DLP ® -Driven, Optical Neural Network Results and Future Design

1. DLP®-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, Natural Gas • Business: Direct mail, Credit Scoring, Appraisal, Summoning Juries • Medical: Breast Cancer, Heart Attack Diagnosis, ER Test Ordering • Sports: Horse and Dog Racing • Science: Solar Flares, Protein Sequencing, Mosquito ID, Weather • Manufacturing: Welding Quality, Plastics or Concrete Testing • Pattern Recognition: Speech, Article Class., Chem. Drawings • No Optical Applications—We are starting with Boolean • most from www.calsci.com/Applications.html

3. 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

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. Learning Algorithm Standard Neural Net Learning • We use a Training or Learning algorithm to adjust the weights, usually in an iterative manner. y1 x1 xN S … … … yM S Target Output (T) Other Info

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

7. Optical Recurrent Neural Network Signal Source (Layer Input) Target Neuron Summation Synaptic Medium (35mm Slide) Postsynaptic Optics Presynaptic Optics Squashing Functions Micromirror Array 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) y(t-1) Σ W(t-1) T(t-1) x(t-1) Planapse

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

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. Optical System DMD or DLP®

13. and Networks Design Details • 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

14. 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

15. Stretch, Squash, and Rotate None Linear Quadratic Cubic etc. 1 x1y0 x0y1 x2y0 x1y1 x0y2 x3y0 x2y1 x1y2 x0y3 etc.

16. DMD Dots Image (pegs) Slide Dots Image (holes) 100 100 200 200 300 300 400 400 500 500 600 600 700 700 800 800 900 900 1000 1000 200 400 600 800 1000 1200 200 400 600 800 1000 1200 Where We Are and Where We Want to Be C C'

17. CCD Image of Known DLP® Positions DMD Dots Image (pegs) 100 200 300 400 500 600 700 800 900 1000 200 400 600 800 1000 1200 Automatically Finds Points via Projecting 42 Individual Pegs C = H ● D H = C ● DP

18. CCD Image of Holes in Slide Film Slide Dots Image (holes) 100 200 300 400 500 600 700 800 900 1000 200 400 600 800 1000 1200 Manually Click on Interference to Zoom In

19. Mark the Center

20. Plans for Automatic Alignment • Methods and Details about automatically finding the holes. Might add a couple of more slides, more matrix manipulation, and even an Excel spreadsheet demonstration.

21. Eighty-four Clicks Later C' = M ● C M = C' ● CP

22. DLP® Projected Regions of Interest D' = H-1●M-1●H●D and C' = H ● D'

23. Nonlinearities Measured light signals vs. Weights for FWL Recurron Opaque slides aren’t, ~6% leakage.

24. Neural Networks and Results • Recurrent AND • Unsigned Multiply • Fixed Weight Learning Recurron

25. Recurrent AND IN IN IN-1 IN-1 1-cycle delay

26. Recurrent AND Neural Network Source Neurons (buffers) Bias (1) -14/16 logsig(16*Σ) 10/16 1 IN Σ IN IN-1 10/16 0 Terminal Neurons IN-1 -1/2 linsig(2*Σ) Σ 1 2/2 0

27. Synaptic Weight Slide Weights 0.5 10/16-1/2 -14/1610/16 2/2

28. Recurrent AND Demo • MATLAB

29. Pulse Image (Regions of Interest)

30. Output Swings Larger than Input

31. Synaptic Weight Slide

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

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

34. FWL Recurron Synaptic Weight Slide

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

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

37. 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

38. DLP®-Driven, Optical Neural Network Results and Future Design Emmett Redd & A. Steven Younger Missouri State University EmmettRedd@MissouriState.edu

39. Source Pulse