Download Associative memory for spatio-temporal patterns based on Spike

Encoding of spatiotemporal patterns
in SPARSE networks
Antonio de Candia*, Silvia Scarpetta**
*Department of Physics,University of Napoli, Italy
**Department of Physics “E.R.Caianiello”
University of Salerno, Italy
Iniziativa specifica TO61-INFN: Biological applications of theoretical physics methods
Oscillations of neural assemblies
In-vitro MEA recording In-vivo MEA recording
In cortex, phase locked oscillations of neural assemblies are used for a wide
variety of tasks, including coding of information and memory
consolidation.(review: Neural oscillations in cortex:Buzsaki et al, Science 2004 Network Oscillations T. Sejnowski Jour.Neurosc. 2006)
Phase relationship is relevant
Time compressed Replay of sequences has been observed
Time compressed REPLAY of sequences
D.R. Euston, M. Tatsuno,
Bruce L. McNaughton
Science 2007
Fast-Forward Playback of Recent
Memory Sequences in
prefrontal Cortex During Sleep.
•Reverse replay has
also been observed:
Reverse replay of
behavioural sequences
in hippocampal place
cell s during the awake
state D.Foster & M.
Wilson Nature 2006
Models of single neuron
• Multi-compartments models
• Hodgkin-Huxley type models
• Spike Response Models
• Integrate&Firing models (IF)
• Membrane Potential and Rate
models
•
Spin Models
W (S i  S i ) 
hi   J ij S j
j
1
1  tanh( S i hi )
2
Spike Timing
Dependent
Plasticity
f
f.
t
A(t  ti )
f
j
t
Experiments:
Markram et al. Science1997
(slices somatosensory cortex)
Bi and Poo 1998 (cultures of
dissociated rat hippocampal
neurons)
f
LTP
LTD
t  ti
f
j
f
From Bi and Poo J.Neurosci.1998
STDP in cultures of dissociated rat hippocampal neurons
Learning is driven by crosscorrelations on timescale of learning kernel A(t)
Setting Jij with STDP
J ij   dt  dt 'i (t ) A(t  t ' ) j (t ' )
Imprinting oscillatory
patterns
 i (t ) 



1
1  cos(  t  i )
2
~   
~
J ij  Re A( ) i  j  2 A(0)



j e
A(t )
i j
~
~ 
i 
if A(0)  0 and A( )  e
P


1
1
~   
J ij   J ij   Re A( ) i  j   cos(i   j    )
N 
N 
 1

t
The network
 Spin model
1
W ( S i   S i )  1  tanh( S i hi )
2
hi   J ij S j
j
 With STDP plasticity
P
1
J ij   J ij   cos(i   j    )
N 
 1

 Sparse connectivity
Network topology
• 3D lattice
• Sparse network, with z<<N connections per
neuron
• gz long range , and (1-gz short range
Definition of Order Parameters m
m  (t ) 
1
N


 j S j (t )

complex quantities
j
If pattern 1 is replayed then
| m1 | 0, | m 2 | 0, | m 3 | 0
Order parameter vs time
Units’ activity vs time
Re(m)
Im(m)
|m|
Capacity vs. Topology
30% long range
alwready gives very
good performance
N=13824
g=1
g=0.3
g=0.1
g=0
Capacity P versus number z of connections per node,
for different percent of long range connections g
Capacity vs Topology
• Capacity P versus percent of long range g
N= 13824
Z=178
  0.1
Clustering coefficient vs g
DC=C-Crand
Experimental measures
in C.elegans give DC =0.23
P= max number of retrievable patterns
Achacoso&Yamamoto Neuroanatomy o
(Pattern is retrieved if order parameter |m| >0.45)
C-elegans for computation (CRC-Press 19
Clustering coefficient vs g
DC=C-Crand
Experimental measures in C.elegans give DC =0.23
Achacoso&Yamamoto Neuroanatomy of
C-elegans for computation (CRC-Press 1992)
Optimum capacity
Assuming 1 long range connection cost as 3 short range connections
Capacity P is show at constant cost, as a function of DC
3NL + NS = 170
N = 13824
DC = C - Crand