Heinz, G.: Heinz, G.: Waves on Wires – Waves on Wires – Introduction to Interference Introduction to Interference Networks Networks What "Integrate and Fire" suggests What "Integrate and Fire" suggests Interference Principle, I.- Networks Interference Principle, I.- Networks 1D-, 2D-, 3D- Projections 1D-, 2D-, 3D- Projections Interference Integrals Interference Integrals I.-Types: Self-I., Cross-I. I.-Types: Self-I., Cross-I. Self-I. (Zoom, Movement, Somato-t. Self-I. (Zoom, Movement, Somato-t. Maps) Maps) Cross-I. (Spatio-Temporal Maps) Cross-I. (Spatio-Temporal Maps) Mixed S/C (Lashleys rats, I.- Mixed S/C (Lashleys rats, I.- overflow) overflow) Author Author: Dr. Gerd Heinz, GFaI, 12489 Berlin Dr. Gerd Heinz, GFaI, 12489 Berlin Albert-Einstein-Str. 16, Floor 5, Room 12B Albert-Einstein-Str. 16, Floor 5, Room 12B www.gfai.de/~heinz www.acoustic-camera.com [email protected]
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Heinz, G.:Heinz, G.: Waves on Wires – Waves on Wires – Introduction to Interference NetworksIntroduction to Interference Networks
HistoryHistory 1992 Introducing velocities and spikes into a (weighted) neural 1992 Introducing velocities and spikes into a (weighted) neural
network I found a symmetry, a network I found a symmetry, a mirror propertymirror property (in -> out map) (in -> out map)
http://www.gfai.de/~heinz/historic/index.htm (slide 9)http://www.gfai.de/~heinz/historic/index.htm (slide 9) 1993 book "Neuronale Interferenzen": new principles and 1993 book "Neuronale Interferenzen": new principles and
http://http://www.gfai.de/~heinz/publications/NI/index.htmwww.gfai.de/~heinz/publications/NI/index.htm 1994 - 98 Development of simulator '1994 - 98 Development of simulator 'PSI-ToolsPSI-Tools' for simulation ' for simulation
of nets and for nerve- and acoustic experimentsof nets and for nerve- and acoustic experiments To demonstrate the qualities of the approach: acoustic To demonstrate the qualities of the approach: acoustic
images, acoustic movies (images, acoustic movies (1994-96, first in the world1994-96, first in the world)) 1996 introduction of the term 1996 introduction of the term 'interference networks (IN)' 'interference networks (IN)'
characterizing the characterizing the 'physical approach to neural networks (NN)''physical approach to neural networks (NN)' Reason: Very different properties to weighted/pattern- NN'sReason: Very different properties to weighted/pattern- NN's 2004 International market entry with Acoustic Cameras2004 International market entry with Acoustic Cameras 2001, 2003, 2005 Awards for acoustic photo- and 2001, 2003, 2005 Awards for acoustic photo- and
Term 'interference': superimposition of wavesTerm 'interference': superimposition of waves Discrete Discrete 'waves on wires''waves on wires' Spherical, Spherical, 3-dimensional architecture3-dimensional architecture Moving time functions (spikes) f(t-Moving time functions (spikes) f(t-))
Central Question: Relativity of Wave Central Question: Relativity of Wave LengthLength Spikes move slowly through nerve system [2 µm/s … 120 Spikes move slowly through nerve system [2 µm/s … 120
m/s]m/s] Spikes have a limited (geometric) size [µm … cm]Spikes have a limited (geometric) size [µm … cm] Velocity v, pulse duration T, grid g, geometrical wavelength s Velocity v, pulse duration T, grid g, geometrical wavelength s
= v = v .. T T
s s g g Interference networkInterference network
s >> gs >> g Pool of neurons (NN.)Pool of neurons (NN.)
s [µm]s [µm]
g [µm] g [µm]
Which proportion is Which proportion is truth?truth?
Which grid is addressed?Which grid is addressed?• Spines?Spines?• Cell bodies?Cell bodies?• Columns?Columns?• It depends?It depends?
