The temporal paradox of Hebbian learning andhomeostatic plasticityFriedemann Zenke1, Wulfram Gerstner2 and Surya Ganguli1

Available online at www.sciencedirect.com

ScienceDirect

Hebbian plasticity, a synaptic mechanism which detects and

amplifies co-activity between neurons, is considered a key

ingredient underlying learning and memory in the brain.

However, Hebbian plasticity alone is unstable, leading to

runaway neuronal activity, and therefore requires stabilization

by additional compensatory processes. Traditionally, a

diversity of homeostatic plasticity phenomena found in neural

circuits is thought to play this role. However, recent modelling

work suggests that the slow evolution of homeostatic plasticity,

as observed in experiments, is insufficient to prevent

instabilities originating from Hebbian plasticity. To remedy this

situation, we suggest that homeostatic plasticity is

complemented by additional rapid compensatory processes,

which rapidly stabilize neuronal activity on short timescales.

Addresses1 Department of Applied Physics, Stanford University, Stanford, CA

94305, USA2 Brain Mind Institute, School of Life Sciences and School of Computer

and Communication Sciences, Ecole Polytechnique Federale de

Lausanne, EPFL, CH-1015 Lausanne, Switzerland

Corresponding author: Zenke, Friedemann (fzenke@stanford.edu)

Current Opinion in Neurobiology 2017, 43:166-176

This review comes from a themed issue on Neurobiology of learning

and plasticity

Edited by Leslie Griffith and Tim Vogels

http://dx.doi.org/10.1016/j.conb.2017.03.015

0959-4388/# 2017 Elsevier Ltd. All rights reserved

IntroductionMore than half a century ago, Donald Hebb [1] laid

down an enticing framework for the neurobiological

basis of learning, which can be succinctly summarized

in the well-known mantra, ‘neurons that fire together

wire together’ [2]. However, such dynamics suffers

from two inherent problems. First, Hebbian learning

exhibits a positive feedback instability: those neurons

that wire together will fire together more, leading to

even stronger connectivity. Second, such dynamics

alone would lead to all neurons in a recurrent circuit

wiring together, precluding the possibility of rich pat-

terns of variation in synaptic strength that can encode,

through learning, the rich structure of experience. Two

Current Opinion in Neurobiology 2017, 43:166–176

fundamental ingredients required to solve these pro-

blems are stabilization [3], which prevents runaway

neural activity, and competition [4�,5,6�], in which

the strengthening of a synapse may come at the ex-

pense of the weakening of others.

In theoretical models, competition and stability are often

achieved by augmenting Hebbian plasticity with addi-

tional constraints [3,5,7�]. Such constraints are typically

implemented by imposing upper limits on individual

synaptic strengths, and by enforcing some constraint

on biophysical variables, for example, the total synaptic

strength or average neuronal activity [6�,7�,8–12]. In

neurobiology, forms of plasticity exist which seemingly

enforce such limits or constraints through synaptic scal-

ing in response to firing rate perturbations [13,14], or

through stabilizing adjustments of the properties of plas-

ticity in response to the recent synaptic history, a phe-

nomenon known as homeostatic metaplasticity

[6�,11,15,16]. Overall, synaptic scaling and metaplasti-

city, as special cases of homeostatic mechanisms that

operate over diverse spatiotemporal scales across neuro-

biology [17–22], are considered key ingredients that

contribute both stability and competition to Hebbian

plasticity by directly affecting the fate of synaptic

strength.

The defining characteristic of homeostatic plasticity is

that it drives synaptic strengths so as to ensure a homeo-

static set point [23,24�], such as a specific neuronal firing

rate or membrane potential. However, it is important that

this constraint is implemented only on average, over long

timescales, thereby allowing neuronal activity to fluctuate

on shorter timescales, so that these neuronal activity

fluctuations, which drive learning through Hebbian plas-

ticity, can indeed reflect the structure of ongoing experi-

ence. This requisite separation of timescales is indeed

observed experimentally; forms of Hebbian plasticity can

be induced on the timescale of seconds to minutes [25–28], whilst most forms of homeostatic synaptic plasticity

operate over hours or days [14,24�,29]. This separation of

timescales, however, raises a temporal paradox: homeo-

static plasticity then may become too slow to stabilize the

fast positive feedback instability of Hebbian learning.

Indeed modeling studies that have attempted to use

homeostatic plasticity mechanisms to stabilize Hebbian

learning [11,30,31�,32�,33,34] were typically required to

speed up homeostatic plasticity to timescales that are

orders of magnitude faster than those observed in experi-

ments (Figure 1).

