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Heinz, G.: Wave Interference Networks - State of Research Historical Remarks Historical Remarks Time codes Space Time codes Space Integral Transformations Integral Transformations Application Acoustic Camera Application Acoustic Camera n Interference Projections & I.-Integrals n 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/~heinzwww.gfai.de/~heinz heinz@gfai.de heinz@gfai.de www.gfai.de/~heinzheinz@gfai.de

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26/09/06© G. Heinz, www.gfai.de/~heinz2 Motivation n Human brain has about 10 10 - 10 11 neurons n Any neuron is typically connected with 1,000 to 10,000 others n Unthinkable amount of connectivity n Neurons communicate using time functions – small pulses with geometrical wavelength in the range between 50µm and 12mm* n Dependent of thickness, time functions flow slowly: µm/s … m/s n Excitements appear, where lots of pulses meet n To analyze a net, we have to ask only for possible places of interference of pulses (ionic, electric, molecular) n Time functions can mathematically be expressed as waves -> Wave interference network research on inhomogeneous nets *see www.gfai.de/~heinz/publications/papers/1994_IWK.pdf

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26/09/06© G. Heinz, www.gfai.de/~heinz3 Great Interference Ideas

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26/09/06© G. Heinz, www.gfai.de/~heinz4 Great Ideas … n Projection: continuous time n interference integral appears mirrored n Reconstruction: inverse time n Interference integral appears non-mirrored dT Vorlage Mirrored projection Primary field Secondary field Interference Projection Vorlage Interference Reconstruction non-mirrored n n Optical lense systems, Sonar n n Beamformíng with delay elements n n Fink "Time Reversal Mirrors" n n Heinz "Acoustic Camera" maximum delay lense

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26/09/06© G. Heinz, www.gfai.de/~heinz5 Supersonic Arrays n A, B, M – Methods n Beam forming (ABF)

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26/09/06© G. Heinz, www.gfai.de/~heinz6 GPS The ultimative space- time solution

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26/09/06© G. Heinz, www.gfai.de/~heinz7 Radio Telescopes n Two directions: –Superimposition of I² (images) - VLA –Superimposition of time functions - SKA Very Large Array (VLA) Superimposition of I² (images) to minimize noise Superimposition of I² (images) to minimize noise

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26/09/06© G. Heinz, www.gfai.de/~heinz8 Square Kilometer Array (SKA) Superimposition of time functions

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26/09/06© G. Heinz, www.gfai.de/~heinz9 WLAN-Transceiver n Digital filters n Timing n Signal-Processing

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26/09/06© G. Heinz, www.gfai.de/~heinz10 n Outstanding ideas about interference, beyond: –Lloyd A. Jeffress 1947Place theory of sound localization –David Bohm/Karl Pribram 1973 ff Holomorphic memory –Shun Ichi Amari 1977Cognition networks –Mosche Abeles 1988 Synfire chains –Wolf Singer 1988Syncrozization in cats cortex –Mark Konishi 1993Place theory of sound localization (2) –Andrew Packard 1995Waves on Squids n 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 Historical Remarks: First Interference Systems

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26/09/06© G. Heinz, www.gfai.de/~heinz11 The Idea: Time codes Space n Well known relations between f(x) and f(t) about velocity n Timing defines interference location n Different timing -> different interference location location x Timing f(t-T) intensity f(x)

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26/09/06© G. Heinz, www.gfai.de/~heinz12 Time Function or Wave? n Identity: time function is a wave n Independent of any circuit structur (local coupled): only delay defines location(!) n Global models allowed, but do not model eating waves (nonlinear superimposition) Delay distance (Fig.: constant velocity) f(t) f(t- )

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26/09/06© G. Heinz, www.gfai.de/~heinz13 Weights or Delays? Nerve Net Difference: Jeffress rule interpreted by weights and delays -> Interference networks Mirrored maps Hebbs rule interpreted by patterns and weights Non-mirrored maps

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26/09/06© G. Heinz, www.gfai.de/~heinz14 Waves Generate Images time-integration over a location in a wavefield produces the Interference Integral (I²) – called "image" Vorlage Zeitfunktionen Bild demo

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26/09/06© G. Heinz, www.gfai.de/~heinz15 Second Remark: Intellectual Power of Mankind n 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 –Area calculation (g=1) –Frequency modulation (FM, PM, QM) –Amplitude modulation (AM, SM) n But: We discuss n channels (n >> 2), not only two: Pyramidal cell has on average 7400 synapses? continuous: discrete:

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26/09/06© G. Heinz, www.gfai.de/~heinz16 Complex Numbers in Interference Systems ImRe = vt = v/f = vt = v/f d sensor sensor Problems for d > : 0°< < 360°

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26/09/06© G. Heinz, www.gfai.de/~heinz17 Complex Numbers and Interference Systems Wavelengths can be shorter as the arrangement of sensors d Wavelengths can be shorter as the arrangement of sensors d n Complex numbers range between 0…360° n A 'phase' is multivalent: wave number is very important Avoid to use complex numbers for d > Avoid to use complex numbers for d > –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?

