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Plasticity and Learning

LECTURE 10

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I. Introduction II. Synaptic placticity rules − The basic Hebb rule

− The covariance rule − BCM Rule

− on!Hebbian rules − "nti!hebbian rules − Ti#ing!based Rules

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Introduction

Hebb’s postulate

“When an axon of cell A is near enough to excite cell Bor repeatedly or persistently takes part in firing it, some growth process

or metabolic change takes place in one or both cells such that A’s

efficiency, as one of the cells firing B, is increased”.

Donald O. Hebb (1949)

The theory is often summarized as "cells that fire together,

wire together ".

http://cogprints.ecs.soton.ac.uk/~harnad/Archive/hebb.html

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Conditioning:

－ The first attempt to model conditioning in terms of

synaptic change. － Behavior ---?--- neural mechanisms

• Development:－ The formation and refinement of

neural circuits need synaptic

elimination.

－ !onal or synaptic competition

in neuromuscular unctions and visualsystem #Consumptive and interference

competition!

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$ong term potentiation #$T%& - $ong term depression

（ $TD）

－Changes that persist for tens of minutes or longer are

generally called $T% and $TD. 't lasts for hours in vitro

and days and (ee)s in vivo

－ The longest-lasting forms appear to re*uire protein

synthesis. － +irst found in ,ippocampus

－ The physiological asis of ,eian learning

－ %roperties and mechanisms of long-term synaptic

plasticity in the mammalian rain may relate to learningand memory.

－ 'nhiitory synapses can also display plasticity ut this

has een less thoroughly investigated oth

e!perimentally and theoretically

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The basic Hebb rule

)(at yt axdt

t dwi

iw /

>=τ

post

iw pre i

: the firing rates of the pre- and postsynaptic neurons

0. $ocal mechanism

1. 'nteractive mechanism2. Time-dependent mechanism

y xi and

learning rate

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The basic Hebb rule is unstable

/111 11

>=⋅== y ydt

d

dt

d ww xw

ww

wτ τ

post

w

pre

ydt d w xw =τ

xw ⋅=⋅==

⋅+−=

∑

∑

j

j j j j

j

j j

xw y x x f

x f w ydt

dy

have (e ssume

τ

". #he processes of synaptic plasticity are typically much slower than the

neural acti$ity dynamics.

%. &f, in addition, the stimuli are presented slowly enough to allow the

network to attain its steady-state acti$ity during training,

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#heoretically, an upper saturation constraint must be imposed to a$oid

unbounded growth. But experimentally,

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Is it due to that the basic Hebb rule has no LTD? Let’s add LTD by

introducing the covariance rule

LTP and LTD at the Schaffer collateral inputs to the C!

region of a rat hippoca"pal slice

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The covariance rule

yw ydt d θ τ −= xw

ydt d w xxw θ τ −=

>< x

postsynaptic threshold e.g.

presynaptic threshold e.g.

>< y

wxxxx

xxw

>>>

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By the basic 'ebb rule, synapses are modified whene$er correlated pre(and postsynaptic acti$ity occurs. )uch correlated acti$ity can occur purely

by chance, rather than reflecting a causal relationship that should be

learned. #o correct for this, the co$ariance rather than correlation(based

rule is often used by network models

ydt

d w >

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The covariance rules# li$e the Hebb rule# are

unstable and non-co"petitive

/&1#

1

1

1

>>>

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%C& 'ule

yw y ydt

d

θ τ −= xw

%ienenstoc$# Cooper and &unro (!)*+, proposed an alternati$e forwhich there is experimental e$idence where the postsynaptic threshold is

dynamic

w

y

y

ydt

d

τ τ

θ

θ

τ

θ

θ

<

−= 1 θy

LTP

LTD

0

Postsynaptic activity

ne e.a"ple-

/sually set-

Hebb rule covariance rule

%C& rule

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－ This is again unstale if θ is fi!ed.

－ ,o(ever if the threshold is allo(ed to gro( faster than v (e

get staility.