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The temporal paradox of Hebb and homeostatic plasticity Zenke, Gerstner and Ganguli 167

Figure 1

inst.ms

second

minute

hourday

week

hour

day

week

second

minute

hour

minute

10min

hour

∗ network simulations

Weigh t normalizatio n in models

von de r Malsbur g [5]Mille r an d MacK ay [7•], Laz ar et al . [109]

Litwin-Kum ar an d Doiro n [55•] ∗

van Rossu m et al . [53] , Zen ke et al . [31•] ∗

Toyoizum i et al . [32•]

Synaptic scalin g in ex periments

Aot o et al . [68] , Ibat a et al . [69]

Greenhill et al . [111]

Turrigian o et al . [13]Li et al . [116]

Kaneko et al . [114]Goel et al . [113]

Model s of metaplastici ty

Clopat h et al . [37•] ∗El Boustan i et al . [72 ] ∗

Gjorgjiev a et al . [54]Jedlicka et al . [104•]

Benuskov a an d Abraha m [117]

Zenke et al . [31•] ∗Pfiste r an d Gerstne r [36]

Metaplastici ty in ex periments

Mocket t et al . [115]

Huang et al . [110]

Christie an d Abraha m [112]

(a) (b)

(c) (d)

Current Opinion in Neurobiology

Comparison of the typical timescale of different forms of homeostatic plasticity in models and in experiments. (a) Weight normalization in models.

Here we plot the characteristic timescale on which synaptic weights are either normalized or scaled. (b) Synaptic scaling in experiments. Here we

plot the typical time at which synaptic scaling is observed. (c) Models of metaplasticity. We plot the characteristic timescale on which the learning

rule changes. (d) Metaplasticity in experiments. Here we show the typical timescale at which metaplasticity is observed. Literature referenced in

the figure [5,7�,13,31�,32�,36,37�,53,54,55�,68,69,72,104�,109–117].

This temporal paradox could have two potential resolu-

tions. First, the timescale of Hebbian plasticity, as cap-

tured by recent plasticity models fit directly to data from

slice experiments [28,35,36,37�,38], may overestimate the

rate of plasticity that actually occurs in vivo. This overes-

timate could arise from differences in slice and in vivopreps, or because complex nonlinear synaptic dynamics,

both present in biological synapses and useful in learning

and memory [39–41], are missing in most, but not all [42–44], data-driven models. While slow plasticity may be a

realistic possibility in cortical areas exhibiting plastic

changes over days [45,46], it may not be a realistic

resolution in other areas, like the hippocampus, which

must rapidly encode new episodic information [47,48].

The second potential resolution to the paradoxical sepa-

ration of timescales between Hebbian and homeostatic

plasticity may be the existence of as yet unidentified

rapid compensatory processes (RCPs) that stabilize Heb-

bian learning. Below, we explore both the theoretical

utility and potential neurobiological instantiations of

these putative RCPs.

The temporal paradox of Hebbian andhomeostatic plasticityTo understand the theoretical necessity for RCPs to

stabilize Hebbian plasticity, it is useful to view a diversity

of synaptic learning models through the unifying lens of

control theory (Figure 2a). Here we can view the ‘fire

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together, wire together’ interplay of neuronal activity and

Hebbian synaptic plasticity as an unstable dynamical

system. Also, we can view a compensatory process as a

feedback controller that observes some aspect of either

neuronal activity or synaptic strength, and uses this

observation to compute a feedback control signal which

then directly affects synaptic strength so as to stabilize

global circuit activity. Indeed homeostatic plasticity is

often thought of as a negative feedback control process

[23,24�,49,50]. In general, the delay in any feedback

control loop must be fast relative to the time-scale over

which the unstable system exhibits run-away activity

[51]. If the loop is slightly slow, the run-away will start

before the stabilizing feedback arrives, generating oscil-

lations within the system. In some cases, if the loop is

even slower, the unstable runaway process might escape

before stabilization is even possible (Figure 2b).

Such oscillations and run-away are demonstrated in

Figure 3 for several compensatory mechanisms with

feedback timescales that are chosen to be too slow,

including the Bienenstock–Cooper–Munro (BCM) rule

[6�,52], and triplet spike-timing-dependent plasticity

(STDP) [36] with either synaptic scaling [13,53] or a

metaplastic sliding threshold, as stabilizing controllers.

