multiplied (or added) channels : field theory, filter-t., integral transformations, modulations… – – Fourier-Transformation Laplace-Transformation – – – – – – – Z-Transformation (Discrete LT) Wavelet-Transformation Hilbert-Transformation Gabor-Transformation Auto correlation Cross correlation Convolution

continuous:

z

(

t

discrete:

z

(

k

) )  

K K b n



a b

 

a x

(

t

)

g

(

t

)

d

t

x

(

n

)

g

(

n

) 

n

– – Area calculation (g=1) Frequency modulation (FM, PM, QM) – Amplitude modulation (AM, SM) But: We discuss n channels (n >> 2), not only two: Pyramidal cell has on average 7400 synapses?

© G. Heinz, www.gfai.de/~heinz 15

Complex Numbers in Interference Systems

Problems for d > l :

Im

a

Re 0 °<

a

< 360 °

l =

vt = v/f

sensor

26/09/06 d © G. Heinz, www.gfai.de/~heinz

sensor 0 °<

a

< 360 °

16

Complex Numbers and Interference Systems

    Wavelengths l can be shorter as the arrangement of sensors d Complex numbers range between 0…360° A 'phase' is multivalent: wave number is very important Avoid to use complex numbers for d > l – Integral transformations not allowed (!) – – No FFT, no Laplace, no Gabor, no Wavelet!

Only time domain calculations possible

Forget Field Theory!

?

-> Work in time domain Can we really imagine?

Quantum physics: Heisenbergs uncertainty relation failed?

© G. Heinz, www.gfai.de/~heinz 26/09/06 17

First Application

www.acoustic-camera.com

Start NoiseImage Examples:

•

Vacuum cleaner

•

Needle printer

•

Sports car microphone array (32 mics)

26/09/06

data recorder

© G. Heinz, www.gfai.de/~heinz

notebook

18

Worldwide

System price ~ 100.000, € Used for car development worldwide

Distributors: Germany, France, Great Britain, Spain, Netherlands, Sweden, Austria, Italy, Switzerland, China, India, South-Korea, Taiwan, Japan, Singapore, Australia, Newsealand, USA, Mexico, Brasilia, Argentina, Chile, South-Africa 26/09/06 © G. Heinz, www.gfai.de/~heinz 19

Nomination of Acoustic Camera for German Future Award 2005

http://www.deutscher-zukunftspreis.de

26/09/06 http://www.gfai.de/~heinz/publications/presse/index.htm

© G. Heinz, www.gfai.de/~heinz 20

Properties of Interference Systems

26/09/06 © G. Heinz, www.gfai.de/~heinz 21

Relativity of Wave Length

   Spikes move slowly through nerve system [2 µm/s … 120 m/s] Spikes have a limited (geometric) size [µm … cm] Velocity v, pulse duration T, grid g, geometrical wavelength s = v .

T

s [µm]

s < g s >> g Interference network Weighted Nets (NN.)

g [µm]

Information processing: Which grid is addressed?

• Spines?

• • • Cell body?

Columns?

It depends!

26/09/06 © G. Heinz, www.gfai.de/~heinz 22

Calculation of Waves: Mask

 Each locations has its own time scheme -> mask algorithm

Mask of a location Inverse Mask Excitement condition

26/09/06 © G. Heinz, www.gfai.de/~heinz 23

What "Integrate and Fire" suggests

The probability to excite a neuron is higher as more closed the partial impulses can reach it random: no excitement synchronous: fire 26/09/06 © G. Heinz, www.gfai.de/~heinz 24

Projection Law

     Waves need to be at the detecting place at the same time Self interference condition (all paths): t 1

=

t 2

= … =

t n Velocities and path length can be different, but delays can not … Optics, GPS, acoustic camera, dig. filter theory Different to Fermat, Huygens … Feynman - trajectories Source NI 1993 26/09/06 © G. Heinz, www.gfai.de/~heinz 25

Sound Localization Model: First Inter-Medial Interference Circuit

Konishis model (1993) basing on: Jeffres L. A.: A place theory of sound localization. J. Comp. Physiol. Psychol. 41 [1948]: 35-39

symmetry line: mirror Tyto alba

right © G. Heinz, www.gfai.de/~heinz left

drawing: d. doebler

26 26/09/06

Interference Projection

 Signals meet at locations with identical delays from source (self-interference)   (all other cases not drawn) Specific neurons begin to communicate  Address relations between locations given by delays  Delays code locations Fig.: Title page of " Neuronale Interferenzen ", Heinz, 1993 Single point observations look like density modulated signals or bursts? They say nothing about destinations!

26/09/06 © G. Heinz, www.gfai.de/~heinz 27

Long Axons: Interference Projection

  Considered generating and detecting fields Which properties exist between generating and detecting locations?

26/09/06 © G. Heinz, www.gfai.de/~heinz 28

Long Axons: Interference Projection

   Spiking neurons have been arrranged Mirrored projection appears as "interference integral" Image conjunction!

– Which difference between Hearing and Seeing? – Ideas?

© G. Heinz, www.gfai.de/~heinz 26/09/06 29

Understanding Bursts

 Circuit (a)  Burst generation with low bias (b)  Code detection with high bias (c)  Neuronal basic functions?!