θ

LTP

LTD

0

Postsynaptic activity

－,ere competition

et(een synapses appears

since strengthening some

synapses results in threshold

increasing meaning that it isharder for others to e

strengthened

－ θ depends on postsynaptic activity. +or instance the thresholdfor $T% decreases (hen postsynaptic activity is lo( #y 3 θ3&

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Synaptic /eight nor"ali0ation

constant

constant

1 =

=

∑∑

j

j

j j

w

w

－ 't is a more direct (ay of enforcing competition

－ 'dea is that postsynaptic neuron can only support a certain

amount of total synaptic (eight so strengthening one leads to

(ea)ening others

－ 1 types: sutractive normalisation and multiplicative

normalisation

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Subtractive nor"alisation

∑

∑∑∑

−=

=⋅=⋅−=

j

j

x

iiw

j

j

j

j

j

j

x

w

x N

y y xdt

dw

w x x N y y

dt d

τ

τ

:or

& 4# wnxnnxw

－ 't is easy to prove that the total increase in the (eights is /.

constant=∑ j jw

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1vidences for

%C& rule

－ #he field potentials e$oked in layer &&& by layer &0 stimulation inslices of $isual cortex prepared for light(depri$ed and control rats 1(2weeks old

－ #he effects can be reser$ed by as little as two days of lightexposure before slice preparation

1vidence for a sliding

threshold2

&t is easier to obtain *#3

in the cortex of dark(

reared animals and it is

harder to induced *#+ in

these cortices

http://www.scholarpedia.org/article/Image:BCM_Kirkwood.png

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1.peri"ental evidences for constant total

synaptic /eights

－ $o(- and high-fre*uency B$ stimuli #$+5 ,+5& are

)no(n to respectively produce homosynaptic 67D

dependent $TD and $T% in 'TC cells.

－ 8hether $+5 and ,+5 also produce inverse heterosynaptic

modifications is unclear.

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45oyer and

3are %667,

8ature!

intercalated 4! neurons of the amygdala- 中间神经元

• the basolateral amygdala 4B*A!- 基底外侧杏仁核

• an array of closely spaced 49":6 9m! stimulating electrodes

• slices of the amygdala

• guinea(pigs 47;: weeks old!

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Plot of 1PSP a"plitude and rise

ti"e versus sti"ulation site45oyer and 3are %667, 8ature!

'omosynaptic *#3 was induced with

'3)3s would occur ?ust before or

during current(e$oked spikes

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LTD

induction

producesheterosyna

ptic LTP

*eft- +ifference between pre( and post(*3)3 amplitudes! for one cell 4top! and a$erage of all cells

5ight-#ime course of changes in response amplitude

45oyer and

3are %667,

8ature!

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'esult is

si"ilar/ith high

fre3uency

sti"uli

45oyer and 3are %667, 8ature!,

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Their results sho/ed that the activity-dependent

enhance"ent or depression of particular inputs to intercalated

neurons is acco"panied by inverse "odifications atheterosynaptic sites# /hich contributes to total synaptic /eight

stabili0ation

The inverse ho"o- versus heterosynaptic plasticity see"s to

be a cell- /ide event# /hich needs an intracellular signaling

syste" that can render synapses 4a/are’ of each other or of the

"ean neuronal activity5

Ho/ do unsti"ulated inputs detect the sti"ulation fre3uency

at the sti"ulated path/ay?

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6on-Hebbian for"s of synaptic plasticity

They modify synaptic strengths solely on the asis of pre- or postsynaptic firing are li)ely to play important roles in

homeostatic developmental and learning processes

• Homeostatic plasticity

't allo(s neurons to sense ho( active they are and to

adust

their properties to maintain stale function

$oosely defined a homeostatic form of plasticity is one

thatacts to stailize the activity of a neuron or neuronal circuit

in the face of perturations such as changes in cell size or

in synapse numer or strength that alter e!citaility.

large numer of plasticity phenomena have no( eenidentified e. . s na tic scalin and homeostasis of

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Synaptic scaling

form of synaptic plasticity that adusts the strength of all of aneuron;s e!citatory synapses up or do(n to stailize firing

avoiding *uiescence and hyper-e!citation at the level of

individual neurons.

Current evidence suggests that neurons detect changes in their

o(n firing rates through a set of calcium!epen!ent sensors

!citatory 5ynapses. Cell 02: @11-@2 Actoer 20 1//

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4#urrigiano "@@@, #&8)!

