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STDP and Network Architectures. Parallel ODE Solver and Event Detector Eugene Lubenov. Networks of Neurons. GE. GI. GR. Spike-Timing Dependent Plasticity. Bi & Poo, J. Neurosci. (1998). Integrate-and-Fire Neuron Model. ODE System for the Membrane Potential. V ge gi. y’ = f (y, t).

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stdp and network architectures

STDP and Network Architectures

Parallel ODE Solver and

Event Detector

Eugene Lubenov

spike timing dependent plasticity
Spike-Timing Dependent Plasticity

Bi & Poo, J. Neurosci. (1998).

integrate and fire neuron model
Integrate-and-Fire Neuron Model

ODE System for the Membrane Potential

V

ge

gi

y’ = f (y, t)

y =

Special Events

e (y, t) = V – V_th

stdp model
STDP Model

ODE System for the STDP Variables

Special Events

Weight Matrix Update Rules

NE

NN

output (Pe)

output (Pr)

NN

NN

GE

GR

input (M)

input (M)

project ingredients
Project Ingredients
  • Matlab (Mathworks)

http://www.mathworks.com/

  • SUNDIALS (LLNL)

http://www.llnl.gov/CASC/sundials/

  • LAM MPI

http://www.lam-mpi.org/

  • Custom C Code
why matlab
Why Matlab?
  • ode suite

event functions

knowing what to expect

  • MAT library

loading parameters and input

saving output

BUT: SERIAL ONLY and SLOW

why sundials
Why SUNDIALS
  • SUite of Nonlinear and DIfferential/ALgebraic equation Solvers

Adams-Moulton (non-stiff), BDF (stiff)

Variable Step, Variable Order (12, 5)

Functional Iteration, Linear System

Direct (full, banded, diag approx J)

Iterative (GMRES)

Sclaled Preconditioned (SPGMR)

BUT: NO EVENT FUNCTIONS

why lam mpi
Why LAM MPI?
  • Multiple Processors

Solve larger problems

Solve problems faster

  • Portable Code

BUT:Problem granularity must be suited to

underlying architecture:

Beowulf cluster coarse granularity

why custom c code
Why Custom C Code?
  • Extend CVode with Event Capabilities
  • Problem specific routines: f(.), e(.)
  • Handle I/O and Message Passing
  • Inline Exponential Variables

BUT:

compatibility: mpicc, mex, gcc

memory: Calloc, mxCalloc, CVodeMalloc

debugging: parallel code

problem stiffness
Problem Stiffness

Moderately Stiff?

WRONG!

Non-Stiff!

network activity
Network Activity

Poisson Inhibition

Rhythmic Inhibition (10 Hz)

network activity1
Network Activity

GE plasticity only

GR plasticity only

network weights
Network Weights

GE Weight Matrix

GE Weight Distribution

network weights1
Network Weights

GR

tr(GR) = 0 and GR*GR’ = 0

conclusion
Conclusion
  • Serial Code (v 2.3.4) good for real problems.
  • Parallel Code (v 1.1.0) needs work, but speedup might be hard to get.
  • Parallel Code (v 1.2.0) implements asynchronous message passing, but still in alpha.
  • Structure emerges from simulations.