 Data addressing possibility -> 26/09/06 © G. Heinz, www.gfai.de/~heinz

Example

30

New Elementary Functions of Neurons

     Code generation Code detection Data addressing details: http://www.gfai.de/~heinz/historic/biomodel/models.htm#bursts http://www.gfai.de/~heinz/publications/papers/2002_NF.pdf

Neighborhood inhibition (identical neurons) Level generation (spike duration > pause) 26/09/06 © G. Heinz, www.gfai.de/~heinz 31

Waves on Squids

     Andrews squid-experiments (1995) show moving excitations between chromatophore-cells Cells are connected via a nerve-like structure Excitation and relaxation can produce waves Time functions appear comparable to nerve Although the mechanism is not exactly known, the effect needs a wave-interference description http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htm

Circular wave © G. Heinz, www.gfai.de/~heinz 26/09/06 32

Local Interaction

   Waves delete in the refractoriness zone: "cleaning" waves Alpha-waves in EEG? Dreams?

Local coupling http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htm

Global, linear Local, non-linear "cleaning" waves in 2-dim. simulation "cleaning" waves on squids (AP, 1995)

gh NI 1993 26/09/06 © G. Heinz, www.gfai.de/~heinz 33

Self -Interference Integrals ( Visual Maps)

Generating fields (g+h) time function plot Detecting fields

   Self interference of waves (i, i, i) Source arrangement defines map Conjunctive, spatial maps © G. Heinz, www.gfai.de/~heinz 34 26/09/06

Self- /Cross- Interference Relations

• Waves meet itself -> " Self -"interference: wave i with i with • Waves meet other waves -> " Cross "-interference: wave i i … with i-1 … 26/09/06

(i, i, i, i) self-interference location (3) (i, 0, i-1, i) cross-int. location (4) cross interference distance (i, i, i, i) self-int.

(1)

© G. Heinz, www.gfai.de/~heinz

(2)

35

Cross Interference Integrals temporal Maps

 Increasing channel number (2…8) reduces cross interference intensity if we consider over-conditioning effects Heinz 1996

(i, i, i, … i) self interference locations

© G. Heinz, www.gfai.de/~heinz

cross-interference locations around

36 26/09/06

Holomorphic Memory

  Lashley was looking his life long for the locality of items learned (1920 … 1950) Rats became teached a way through a labyrinth. He removed systematically small parts of the brain and proved the before learned Summary of his experiments:

3-channel Simulation

 The series of experiments ... “has discovered nothing directly of the real nature of the engram“ Interpretation:    Cross interferences look like self interferences (!) "Tutographic" brain, if it is an interference system We can not avoid the holomorphy!

Region of self-interference Region of cross-interferences around

26/09/06 © G. Heinz, www.gfai.de/~heinz 37

Delay Shift Moves Interference Integrals (I²)

 Variation of delay of one channel produces a moving interference integral (glia potential influences speed & location) 26/09/06 © G. Heinz, www.gfai.de/~heinz 38

Velocity Variation Zooms Interference Integrals

  Variation of background velocity in the detecting field zooms the interference integrals (neuroglia) Cross interferences appear for low velocities 26/09/06 © G. Heinz, www.gfai.de/~heinz 39

A Closer Look to Memory Density

 As slower is the velocity in the detecting field, as smaller is the addressable region, as higher must be the density and the addressable memory volume wavelength [µm] = velocity [µm/ms] * duration [ms]

v = 50 µm/ms v = 10 µm/ms

© G. Heinz, www.gfai.de/~heinz 26/09/06 40

~ 7,5 ms

Rule of Fire Rate

    Cross interference pattern depends on channel number & refractory period We increase the average fire rate (reduced cross interference distance) Field overflow occurs: Cross interference overflows the self-interf., level generation!

Hypothesis: if pain is cross interference overflow, then this simple interference circuit models that behaviour 26/09/06

~ 5 ms ~ 4 ms ~ 1,5 ms

© G. Heinz, www.gfai.de/~heinz 41

Analogy to Filter Theory

  Neuron changes from a simple threshold gate to a digital filter circuit Direct translation into digital filter structure is possible

digital filter circuit Distributed wire with delay

26/09/06 © G. Heinz, www.gfai.de/~heinz

Electrical node (!)

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Over-Conditioned Networks

     Using high numbers of channels the delays on different paths do not match, resulting in blurred excitements far away from axis Example: four channels project on a two dimensional layer, see bottom image Four channels do not match on a 2-dim. field (max. 3) numb_channels = space_dimension +1 n= d + 1 or d = n - 1 High space dimensions for high channel numbers necessary Nerves need folded, inhomogeneous networks (!) © G. Heinz, www.gfai.de/~heinz 26/09/06

clean blurred

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Summary: Spatio-Temporal Maps

 "Interference integral" = integration of time function of each location over time 1.

Self-interference properties define – Somato-topic maps (mirrored projections) – – – Noise location (owl, dolphin) Optical pictures, Acoustic Camera Scaling (zoom, movement) 2.

Cross-interference properties define – – – Frequency maps Code and behavior maps Pain?

26/09/06 © G. Heinz, www.gfai.de/~heinz 44



Summary

Little time shifts have dramatic influence on locations of interference, supposed we have small pulses    To analyze nerve networks we introduce the term Interference Network as a physical oriented approach to neurocomputing We introduced interference integrals interference to visit locations of Investigating the influence of small delays we find a lot of new effects: movement, zooming, conjugation, permutation, overflow, new neuronal basic functions     Analyzing projections we find over-condition effects regarding n-dimensional, inhomogeneous delay spaces It is not possible to ignore small delays – pattern simulations (NN) deliver wrong results It is not allowed, to use complex numbers to model interference systems We have to re-think neural network research completely  26/09/06 And we have to re-think field theory into time domain © G. Heinz, www.gfai.de/~heinz 45

Future

  IN-research will be included in the "BMBF- Informations- und Kommunikationstechnologien Programm (IKT2020)" We try to start a pilot project (until now 13 proposals)  Find 1 GB more on

www.gfai.de/~heinz

Thanks for your attention.

© G. Heinz, www.gfai.de/~heinz 26/09/06 46