For example, the BCM rule (Figure 3a) can be thought of

as a feedback control system where the controller

observes a recent average of the postsynaptic output firing

Current Opinion in Neurobiology 2017, 43:166–176

168 Neurobiology of learning and plasticity

Figure 2

Synaptic strength

Neuronal activi ty

System:

Controller

External stimuli

Plastici ty

ObservationsControl signal 0

10

20 τ = 10ms

−100

1020 τ = 200ms

−450

4590 τ = 300ms

500ms

Ang

le(d

eg)

ΘF

(a) (b)

Current Opinion in Neurobiology

A control theoretic view of homeostatic plasticity and Hebbian learning. (a) The coupled dynamics of Hebbian plasticity and neural activity

constitutes an unstable dynamical system. Homeostatic plasticity, and more generally any compensatory mechanism, can be viewed as a

controller that observes aspects of neuronal activity and synaptic strengths, and uses these observations to compute a feedback control signal

that acts on synaptic dynamics so as to stabilize circuit properties. (b) The cart pole problem is a simple example of stabilizing a non-linear

dynamical system with feedback. The task of the controller is to exert horizontal forces on the cart to maintain the rod (m = 1 kg) in an upright

position. For simplicity we assume a weightless cart with no spatial constraints on the length of the track. The controller has access to an

exponential average (time constant t) over recent observations of both the angle u and angular velocity u˙of the pole. For small values of t the

controller can successfully maintain the rod upright (u � 0; top panel). However, as t and the associated time lag in the observed quantities gets

larger, oscillations arise (middle panel) and eventually the system becomes unstable (bottom panel).

rate of a neuron, and uses this information to control both

the sign and amplitude of associative plasticity; if the

recent average is high (low), plasticity is modulated to

be anti-Hebbian (Hebbian). However, to achieve stability,

the BCM controller must average recent output-activity

over a short enough time-scale to modulate plasticity

before this activity itself runs away (Figure 3a;

[11,31�,32�]). This result is not limited to BCM like rate

models, but applies equally to STDP models which rely on

similar metaplasticity processes to ensure stability

(Figure 3bc; [31�,36,37�,54]). These modified STDP rules

can be thought of as employing feedback controllers which

also observe a recent average of output firing rate, but use

this information to modulate the STDP window, thereby

stabilizing the system by changing relative rates of long-

term potentiation (LTP) and long-term depression (LTD).

Another class of models relies on re-normalization of

afferent synaptic weights to stabilize Hebbian plasticity.

We distinguish between models with instantaneous algo-

rithmic re-normalization of the weights [4�,5,7�,55�] and

models which proportionally scale synaptic weights in an

activity dependent way [8,31�,56]. In the former case the

controller observes total synaptic strength and uses this

information to adjust synapses to keep this total strength

constant. In the latter case, the controller observes neu-

ronal firing rate, or recent average thereof, and uses this

information to proportionally adjust afferent synaptic

weights to enforce either a specified target output, or a

Current Opinion in Neurobiology 2017, 43:166–176

total synaptic strength. Just as in the case of metaplasticity

discussed above, the temporal average of the activity

sensor has to be computed over a short timescale, related

to the timescale over synaptic strengths and neuronal

activity change, to ensure stability (Figure 3d

[31�,32�,33]). Moreover, the rate at which the synaptic

scaling process itself causes synaptic strengths to scale

must be finely tuned to a narrow parameter regime that is

neither too fast nor too slow [31�,32�,33,53]; if too slow,

then stabilization is not possible, while if too fast, the

stabilization process overshoots, causing oscillations.

Finally, some STDP models can be intrinsically stable,

especially in feedforward circuits. One example are

pair-based STDP models in which the integral of the

STDP window is slightly biased toward depression.

When weights are additionally limited by hard bounds,

this can lead to bimodal weight distributions and firing

rate stabilization [9,57]. However, these learning rules

typically require fine-tuning and become unstable

when input correlations are non-negligible. Other sta-

ble models arise from a weight dependence in the

learning rule such that high (low) synaptic strength

makes LTP (LTD) weaker [53,58–62]. Such a stabiliz-

ing weight dependence is advantageous because it can

lead to more plausible unimodal weight distributions as

observed empirically [60,62]. However, the unimodal

weight distribution, by precluding multi-stability in the

configurations of synaptic strengths, typically leads to

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The temporal paradox of Hebb and homeostatic plasticity Zenke, Gerstner and Ganguli 169

Figure 3

0

1

2

3

0 20 40 60 80 100

Act

ivity

(a.u

.)