What "Integrate and Fire" suggestsWhat "Integrate and Fire" suggests
„„The probability to excite a neuron is higher as more The probability to excite a neuron is higher as more closed the partial impulses can reach it“ closed the partial impulses can reach it“ (Heinz, NI, 1993)(Heinz, NI, 1993)
random: no excitement synchronous: random: no excitement synchronous: firefire
Projection Law Projection Law (Heinz'93)(Heinz'93) Waves need to be at the detecting place at the same Waves need to be at the detecting place at the same
Classic Beam-Approach of OpticsClassic Beam-Approach of Optics
Light way (beam) defined by a Light way (beam) defined by a minimum of a path minimum of a path integralintegral (Fermat, Huygens, Maupertuis, Newton, Euler, (Fermat, Huygens, Maupertuis, Newton, Euler, Lagrange, Hamilton, Leibniz, Jacobi, Helmholtz, Maxwell, Lagrange, Hamilton, Leibniz, Jacobi, Helmholtz, Maxwell, Heisenberg, Schrödinger, Feynman)Heisenberg, Schrödinger, Feynman)
Fermat: Minimum principle, shortest way of lightFermat: Minimum principle, shortest way of light Huygens, Huygens, Maupertuis: smallest action, waveMaupertuis: smallest action, wave theory theory
dtqqLdsmvSq
q
q
q
)',( 2
1
2
1
qq22
qq11
q(t)q(t)
Lagrange function = (T-V); T kinetic, V potential energyLagrange function = (T-V); T kinetic, V potential energy
(compare H. Lübbig 1998, W. Kuhn 2001)(compare H. Lübbig 1998, W. Kuhn 2001)
Signals meet at Signals meet at locations with identical locations with identical delays from source delays from source (self-interference)(self-interference)
(all other cases not (all other cases not drawn)drawn)
Specific neurons begin Specific neurons begin to communicateto communicate
Address relations Address relations between locations between locations given by delaysgiven by delays
Time codes locationTime codes locationSingle point observations Single point observations look like density look like density modulated signals or modulated signals or bursts?bursts?
Understanding the Wave AbstractionUnderstanding the Wave Abstraction Each neuron has different delays to source pointsEach neuron has different delays to source points For didactic purposes we use some abstractions: For didactic purposes we use some abstractions:
– homogeneous velocityhomogeneous velocity– equidistant neurons (as pixels of an image)equidistant neurons (as pixels of an image)
Detecting field is a bitmap of pixels (symbolizing Detecting field is a bitmap of pixels (symbolizing neurons)neurons)
Understanding Gen.- and Det.- MasksUnderstanding Gen.- and Det.- Masks Each locations has its own time scheme, has its own mask Each locations has its own time scheme, has its own mask
2-dim. Wave Field Simulation2-dim. Wave Field Simulation If we consider all possible paths, any emission is If we consider all possible paths, any emission is
on a circle of delay on a circle of delay around any source: we call around any source: we call it 'wave'it 'wave'
I² are composed of waves I² are composed of waves Didactic suggestions: Didactic suggestions:
"Your "Your file gfai_30_.avi (file gfai_30_.avi (GFaI-movie) reminds me of a GFaI-movie) reminds me of a trapped wave packet scattered inside a chamber. It also trapped wave packet scattered inside a chamber. It also reminds me of ray tracing inside an inhomogeneous reminds me of ray tracing inside an inhomogeneous wave duct where one can compute the wave wave duct where one can compute the wave trajectories using Snell's law. trajectories using Snell's law. So I understand that So I understand that interference effects can be computed using geometry interference effects can be computed using geometry (the propagation path as a function of space and time) (the propagation path as a function of space and time) instead of wave mechanics.instead of wave mechanics. Feynman used the path Feynman used the path integral approach to build up a sum of probabilities for integral approach to build up a sum of probabilities for quantum trajectories instead of using the Schrodinger quantum trajectories instead of using the Schrodinger wave equation." wave equation."