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26/09/06© G. Heinz, www.gfai.de/~heinz18 First Application www.acoustic-camera.com microphone array (32 mics)data recordernotebook Vacuum cleaner Sports car Needle printer Examples: Start NoiseImage

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26/09/06© G. Heinz, www.gfai.de/~heinz19 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 System price ~ 100.000,- € Used for car development worldwide

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26/09/06© G. Heinz, www.gfai.de/~heinz20 Nomination of Acoustic Camera for German Future Award 2005 http://www.gfai.de/~heinz/publications/presse/index.htm http://www.deutscher-zukunftspreis.de

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26/09/06© G. Heinz, www.gfai.de/~heinz21 Properties of Interference Systems

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26/09/06© G. Heinz, www.gfai.de/~heinz22 Relativity of Wave Length n Spikes move slowly through nerve system [2 µm/s … 120 m/s] n Spikes have a limited (geometric) size [µm … cm] n Velocity v, pulse duration T, grid g, geometrical wavelength s = v. T s gInterference network s < gInterference network s >> gWeighted Nets (NN.) s [µm] g [µm] Information processing: Which grid is addressed? Spines?Spines? Cell body?Cell body? Columns?Columns? It depends!It depends!

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26/09/06© G. Heinz, www.gfai.de/~heinz23 Calculation of Waves: Mask n Each locations has its own time scheme -> mask algorithm Mask of a location Inverse Mask Excitement condition

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26/09/06© G. Heinz, www.gfai.de/~heinz24 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

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26/09/06© G. Heinz, www.gfai.de/~heinz25 Projection Law n Waves need to be at the detecting place at the same time Self interference condition (all paths): 1 = 2 = … = n Self interference condition (all paths): 1 = 2 = … = n n Velocities and path length can be different, but delays can not n … Optics, GPS, acoustic camera, dig. filter theory n Different to Fermat, Huygens … Feynman - trajectories Source NI 1993

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26/09/06© G. Heinz, www.gfai.de/~heinz26 drawing: d. doebler Sound Localization Model: First Inter-Medial Interference Circuit Tyto alba 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 right left

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26/09/06© G. Heinz, www.gfai.de/~heinz27 Interference Projection n Signals meet at locations with identical delays from source (self-interference) n (all other cases not drawn) n Specific neurons begin to communicate n Address relations between locations given by delays n Delays code locations Fig.: Title page of "Neuronale Interferenzen", Heinz, 1993 Neuronale InterferenzenNeuronale Interferenzen Single point observations look like density modulated signals or bursts? They say nothing about destinations!

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26/09/06© G. Heinz, www.gfai.de/~heinz28 Long Axons: Interference Projection n Considered generating and detecting fields n Which properties exist between generating and detecting locations?

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26/09/06© G. Heinz, www.gfai.de/~heinz29 Long Axons: Interference Projection n Spiking neurons have been arrranged n Mirrored projection appears as "interference integral" n Image conjunction! –Which difference between Hearing and Seeing? –Ideas?

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26/09/06© G. Heinz, www.gfai.de/~heinz30 Understanding Bursts n Circuit (a) n Burst generation with low bias (b) n Code detection with high bias (c) n Neuronal basic functions?! n Data addressing possibility -> Example

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26/09/06© G. Heinz, www.gfai.de/~heinz31 New Elementary Functions of Neurons n Code generation n Code detection n Data addressing n Neighborhood inhibition (identical neurons) n Level generation (spike duration > pause) details: http://www.gfai.de/~heinz/historic/biomodel/models.htm#bursts http://www.gfai.de/~heinz/publications/papers/2002_NF.pdf

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26/09/06© G. Heinz, www.gfai.de/~heinz32 Waves on Squids n Andrews squid-experiments (1995) show moving excitations between chromatophore-cells n Cells are connected via a nerve-like structure n Excitation and relaxation can produce waves n Time functions appear comparable to nerve n 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

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26/09/06© G. Heinz, www.gfai.de/~heinz33 Local Interaction n Waves delete in the refractoriness zone: "cleaning" waves n Alpha-waves in EEG? Dreams? n Local coupling http://www.gfai.de/~heinz/historic/biomodel/squids/squids.htm "cleaning" waves on squids (AP, 1995) Global, linear Local, non-linear "cleaning" waves in 2-dim. simulation gh NI 1993

