From brain activities to mathematical models The TempUnit model, a study case for GPU computing in...
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Transcript of From brain activities to mathematical models The TempUnit model, a study case for GPU computing in...
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