1. Optical RESERVOIR COMPUTING
Presented By
PRIYANKAR ROYCHOWDHURY

2. What is Reservoir Computing?
A Decade old Concept in field of Machine Learning
Used to train Recurrent Neural Networks
Systems are trained based on examples, instead of programmed with Algorithms

3. ARTIFICIAL NEURAL NETWORKS:

4. RECURRENT NEURAL NETWORKS:
MEMORY FUNCTION INCLUDED

5. What happens in RC? COMPUTATION MAPPING EMULATION INPUT OUTPUT OUTPUT

6. SCHEMATIC VIEW OF A RESERVOIR COMPUTER

7. Inside RC: A high-dimensional non-linear dynamical system
A Reservoir consists of a set of randomly connected neurons/nodes
Responses of all Neurons to an Input Signal are weighted and combined through a linear read-out function at the Output Layer
Output Signal is calculated at Output Layer

8. Mathematical Analysis:
A collection of Internal Nodes, whose states evolve in Discrete Time
As an Equation:

9. Mathematical Analysis:
N = No. of Nodes
FNL = A Non-linear Function
u(n) = Input Signal
Mi = Input Mask Vector
A = Interconnection Matrix
α = Feedback Gain
β = Output Gain

10. Mathematical Analysis:
Wi = Output Weights
ŷ(n) = Actual Output

11. Inside RC:
Number of Neurons for state-of-the-art performance:
Later it was demonstrated that a single non-linear node with delay can achieve same performance as RNN
This simplification of architecture was break-through; it provided the way towards experiments at high speeds

12. Task Processing in RC: ONE TASK IN ONE RC
ONE INPUT DATA
ONE OUTPUT DATA
Independent Tasks simultaneously processed in separate RC systems
Disadvantages: costly, energy-efficient, complex control, bulky large systems

13. Parallel Computation on Same Data :
RESPECTIVE OUTPUTS
SINGLE INPUT DATA STREAM
PROCESSING OF
DIFFERENT TASKS
APPLICATIONS: Speech and Speaker Recognition, Different Boolean Logic Operations on Same Data

14. Challenges in Parallel Computations on Multiple Data Streams:
All Input Data Streams can get mixed in the Reservoir causing Cross-talk
Response of Nodes more sensitive to Global Stimulus rather than to Specific Stimuli
Existing Electronics Technology cannot deal with this problem

15. Solution: Need for an Alternative Technology other than Electronics
Photonics can solve this problem
Parallelism can be achieved in Photonics due to Wavelength Division Multiplexing

16. Hardware of Photonics:
Transmitter: Multilongitudinal mode Lasers e.g Semiconductor Ring Laser, Microring Lasers
Communication Medium: Silicon Photonic Waveguide
Wavelength Selector: MicroRing Resonator (MRR)
SOA: Silicon Optical Amplifier
Optical Attenuator
Receiver: Photodetector

17. Optical Communication in Computing:

18. Schematic of all Optical Reservoir Computer:

19. Virtualization in RC: 50 Nodes in the System:
Total Bandwidth really used is 15 MHz
Available Bandwidth is determined by Cut-off Frequency of Feedback PhotoDiode: 125 MHz

20. Virtualization in RC:
Observation: System is underutilized, 36% of available Bandwidth is being used
Maximum Possible Nodes can be 424
Solution is: Virtualization

21. Method of Virtualization in RC:
8 Interleaved Reservoirs of 50 Nodes Each
This can result in 8 sets of N Internal Variables, without any connection between each Set
Time Interleaving is possible; It will enable independent and simultaneous Processing of Information

22. Time Interleaving based Virtualization in RC:

23. ŷ(n+1) = 0.3ŷ(n) + 0.5ŷ(n)( ∑9i=0ŷ(n-i)) + 1.5u(n-9)u(n) + 0.1
Benchmark:
NARMA 10 Task (10-th Order Non-Linear Auto Regressive Moving Average Equation)
An input u(n) randomly drawn from a Uniform Distribution [0,0.5] is injected
Equation defining Targeted Output:
ŷ(n+1) = 0.3ŷ(n) + 0.5ŷ(n)( ∑9i=0ŷ(n-i)) + 1.5u(n-9)u(n) + 0.1

24. Experimental Results: