DLP Technology-Driven, Optical Neural Network Results and Future Design. Emmett Redd Professor Missouri State University

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1 DLP Technology-Driven, Optical Neural Network Results and Future Design Emmett Redd Professor Missouri State University

2 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

3 Optical Computing & Neural Networks Optical Parallel Processing Gives Speed Lenslet s Enlight Giga Multiply and Accumulate per second Order 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

4 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

5 Standard Neural Net Learning We use a Training or Learning algorithm to adjust the weights, usually in an iterative manner. x1 Σ y1 xn Σ ym Target Output (T) Learning Algorithm Other Info

6 FWL-NN is equivalent to a standard Neural Network + Learning Algorithm Σ Σ FWL-NN Σ Σ + Learning Algorithm

7 Signal Source (Layer Input) Optical Recurrent Neural Network Synaptic Medium (35mm Slide) Postsynaptic Optics Target Neuron Summation Micromirror Array Presynaptic Optics Squashing Functions Recurrent Connections Layer Output A 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.

8 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

9 Optical Fixed-Weight Learning Synapse Tranapse x(t) Σ y(t-1) W(t-1) T(t-1) x(t-1) Planapse

10 Page Representation of a Recurron U(t-1) Bias Tranapse B(t) A(t) Tranapse Tranapse Σ O(t-1) Planapse

11 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

12 DMD or DLP Optical System

13 Signal Source (Layer Input) Optical Recurrent Neural Network Synaptic Medium (35mm Slide) Postsynaptic Optics Target Neuron Summation Micromirror Array Presynaptic Optics Squashing Functions Recurrent Connections Layer Output A 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.

14 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 AND Unsigned Multiply FWL Recurron

15 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

16 Stretch, Squash, and Rotate D x1 L xp y1 y L P 2 2 x1 L x P = xy 1 1 L xp yp 2 2 y1 L y P 1 L 1 1 x 1 y 0 x 0 y 1 x 2 y 0 x 1 y 1 x 0 y 2 x 3 y 0 x 2 y 1 x 1 y 2 x 0 y 3 etc. None Linear Quadratic Cubic etc.

17 Where We Are and Where We Want to Be DMD Dots Image (pegs) Slide Dots Image (holes) C C'

18 CCD Image of Known DLP Positions DMD Dots Image (pegs) Automatically Finds Points via Projecting 42 Individual Pegs C = H D H = C D P

19 CCD Image of Holes in Slide Film Slide Dots Image (holes) Manually Click on Interference to Zoom In

20 Mark the Center ZOOM OF DIFFRACTION PATTERN #1. Click on center

21 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 1 st minimum Ax 2 +Bxy+Cy 2 +Dx+Ey+1 = 0 Find its center x c =(BE-2CD)/(4AC-B 2 ), y c =(BD- 2AE)/(4AC-B 2 ) Hole location

22 Ellipse Fitting Changeable center and orientation parameters 4 3 theta x y x' y' E General Equation resulting from rotating and translating x^2/16 + y^2/9 = 1 by h, k, and theta. A B C D E F Recovered center and orientation parameters h k theta Gaussian Elimination Below

23 Eighty-four Clicks Later Slide Dots Image (holes) C' = M C M = C' C P

24 DLP Projected Regions of Interest D' = H -1 M -1 H D and C' = H D'

25 Nonlinearities Measured light signals vs. Weights for FWL Recurron Opaque slides aren t, ~6% leakage

26 Neural Networks and Results Recurrent AND Unsigned Multiply Fixed Weight Learning Recurron

27 Recurrent AND I N 1-cycle delay I N-1 I N I N-1

28 Source Neurons (buffers) Recurrent AND Neural Network Bias (1) -14/16 logsig(16*σ) I N 10/16 Σ 1 10/16 0 I N I N-1 Terminal Neurons -1/2 linsig(2*σ) I N-1 2/2 Σ 1 0

29 Synaptic Weight Slide Weights /16-1/2-14/16 10/16 2/2

30 MATLAB Recurrent AND Demo

31 Pulse Image (Regions of Interest)

32 Output Swings Larger than Input

33 Synaptic Weight Slide

34 Unsigned Multiply Results About 4 bits Blue-expected Black-obtained Red-squared error

35 Page Representation of a Recurron U(t-1) Bias Tranapse B(t) A(t) Tranapse Tranapse Σ O(t-1) Planapse

36 FWL Recurron Synaptic Weight Slide

37 Optical Fixed-Weight Learning Synapse Tranapse x(t) Σ y(t-1) W(t-1) T(t-1) x(t-1) Planapse

38 Signal Source (Layer Input) Optical Recurrent Neural Network Synaptic Medium (35mm Slide) Postsynaptic Optics Target Neuron Summation Micromirror Array Presynaptic Optics Squashing Functions Recurrent Connections Layer Output A 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.

39 Future: Integrated Photonics Photonic (analog) i. Concept α. Neuron β. Weights γ. Synapses Photonics Spectra and Luxtera

40 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

41 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.

42 DLP -Driven, Optical Neural Network Results and Future Design Emmett Redd & A. Steven Younger Missouri State University

43 Source Pulse