Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII...
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![Page 1: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/1.jpg)
Liquid State Machines
and
Large Simulations
of Mammalian Visual System
Grzegorz M. Wójcik
14 XII 2004
![Page 2: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/2.jpg)
Introduction
• Neuron
• Brain
• Visual System and Visual Cortex
• Hodgkin-Huxley Model
• Liquid State Machine
• Self Organizing Criticality
• Results and plans for the future
![Page 3: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/3.jpg)
Neuron
• Soma, axon, synapses, dendrites• Role of ion channels
![Page 4: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/4.jpg)
The Brain
![Page 5: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/5.jpg)
Visual System and Visual Cortex
![Page 6: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/6.jpg)
Hodgkin-Huxley Model
• Neuron – Set of electric circuits
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![Page 7: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/7.jpg)
LSM
• LSM – Liquid State Machine (Maass, 2002)
![Page 8: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/8.jpg)
Typical model of VS
![Page 9: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/9.jpg)
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
![Page 10: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/10.jpg)
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
![Page 11: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/11.jpg)
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
![Page 12: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/12.jpg)
Avalanches of Spike Potentials
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Avalanches of Spike Potentials
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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
]
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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
![Page 16: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/16.jpg)
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
![Page 17: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/17.jpg)
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
![Page 18: Liquid State Machines and Large Simulations of Mammalian Visual System Grzegorz M. Wójcik 14 XII 2004.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bff51a28abf838cbd917/html5/thumbnails/18.jpg)
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