dlp technology-driven, optical neural network results and
TRANSCRIPT
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DLP® Technology-Driven, Optical Neural Network Results and
Future Design
Emmett ReddProfessorMissouri State University
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Neural Network Applications
• Stock Prediction: Currency, Bonds, S&P 500 and Natural Gas• Business: Direct mail, Credit Scoring, Appraisal and Summoning Juries• Medical: Breast Cancer, Heart Attack Diagnosis and ER Test Ordering• Sports: Horse and Dog Racing• Science: Solar Flares, Protein Sequencing, Mosquito ID and Weather• Manufacturing: Welding Quality, Plastics or Concrete Testing• Pattern Recognition: Speech, Article Class. and Chem. Drawings• No Optical Applications—We are starting with Boolean• most from www.calsci.com/Applications.html
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Optical Computing & Neural Networks
• Optical Parallel Processing Gives Speed– Lenslet’s Enlight 256—8000 Giga Multiply and
Accumulate per second– Order 1011 connections per second possible with
holographic attenuators• Neural Networks
– Parallel versus Serial– Learn versus Program– Solutions beyond Programming– Deal with Ambiguous Inputs– Solve Non-Linear problems– Thinking versus Constrained Results
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Optical Neural Networks
• Sources are modulated light beams (pulse or amplitude)
• Synaptic Multiplications are due to attenuation of light passing through an optical medium (30 fs)
• Geometric or Holographic• Target neurons sum signals from many source
neurons.• Squashing by operational-amps or nonlinear
optics
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Standard Neural Net Learning• We use a Training or Learning algorithm to adjust
the weights, usually in an iterative manner.
…x1
xN
y1
…yM
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Learning Algorithm
Target Output (T) Other Info
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FWL-NN is equivalent to a standard Neural Network + Learning Algorithm
Σ
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FWL-NN
+Learning Algorithm
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Optical Recurrent Neural Network
Squashing Functions
Synaptic Medium(35mm Slide)
Target Neuron Summation
Signal Source (Layer Input)
Layer OutputA Single Layer of an Optical Recurrent Neural Network. Only four synapses are shown. Actual networks will have a large number of synapses. A multi-layer network has several consecutive layers.
Micromirror Array
PresynapticOptics
Postsynaptic Optics
Recurrent Connections
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Definitions
• Fixed-Weight Learning Neural Network (FWL-NN) – A recurrent network that learns without changing synaptic weights
• Potency – A weight signal• Tranapse – A Potency modulated synapse• Planapse – Supplies Potency error signal• Zenapse – Non-Participatory synapse• Recurron – A recurrent neuron• Recurral Network – A network of Recurrons
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Optical Fixed-Weight Learning Synapse
W(t-1)
x(t)
Σ
x(t-1)
T(t-1)
Planapse
Tranapse
y(t-1)
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Page Representation of a Recurron
Tranapse
Planapse
Tranapse
Tranapse
U(t-1)
A(t)
B(t)
Bias
O(t-1)Σ
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Optical Neural Network Constraints
• Finite Range Unipolar Signals [0,+1]• Finite Range Bipolar Attenuation[-1,+1]• Excitatory/Inhibitory handled separately• Limited Resolution Signal• Limited Resolution Synaptic Weights• Alignment and Calibration Issues
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Optical System
DMD or DLP®
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Optical Recurrent Neural Network
Squashing Functions
Synaptic Medium(35mm Slide)
Target Neuron Summation
Signal Source (Layer Input)
Layer OutputA Single Layer of an Optical Recurrent Neural Network. Only four synapses are shown. Actual networks will have a large number of synapses. A multi-layer network has several consecutive layers.
Micromirror Array
PresynapticOptics
Postsynaptic Optics
Recurrent Connections
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Design Details and Networks
• Digital Micromirror Device • 35 mm slide Synaptic Media• CCD Camera • Synaptic Weights - Positionally Encoded
- Digital Attenuation• Allows flexibility for evaluation.
Recurrent ANDUnsigned MultiplyFWL Recurron
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DMD/DLP®—A Versatile Tool
• Alignment and Distortion Correction– Align DMD/DLP® to CCD——PEGS– Align Synaptic Media to CCD——HOLES– Calculate DMD/DLP® to Synaptic Media
Alignment——Putting PEGS in HOLES– Correct projected DMD/DLP® Images
• Nonlinearities
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Stretch, Squash, and Rotate
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P
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P P
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x xy y
x xD
x y x yy y
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥
= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
L
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x1y0 x0y1
x2y0 x1y1 x0y2
x3y0 x2y1 x1y2 x0y3
etc.
None
Linear
Quadratic
Cubic
etc.
