STDP and Network Architectures Parallel ODE Solver and Event Detector Eugene Lubenov.

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Presentation transcript:

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 Special Events V ge gi y = y’ = f (y, t) e (y, t) = V – V_th

STDP Model ODE System for the STDP Variables Special Events Weight Matrix Update Rules input (M) output (Pe) GE NE NN input (M) GR NN output (Pr)

Project Ingredients Matlab (Mathworks) SUNDIALS (LLNL) LAM MPI Custom C Code

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 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? 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? 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

Performance: Serial vs Parallel

Performance: Parallel Scalability

Problem Stiffness Moderately Stiff?WRONG!Non-Stiff!

Correctness: V

Correctness: M, Pe, Pr

Correctness: GE, GR

Network Activity Poisson InhibitionRhythmic Inhibition (10 Hz)

Network Activity GE plasticity onlyGR plasticity only

Network Weights GE Weight MatrixGE Weight Distribution

Network Weights GR tr(GR) = 0 and GR*GR’ = 0

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.

Future Directions