A model of multiplicati$e scaling through the

remo$al of A3A receptors

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ctivity can also modify the intrinsic excitability and

response properties of neurons

• 7odels of such intrinsic plasticity sho( that neurons can e

remar)aly roust to e!ternal perturations if they a!"ust their

con!uctances to maintain specified functional characteristics

• #ntrinsic an! synaptic plasticity can interact in interesting

(ays. +or e!ample shifts in intrinsic e!citaility cancompensate for changes in the level of input to a neuron caused

y synaptic plasticity.

Ho"eostasis of intrinsic e.citability of neurons

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Ho"eostasis of intrinsic e.citability of neurons

#heoretical and experimental work suggests that intracellular a%

concentration might regulate the balance of inward and outward currents

generated by a neuron

4#urrigiano "@@@, #&8)!

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nti-Hebbian plasticity

't causes synapses to decrease #rather than increase& in

strength (hen there is simultaneous pre- and postsynaptic

activity.

• 't is elieved to e the predominant form of plasticity at

synapses in mormyrid electric fish and those from parallel fiers

to %ur)ine cells in the cereellum

• nti-,eian modification tends to ma)e (eights decrease(ithout ound

)(at yt axdt

t dwi

iw /

>−=τ

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Ti"ing-%ased 'ules

*#3 is induced by repetiti$e

stimulation with positively

correlated spike times of post and

pre(synaptic neuron

*+3 is induced by repetiti$e

stimulation with negatively

correlated spike times of post and

pre(synaptic neuron

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Spi$e Ti"ing Dependent Plasticity (STDP,

An intracellular

recording of a pair of

cortical pyramidal

cells in a slice

experiment

4arkram et al., "@@C!

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－ *#3 and *#+ of

retinotectal synapsesrecorded in vivo in

Xenopus tadpoles

4Dhang et al., "@@E!

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5imulating the spi)e-timing dependence of synaptic plasticity

re*uires a spi)ing model #e.g. 'ntegrate-and-+ire 7odels&.

,o(ever an appro!imate model can e constructed on the

asis of firing rates

&C#D/

τ τ

τ τ τ τ τ τ

H H

t xt y H t xt y H d dt

dwii

iw

−=−

−−+−= ∫ ∞

(here

6ote aove e*uation is ased on a ,eian rule

• The 5TD% rule descries an asymmetric learning rule

$T% $TD

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• out H #τ &: a function li)e the solid line in previous figure.

∆=∆ −

+

∆−

∆−+

./if /if

E

E

t e At e At H

t

t

τ

τ

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Se3uence learning based on STDP

#he #iming(Based plasticity rule is applied throughout a training

period during which the stimulus being presented mo$es to the right

and excites the different neurons in the network seuentially

After the training period, the neuron with sa F 6 recei$es strengthened

input from the sa FG% neuron and weakened input from the neuron with

sa F %

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'f the same time-dependent stimulus is presented again after

training the neuron (ith sa F / (ill respond earlier than it did

prior to training

• The training e!perience causes neurons to learn a time

se$uence

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nother e.a"ple on ti"e se3uence learning in placefields

4ehta et al. "@@CH %666!

3lace field is negati$ely skewed after experience

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variety in plasticity

+ifferent cortical regions, such as

hippocampus and $isual cortex ha$e

somewhat different forms of synaptic

plasticity.

4Abbott and 8elson %666, 8ature!

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fe/ properties of LTP and LTD

$ong-term plastic changes can e induced in aout 0 s or less

#i.e. (ithin a rather short period similar to short-term

plasticity&

The induced change in synaptic (eight typically lasts forhours #if no further changes are induced&

The longest-lasting forms appear to re*uire protein synthesis

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Three types o$ training procedures

/nsuper$ised 4or sometimes self(super$ised! learning.

－ A network responds to a series of inputs during training

solely on the basis of its intrinsic connections and

dynamics

)uper$ised learning

－ A desired set of input(output relationships is imposed onthe network by a Iteacher’ during training.

－ 8etworks that perform particular tasks can be

constructed in this way

• 5einforcement learning － &t is somewhat intermediate between these cases.

－ #he network output is not constrained by a

teacher, but e$aluati$e feedback on network

performance is pro$ided in the form of reward or

punishment

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Ho"e/or$

1. 与基本 Hebb 学习律比较 # %C& 学习律在哪些方面做了改进 ? 意义何在 ?

!"#$%&'() (Homeostatic plasticity%。

* +,-./神经0123间45学习67-89:;学习律?

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