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Where We Are and Where We Want to Be
DMD Dots Image (pegs)
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Slide Dots Image (holes)
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C C'
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DMD Dots Image (pegs)
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CCD Image of Known DLP® Positions
Automatically Finds Points via Projecting 42 Individual Pegs
C = H ● D
H = C ● DP
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Slide Dots Image (holes)
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CCD Image of Holes in Slide Film
Manually Click on Interference to Zoom In
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ZOOM OF DIFFRACTION PATTERN #1. Click on center
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Mark the Center
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Options for Automatic Alignment
• Make holes larger so diffraction is reduced– A single large Peg might illuminate only one Hole at a
time– Maximum intensity would mark Hole location
• Fit ellipse to 1st minimum— Ax2+Bxy+Cy2+Dx+Ey+1 = 0– Find its center— xc=(BE-2CD)/(4AC-B2), yc=(BD-
2AE)/(4AC-B2) – Hole location
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Changeable center and orientation parameters4 3 theta
-4 2 0.523598767 0.5 0.523598767
x 4 -4 0 0y 0 0 3 -3
-2 2x' -0.535898367 -7.464101633 -5.5 -2.5 -2 -2 -1.663745 -7.464101615 -3.369187 -6.322583664y' 3.999999969 3.09401E-08 4.598076 -0.598076 5.12147 -0.270636326 0 0 -1 -1
-4 0 -4 0
General Equation resulting from rotating and translating x 2̂/16 + y 2̂/9 = 1 by h, k, and theta.A B C D E F
10.75 -6.062177764 14.25000005 98.12436 -81.24871 133.4970 0 0 0 0 0 0 0 0 0
Recovered center and orientation parametersh k theta
-4 2 0.5235987674 4 2.768049 55.71281292 11.35142 39.97506419
-10.2429 0.541272651 0 0 3.369187 6.32258366426.2294 0.073244021 0 0 1 1
-2 -2 -1.663745 -7.464101615 -3.369187 -6.322583664Gaussian Elimination Below 5.12147 -0.270636326 0 0 -1 -1
4 -10.24293658 26.22943744 -2 5.121468 -14 0.541272651 0.073244021 -2 -0.270636 -1
2.76805 0 0 -1.663745 0 -155.7128 0 0 -7.464102 0 -111.3514 3.369186883 1 -3.369187 -1 -1
1 -2.560734145 6.557359359 -0.5 1.280367 -0.250 10.78420923 -26.15619342 0 -5.392105 00 7.088237103 -18.15109078 -0.279721 -3.544119 -0.307990 142.6657023 -365.3289352 20.3923 -71.33285 12.92820 32.43715631 -73.43534183 2.306523 -15.53398 1.83786
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Ellipse Fitting
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Slide Dots Image (holes)
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Eighty-four Clicks Later
C' = M ● C
M = C' ● CP
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DLP® Projected Regions of Interest
D' = H-1●M-1●H●D
and
C' = H ● D'
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Nonlinearities
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Measured light signals vs. Weights for FWL Recurron
Opaque slides aren’t, ~6% leakage.
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Neural Networks and Results
• Recurrent AND• Unsigned Multiply• Fixed Weight Learning Recurron
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IN
IN-1IN • IN-1
1-cycledelay
Recurrent AND
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IN
IN-1
IN • IN-1
Bias (1)
Source Neurons (buffers)
Terminal Neurons
-14/16
10/16
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-1/2
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logsig(16*Σ)
linsig(2*Σ)
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Recurrent AND Neural Network
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Synaptic Weight Slide
Weights
0.5 10/16 -1/2
-14/16 10/16 2/2
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Recurrent AND Demo
• MATLAB
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Pulse Image (Regions of Interest)
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Output Swings Larger than Input
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Synaptic Weight Slide
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Unsigned Multiply Results
About 4 bits
Blue-expected
Black-obtained
Red-squared error
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Page Representation of a Recurron
Tranapse
Planapse
Tranapse
Tranapse
U(t-1)
A(t)
B(t)
Bias
O(t-1)Σ
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FWL Recurron Synaptic Weight Slide
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Optical Fixed-Weight Learning Synapse
W(t-1)
x(t)
Σ
x(t-1)
T(t-1)
Planapse
Tranapse
y(t-1)
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Optical Recurrent Neural Network
Squashing Functions
Synaptic Medium(35mm Slide)
Target Neuron Summation
Signal Source (Layer Input)
Layer OutputA Single Layer of an Optical Recurrent Neural Network. Only four synapses are shown. Actual networks will have a large number of synapses. A multi-layer network has several consecutive layers.
Micromirror Array
PresynapticOptics
Postsynaptic Optics
Recurrent Connections
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Future: Integrated Photonics
• Photonic (analog)• i. Concept• α. Neuron• β. Weights• γ. Synapses
Photonics Spectra and Luxtera
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Continued
• ii. Needs• α. Laser• β. Amplifier (detectors and control)• γ. Splitters• δ. Waveguides on Two Layers• ε. Attenuators• ζ. Combiners• η. Constructive Interference• θ. Destructive Interference• ι. Phase
Photonics Spectra and Luxtera
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Interest Generated?
• We wish to implement Optical Neural Networks in Silicon—Including Fixed Weight Learning.
• To do so, we need Collaborators.• Much research remains, but an earlier start means an
earlier finish.• Please contact me if interested.
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DLP®-Driven, Optical Neural Network Results and Future Design
Emmett Redd & A. Steven YoungerMissouri State [email protected]
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Source Pulse