Memories on multiple timescales: the importance of heterogeneity and memory transfer

Stefano Fusi

Idealized synapses (~N)

Bounded synapses (~log N)

MANY SYNAPSES = MANY MEMORIES

Amit, Fusi (1992,1994), Brunel, Carusi, Fusi (1998), Fusi (2001)

(N)

time time

timetime

Slow learning

Heterogeneity

FAST SLOW

N = Number of synapses (1010)

qs = Smallest rate (slowest timescale) = 10-3

…

m groups

FAST SLOW

q1 qm-1q2 qm=qs

qk=(qs)k/m

N/m N/m N/m N/m

m=10

Homogenous q=q

s

Hom

ogenous q=q

1

Heterogeneous

m=50

qs√N

√Nlog(1/qs)

qs√Nqs√N

√m

Memory transfer

FAST SLOW

m=10

m=50

m=100

√Nlog(1/qs)

qs√N

√N√m

1/qsm/qs

FAST SLOW

The cascade model

1/ ~Signal Noise t N

Fusi, Drew, Abbott, Neuron (2005)StrongWeak

……

~Memory lifetime N

METAPLASTICITY

PLASTICITY

1/n

2n-1

n=number of levels in the cascadeInitial signal/noise

Sign

al/N

oise

Power law range

Important ingredients

• Multiple timescales• Efficient forms of interactions to transfer

memories

Alex Roxin

Larry AbbottPatrick Drew

Collaborators

q=0.1

q=0.01

q=0.001

q=0.1

q=0.01

q=0.001

q=0.1

q=0.8

Bounded synapses RANGE=1

Bounded synapses RANGE=10, balanced

Bounded synapses, any RANGE, imbalanced

Unrealistic unbounded synapses (~

N)

Unrealistic unbounded synapses (~

N)

Bounded synapses RANGE=10, balanced

Bounded synapses, any RANGE, imbalancedSoft bounds synapses RANGE=10

Homogeneousq=0.1

Homogeneousq=0.6

Heterogeneous

q=0.1

q=0.8