Optical RESERVOIR COMPUTING Presented By PRIYANKAR ROYCHOWDHURY

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

ARTIFICIAL NEURAL NETWORKS:

RECURRENT NEURAL NETWORKS: MEMORY FUNCTION INCLUDED

What happens in RC? COMPUTATION MAPPING EMULATION INPUT OUTPUT OUTPUT

SCHEMATIC VIEW OF A RESERVOIR COMPUTER

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

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

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

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

Inside RC: Number of Neurons for state-of-the-art performance: 100-1000 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

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

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

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

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

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

Optical Communication in Computing:

Schematic of all Optical Reservoir Computer:

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

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

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

Time Interleaving based Virtualization in RC:

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

Experimental Results: