Liquid State Machines

and

Large Simulations

of Mammalian Visual System

Grzegorz M. Wójcik

14 XII 2004

Introduction

• Neuron

• Brain

• Visual System and Visual Cortex

• Hodgkin-Huxley Model

• Liquid State Machine

• Self Organizing Criticality

• Results and plans for the future

Neuron

• Soma, axon, synapses, dendrites• Role of ion channels

The Brain

Visual System and Visual Cortex

Hodgkin-Huxley Model

• Neuron – Set of electric circuits

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LSM

• LSM – Liquid State Machine (Maass, 2002)

Typical model of VS

Our Model of Visual System

„„Readout”Readout”100 – 2500 HH 100 – 2500 HH

neuronsneurons

„„Liquid”Liquid”25 × HHLSM25 × HHLSM

600 HH 600 HH neuronsneurons

„„Eye”Eye”(Retina)(Retina)100 HH 100 HH neuronsneurons

SOC Phenomena

• SOC – Self Organizing Criticality• Lots of complex systems in the Universe

behave following the exponential law:

SSD ~)(

• We have analyzed the work of different readouts from 10x10 to 51x51 neurons

Readout Structure (PVC)N20,20 N20,21 N20,22 N20,23 N20,24 N20,25 N20,26 N20,27 N20,28 N20,29 N20,30

N21,20 N21,22 N21,23 N21,24 N21,25 N21,25 N21,26 N21,27 N21,28 N21,29 N21,30

N22,20 N22,21 N22,22 N22,23 N22,24 N22,25 N22,26 N22,27 N22,28 N22,29 N22,30

N23,20 N23,21 N23,22 N23,23 N23,24 N23,25 N23,26 N23,27 N23,28 N23,29 N23,30

N24,20 N24,21 N24,22 N24,23 N24,24 N24,25 N24,26 N24,27 N24,28 N24,29 N24,30

N25,20 N25,21 N25,22 N25,23 N25,24 N25,25 N25,26 N25,27 N25,28 N25,29 N25,30

N26,20 N26,21 N26,22 N26,23 N26,24 N26,25 N26,26 N26,27 N26,28 N26,29 N26,30

N27,20 N27,21 N27,22 N27,23 N27,24 N27,25 N27,26 N27,27 N27,28 N27,29 N27,30

N28,20 N28,21 N28,22 N28,23 N28,24 N28,25 N28,26 N28,27 N28,28 N28,29 N28,30

N29,20 N29,21 N29,22 N29,23 N29,24 N29,25 N29,26 N29,27 N29,28 N29,29 N29,30

N30,20 N30,21 N30,22 N30,23 N30,24 N30,25 N30,26 N30,27 N30,28 N30,29 N30,30

Avalanches of Spike Potentials

Avalanches of Spike Potentials

Time of Simulation (1 processor)

400 600 800 1000 1200N um ber o f C e lls

0

200000

400000

600000

800000

1000000

Sim

ula

tion

Tim

e [s

]

Time of Simulation (1 processor)

0.4 0.80.6 10.2

Probab ility o f exocitosis

0

200000

400000

600000

800000

1000000

Sim

ulat

ion

time

[s]

33x33

Time of Simulation (6 processors)

0 0.4 0.80.2 0.6 1

P robab ility o f Exocitos is

0

400000

800000

1200000

1600000

Sim

ulat

ion

Tim

e

51x51

Summary

• In the model of primary visual cortex some SOC phenomena occur

• They may be connected i.e. with visual consciousness

• Parallelization dramatically shortens the time of simulation

Future Plans

• We are creating more sophisticated model of the mammalian visual system

• We will continue on the investigation of SOC phenomena• Parallel version of GENESIS (for the MPI environment)

will then be applied• As a part of CLUSTERIX model we will simulate large

biological neural networks consisting up to half million artificial cells

• This will help us to understand some processes occurring in the brain

• GRID tests for numerical solving of nonlinear differential equations will be conducted as well

THE END