Andrews squid-experiments (1995) show moving Andrews squid-experiments (1995) show moving excitations between chromatophore-cellsexcitations between chromatophore-cells
Cells are connected via a nerve-like structureCells are connected via a nerve-like structure Excitation and relaxation can produce wavesExcitation and relaxation can produce waves Time functions appear Time functions appear
comparable to nervecomparable to nerve Although the mechanism is Although the mechanism is
not exactly known, the effect not exactly known, the effect needs a wave-interference needs a wave-interference descriptiondescription
Long time-integration pulls up Long time-integration pulls up the energy of wave-hit-the energy of wave-hit-locations (self interference locations (self interference locations)locations)
Source arrangement defines Source arrangement defines the mapsthe maps
Maps can be conjunctive Maps can be conjunctive (g+h)(g+h)
• Self interference increases the excitability of a neuronSelf interference increases the excitability of a neuron• Self interference properties define 'mirrored projections'Self interference properties define 'mirrored projections'• The term 'wave' abstracts a two- or higher dimensional The term 'wave' abstracts a two- or higher dimensional
movement of many spikes through any delaying spacemovement of many spikes through any delaying space• It is not possible to interpret anything, if we observe only It is not possible to interpret anything, if we observe only
one channel of a projectionone channel of a projection• Timing defines the location: Only wave addressed neurons Timing defines the location: Only wave addressed neurons
can learncan learn• Self interference is very sensitive against any parameter Self interference is very sensitive against any parameter
drift, circuits need auto-control and regulation drift, circuits need auto-control and regulation (-> Hebb's rule in a different light)(-> Hebb's rule in a different light)
• Local superimposition needs 'cleaning waves' before any Local superimposition needs 'cleaning waves' before any neuron can be addressedneuron can be addressed
Cross-Int. Integrals: "Spatio-Temporal Cross-Int. Integrals: "Spatio-Temporal Maps"Maps" Cross interference defines all temporal mapsCross interference defines all temporal maps We consider identical, periodical fire on all channelsWe consider identical, periodical fire on all channels Cross interference is maximum for two channels Cross interference is maximum for two channels
-> which channel number has the-> which channel number has the auditory system? Only two? auditory system? Only two?
We like 'harmony' in soundWe like 'harmony' in sound 'Harmonies' address similar points'Harmonies' address similar points
LashleyLashley was looking his life long for the locality of items was looking his life long for the locality of items learned (1920 … 1950) learned (1920 … 1950)
Rats became teached a way through a labyrinth. He Rats became teached a way through a labyrinth. He removed systematically small parts of the brain and removed systematically small parts of the brain and proved the before learnedproved the before learned
Summary of his experiments: Summary of his experiments: The series of experiments ... The series of experiments ...
“has discovered nothing “has discovered nothing directly of the real nature directly of the real nature of the engram“of the engram“
Interpretation: Interpretation: Cross interferences look like Cross interferences look like
self interferences (!)self interferences (!) "Tutographic" brain, if it "Tutographic" brain, if it
is an interference systemis an interference system We can not avoid the dualityWe can not avoid the duality
Self- and Cross- Interference InteractionSelf- and Cross- Interference Interaction
Region of cross-interferences aroundRegion of cross-interferences around
Region of self-interferenceRegion of self-interference
Variation of relative delay changes wave directionVariation of relative delay changes wave direction Glia can modulate the velocity of nervesGlia can modulate the velocity of nerves
Variation of delay of one channel produces a moving Variation of delay of one channel produces a moving interference integral (glia potential influences speed & interference integral (glia potential influences speed & location)location)
Velocity Variation Zooms IntegralsVelocity Variation Zooms Integrals Variation of background velocity in the detecting field Variation of background velocity in the detecting field
zooms the interference integrals (neuroglia)zooms the interference integrals (neuroglia) Cross interferences appear for low velocitiesCross interferences appear for low velocities
A Closer Look to Memory DensityA Closer Look to Memory Density
As slower is the velocity in the detecting field, as As slower is the velocity in the detecting field, as smaller is the addressable region, as higher is the smaller is the addressable region, as higher is the density and the addressable memory volumedensity and the addressable memory volume
If we ask "How do you do?", we get different answers:If we ask "How do you do?", we get different answers:– Professor: (pause) "ohhhh" (pause) "don't know?"Professor: (pause) "ohhhh" (pause) "don't know?"– Tennis profi: "Oh fine, I won the mastership!"Tennis profi: "Oh fine, I won the mastership!"
Zooming & Movement for Pattern Zooming & Movement for Pattern MatchingMatching
To recognize a person or face, we have to "scale" the To recognize a person or face, we have to "scale" the image to the same size and position (zooming and image to the same size and position (zooming and movement)movement)
Our eyes have no optical zoomOur eyes have no optical zoom Adoption with electronic scaling? path: Adoption with electronic scaling? path: retina to visual retina to visual
cortexcortex?? (Comparable task for somato-topic projections in (Comparable task for somato-topic projections in
Cross interference Cross interference pattern depends on pattern depends on channel number & channel number & refractory periodrefractory period
We increase the We increase the average fire rate average fire rate (reduced cross-(reduced cross-interference distance) interference distance)
Field overflow occurs: Field overflow occurs: Cross interference Cross interference overflows the self-overflows the self-interf.,interf.,loss of information!loss of information!
Hypothesis: if pain is Hypothesis: if pain is cross interference cross interference overflow, then this overflow, then this simple interference simple interference circuit models that circuit models that behaviourbehaviour
"Interference integral" = integration of time "Interference integral" = integration of time function of each location over timefunction of each location over time
Bio-Neuro-ResearchBio-Neuro-Research Data addressing Data addressing
– Refractoriness and bidirectional exchangeRefractoriness and bidirectional exchange– Geometrical wave lengthGeometrical wave length– Cleaning waves (non-linear superimposition)Cleaning waves (non-linear superimposition)
Data processing Data processing
– Temporal correspondence of arrangementsTemporal correspondence of arrangements– Data compression & segmentationData compression & segmentation– Interference learning, self-organisationInterference learning, self-organisation
Spatial projectivitySpatial projectivity
– High channel numbers? Field size contra channel numberHigh channel numbers? Field size contra channel number Cross-interference properties (temporal selectivity)Cross-interference properties (temporal selectivity)
– Creating behaviourCreating behaviour– Relations between net geometry and behaviourRelations between net geometry and behaviour
Thanks to Benny Hochner (Hebrew Univ. Jerusalem), Tamar Thanks to Benny Hochner (Hebrew Univ. Jerusalem), Tamar Flash (Weizmann Inst. Rehovot) and Mosche Abeles (Bar-Ilan Flash (Weizmann Inst. Rehovot) and Mosche Abeles (Bar-Ilan Univ. Ramat Gan) for invitation, talks and discussions. Univ. Ramat Gan) for invitation, talks and discussions.
Thanks to my wife Gudrun. She helped me over years of Thanks to my wife Gudrun. She helped me over years of missing acknowledgements without doubt.missing acknowledgements without doubt.
Interference Conditions in DetailInterference Conditions in Detail
Generating Mask M, detecting (inverse) Mask M* M + Generating Mask M, detecting (inverse) Mask M* M + M* = TM* = T„all ways have the same delay" (Hz'93)„all ways have the same delay" (Hz'93)
Cross interference: Cross interference: „… plus /minus foregoer/follower"„… plus /minus foregoer/follower"
Inhomogenity and Over-ConditioningInhomogenity and Over-Conditioning
A one-dimensional projection needs two channelsA one-dimensional projection needs two channels A two-dimensional projection needs three channelsA two-dimensional projection needs three channels (the system is called 'over-conditioned', if more channels (the system is called 'over-conditioned', if more channels
match)match)
. . .. . . For a n dimensional projection d we need n+1 channelsFor a n dimensional projection d we need n+1 channels
d = n+1d = n+1
How to realize high dimensions?How to realize high dimensions?– Distorted, folded spaceDistorted, folded space– Diameter (velocity) variation of dendritesDiameter (velocity) variation of dendrites– Non-linear wiringNon-linear wiring
Colored Interference SystemsColored Interference Systems Nerves diameter vary, different carrier mechanismsNerves diameter vary, different carrier mechanisms Waves can meetWaves can meet
Scene Representation andScene Representation andInformation ReductionInformation Reduction Delay learning can compose single Delay learning can compose single
points, representing whole scenespoints, representing whole scenes Example: 30 neurons "GH" can be Example: 30 neurons "GH" can be
represented using only 3 represented using only 3 interference locations interference locations
Permutation and Decomposition of ScenesPermutation and Decomposition of Scenes Down: high dim. scenes can be decomposed to lower Down: high dim. scenes can be decomposed to lower
dimensionsdimensions Up: low dim. scenes can create higher dim. scenes using Up: low dim. scenes can create higher dim. scenes using
Projection contra ReconstructionProjection contra Reconstruction
Natural time runs only in one Natural time runs only in one direction:direction:– ProjectionProjection– Mirror property (!)Mirror property (!)
Computer time can run back Computer time can run back – ReconstructionReconstruction– Non-mirrored (!)Non-mirrored (!)– For technical purposes (AK)For technical purposes (AK)– Pseudo-wave-field problemPseudo-wave-field problem
the direction of time axis the direction of time axis defines the difference between defines the difference between themthem
We have to live with a We have to live with a small number of small number of channelschannels
Any time-function Any time-function recorded by a sensor recorded by a sensor (microphone, (microphone, electrode) has lost the electrode) has lost the wave-field informationwave-field information
In reconstruction it In reconstruction it produces a new wave produces a new wave field (secondary wave field (secondary wave field)field)
This is complete This is complete different to the original different to the original wave fieldwave field
But we have to work But we have to work with!with!
Secondary Wave FieldSecondary Wave Field
Original Wave FieldOriginal Wave Field
Recording Sensor
Emission
Understanding Primary and Secondary Wave Understanding Primary and Secondary Wave FieldsFields
Interference integral Interference integral appears appears non-mirrorednon-mirrored
dT
dT
dT
templateMirrored projection
Primary field
Secondary fieldInterference Projection f(t-T)
template
Interference Reconstruction f(t+T)
Inverse time
Optical lense systems, SonarOptical lense systems, Sonar Nerve systems (!)Nerve systems (!) Beamformíng with delay elementsBeamformíng with delay elements
Fink "Time Reversal Mirrors"Fink "Time Reversal Mirrors" Acoustic CameraAcoustic Camera
"Interference Projection" "Interference Projection" published in BioNet‘96published in BioNet‘96
First acoustic image First acoustic image 1994 used the 1994 used the Interference-Interference-Transformation (HIT) as Transformation (HIT) as "reconstruction" (not "reconstruction" (not published)published)
A Wave Model for Penfields Homunculus...A Wave Model for Penfields Homunculus... A hyperbola defines a fixed delay difference to two A hyperbola defines a fixed delay difference to two
points F, F' points F, F' Different hyperbolas define different delay differences Different hyperbolas define different delay differences
a/a', c/c'a/a', c/c' Pulses meet at different locations, see drawingPulses meet at different locations, see drawing (Self-I. location is defined by wave front direction)(Self-I. location is defined by wave front direction)
Homunculus and the Thumb ExperimentHomunculus and the Thumb Experiment Motion moves projections Motion moves projections
dependent of position, see thumb dependent of position, see thumb experimentexperiment
Ganglion spinale creates a Ganglion spinale creates a hyperbolic projection into hyperbolic projection into medulla spinalismedulla spinalis
So the movement is So the movement is compensated, thumb position compensated, thumb position (up/down) does not influence (up/down) does not influence homunculus positionhomunculus position
-> Nerve system needs -> Nerve system needs 'normalized' or scaled maps – 'normalized' or scaled maps – free of body distortionsfree of body distortions
Penfield's "Homunculus" seems Penfield's "Homunculus" seems to be a scaled projectionto be a scaled projection
Shift of somato-topic maps can Shift of somato-topic maps can be compensatedbe compensated– Sensory mapsSensory maps– Motor mapsMotor maps
Self interference location Self interference location appear, where wave appear, where wave direction and screen have direction and screen have identical orientationidentical orientation
Scale-normalization of Scale-normalization of images needs zooming and images needs zooming and movementmovement
Visual cortex as a Visual cortex as a normalized wave field normalized wave field screen?screen?
To detect scenes or To detect scenes or frequencies or codes, to frequencies or codes, to control bodies, to create control bodies, to create behaviour…behaviour…