From brain activities to mathematical models

The TempUnit model, a study case for GPU computing in

scientific computation.

MN

CM

IN

Muscle

Cortex

Moelle

Périph:MuscleMouvement

What part of the brain?

How to study it ?

First attempt: use of a MLP• What is a MLP?

First Attempt: MLP (2)

Results (1)

Results (2)

Crack the code !!• Frequency code (Number of spikes in a time

lap) ?• Spatial coding (distributed trough the

network) ?• Temporal code (Precise binary pattern) ?• Spatio-temporal code (Synchronies) ?• Something else ?

The modelx

Xt

Learn the parameters vi

• Solving a system of linear equation oversized.• Much faster and straightforward than

backpropagation for the MLPExample of a learned basis function

Performances compared to MLP

Check Chap. 12

Graph of Neuronal Activity• The output activity of a TempUnit neural

network can be described by a graph directly related to its connectivity– You determine the topology of your graph easily

• Allow to determine the input activity for a particular desired output

Can a real biological neuron do that ?

Pattern recognition

learning rules for unsupervised learning

EPSP from the integrate-and-fire model

0

r

ax

s

ax t

rsr

t

rs

ek

ek

To find the position of the maximum (peak), one has to resolve the following equation:

ax

tt

rs

teek

tu r

ax

s

ax

)(

(Gerstner & Kistler, 2002)

rsax

r

sax

r

s

t

ln

1

1

From the integrate and fire, the α function:

time

The new equation of the TempUnit model:

• With μ, the maximum value:

r

axrs

ax

r

sax

r

s

sax

rsax

r

sax

r

s

eers

ln

1

1ln

1

1

1

v

pt

eep

kptu

saxv

pt

v

pt

srs

r

sax

s

sax

1),(

time

p=0

p=6

p : position of the synapse

From equations to a simulation software