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26/09/06© G. Heinz, www.gfai.de/~heinz34 Self-Interference Integrals (Visual Maps) n Self interference of waves (i, i, i) n Source arrangement defines map n Conjunctive, spatial maps Detecting fields Generating fields (g+h) time function plot

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26/09/06© G. Heinz, www.gfai.de/~heinz35 Self- /Cross- Interference Relations Waves meet itself -> "Self-"interference: wave i with i with i …Waves meet itself -> "Self-"interference: wave i with i with i … Waves meet other waves -> "Cross"-interference: wave i with i-1 …Waves meet other waves -> "Cross"-interference: wave i with i-1 … (i, i, i, i) self-interference location (i, i, i, i) self-int. (i, 0, i-1, i) cross-int. location (1) (3) (2) (4) cross- interference distance

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26/09/06© G. Heinz, www.gfai.de/~heinz36 Cross Interference Integrals - temporal Maps n Increasing channel number (2…8) reduces cross interference intensity if we consider over-conditioning effects Heinz 1996 (i, i, i, … i) self- interference locations cross-interference locations around

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26/09/06© G. Heinz, www.gfai.de/~heinz37 n Lashley was looking his life long for the locality of items learned (1920 … 1950) n 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: n The series of experiments... “has discovered nothing directly of the real nature of the engram“ Interpretation: n Cross interferences look like self interferences (!) n "Tutographic" brain, if it is an interference system n We can not avoid the holomorphy! Holomorphic Memory Region of cross-interferences around Region of self-interference 3-channel Simulation

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26/09/06© G. Heinz, www.gfai.de/~heinz38 Delay Shift Moves Interference Integrals (I²) n Variation of delay of one channel produces a moving interference integral (glia potential influences speed & location)

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26/09/06© G. Heinz, www.gfai.de/~heinz39 Velocity Variation Zooms Interference Integrals n Variation of background velocity in the detecting field zooms the interference integrals (neuroglia) n Cross interferences appear for low velocities

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26/09/06© G. Heinz, www.gfai.de/~heinz40 A Closer Look to Memory Density n 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

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26/09/06© G. Heinz, www.gfai.de/~heinz41 Rule of Fire Rate n Cross interference pattern depends on channel number & refractory period n We increase the average fire rate (reduced cross- interference distance) n Field overflow occurs: Cross interference overflows the self-interf., level generation! n Hypothesis: if pain is cross interference overflow, then this simple interference circuit models that behaviour ~ 7,5 ms ~ 5 ms ~ 4 ms ~ 1,5 ms

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26/09/06© G. Heinz, www.gfai.de/~heinz42 Analogy to Filter Theory n Neuron changes from a simple threshold gate to a digital filter circuit n Direct translation into digital filter structure is possible Distributed wire with delay Electrical node (!) digital filter circuit

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26/09/06© G. Heinz, www.gfai.de/~heinz43 Over-Conditioned Networks n Using high numbers of channels the delays on different paths do not match, resulting in blurred excitements far away from axis n Example: four channels project on a two- dimensional layer, see bottom image n n Four channels do not match on a 2-dim. field (max. 3) numb_channels = space_dimension +1 n= d + 1 or d = n - 1 n n High space dimensions for high channel numbers necessary n n Nerves need folded, inhomogeneous networks (!) clean blurred

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26/09/06© G. Heinz, www.gfai.de/~heinz44 n "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? Summary: Spatio-Temporal Maps

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26/09/06© G. Heinz, www.gfai.de/~heinz45 Summary n Little time shifts have dramatic influence on locations of interference, supposed we have small pulses n To analyze nerve networks we introduce the term Interference Network as a physical oriented approach to neurocomputing n We introduced interference integrals to visit locations of interference n Investigating the influence of small delays we find a lot of new effects: movement, zooming, conjugation, permutation, overflow, new neuronal basic functions n Analyzing projections we find over-condition effects regarding n-dimensional, inhomogeneous delay spaces n It is not possible to ignore small delays – pattern simulations (NN) deliver wrong results n It is not allowed, to use complex numbers to model interference systems n We have to re-think neural network research completely n And we have to re-think field theory into time domain

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26/09/06© G. Heinz, www.gfai.de/~heinz46 Future n IN-research will be included in the "BMBF- Informations- und Kommunikationstechnologien Programm (IKT2020)" n We try to start a pilot project (until now 13 proposals) n Find 1 GB more on www.gfai.de/~heinz www.gfai.de/~heinz Thanks for your attention.

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