Liquid State Machines

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• Liquid State Machines
• and
• Large Simulations
• of Mammalian Visual System
• Grzegorz M. Wójcik
• 14 XII 2004

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Introduction

• Neuron
• Brain
• Visual System and Visual Cortex
• Hodgkin-Huxley Model
• Liquid State Machine
• Self Organizing Criticality
• Results and plans for the future

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Neuron

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

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The Brain
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Visual System and Visual Cortex
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Hodgkin-Huxley Model

• Neuron Set of electric circuits

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LSM

• LSM Liquid State Machine (Maass, 2002)

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Typical model of VS
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Our Model of Visual System
Eye (Retina) 100 HH neurons
Readout 100 2500 HH neurons
Liquid 25 HHLSM 600 HH neurons
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SOC Phenomena

• SOC Self Organizing Criticality
• Lots of complex systems in the Universe behave
  following the exponential law

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

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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
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Avalanches of Spike Potentials
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Avalanches of Spike Potentials
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Time of Simulation (1 processor)
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Time of Simulation (1 processor)
33x33
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Time of Simulation (6 processors)
51x51
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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

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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

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THE END