Time ( τω )

νin νout νout νoutω

0

30

60

−5 0 5 10 15 20 25

Plasticity enabled

Firi

ngra

te(H

z)

Synaptic scalingMetaplasticity

−5 0 5 10 15 20 25

−5 0 5 10 15 20 25

Synaptic scalingMetaplasticity

−5 0 5 10 15 20 25

−5 0 5 10 15 20 25

Neu

ron

(×10

00)

Neu

ron

(×10

00)

Time (s)

receiving corr elate d input

(a)

(b)

(c)

(d)

Current Opinion in Neurobiology

Instability in different plasticity models. (a) Unstable oscillations in the

BCM model for a simple feed-forward circuit [6�,11]. Model:

twdwdt ¼ aninnoutðnout�b~n2

out), tcddt

~nout ¼ nout�~nout with nout ¼ wnin,

tw ¼ 0:9tc; nin � 1 in arbitrary units (a.u.) and a and b are dimensionful

scalar constants that ensure correct units; we take simply

a = b = 1. Here ~nout can be thought of as the observation of a

controller, corresponding to an average of output neuronal activity nout

over time-scale tc. Moreover, the multiplicative term in parenthesis in

the weight dynamics can be interpreted as a control signal that

modulates both the sign and amplitude of associative plasticity,

dictating a stabilizing anti-Hebbian rule if the recent average ~nout is too

large. If the control dynamics tc is too slow relative to the synaptic

plasticity dynamics tw, unstable oscillations arise. (b–d) Runaway

activity in a recurrent neural network simulation consisting of

25 000 excitatory and inhibitory integrate-and-fire neurons and plastic

excitatory synapses using a minimal triplet STDP model [36] with

different homeostatic mechanisms such as sliding threshold

metaplasticity (violet) and synaptic scaling (green), both described in

detail in [31�]. (b) Population firing rate as a function of time. (c,d)

Raster plot of spiking activity. The bottom 3 groups of 100 neurons

received rate modulated spiking input with 100ms correlation time

constant to emulate sensory input to a small set of neurons. The

timescale of sliding threshold metaplasticity was tc = 3 min. The

timescale for the rate detector and the scaling dynamics for synaptic

scaling were tc = 10 s and tscl = 1 hour respectively. Because of these

slow stabilization dynamics, the fast interplay between Hebbian

plasticity and recurrent network dynamics leads to rapid population

firing rate destabilization within 10–20 s for both learning rules.

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the rapid erasure of synaptic memory traces in the pres-

ence of background activity driving plasticity [61,63].

Moreover, when such weight dependent synaptic learning

rules are embedded in a recurrent neuronal circuit without

any additional control mechanisms, they can succumb to

runaway neural activity as experience dependent neural

correlations emerge in the recurrent circuit [61,64,65].

In summary, empirical findings and control-theoretic con-

siderations suggest that compensatory mechanisms capable

of stabilizing Hebbian plasticity must operate on tightly

constrained timescales. In practice, such compensatory

mechanisms must act on similar or even faster timescales

than Hebbian plasticity itself [31�,32�,36,37�,54,55�,56].

STDP, as one of the most common manifestations of

Hebbian plasticity in the brain, can be induced in a matter

of seconds to minutes [25–27,66,67]. Homeostatic plastici-

ty, on the other hand, acts on much longer timescales of

hours to days [14,16,19,29,68–70]. This separation of time-

scales poses a temporal paradox as it renders most data-

driven STDP models unstable [3,71]. In spiking network

models, this instability has severe consequences

(Figure 3b–d); it precludes the emergence of stable syn-

aptic structures or memory engrams [31�,61,64], unless the

underlying plasticity models are augmented by RCPs

[31�,55�,56,72,73�]. Overall, these considerations suggest

that one or more RCPs exist in neurobiological systems,

which are missing in current plasticity models.

Putative rapid compensatory processesWhat putative RCPs could augment Hebbian plasticity

with the requisite stability and competition? Here we

focus on several possibilities, operating at either the

network, the neuronal or the dendritic level

(Figure 4a). However, we note that these possibilities

are by no means exhaustive.

At the network level, recurrent or feedforward synaptic

inhibition could influence and potentially stabilize plas-

ticity at excitatory synapses directly. For instance, [74]

demonstrated via dynamic-clamp that a simulated in-

crease in total excitatory and inhibitory background con-

ductance, which could originate from elevated levels of

network activity, rapidly reduces the amplitude of LTP,

but not LTD, of the STDP window. This rapid effect may

be mediated through changes in calcium dynamics in

dendritic spines and could constitute an RCP. Another

study [75] showed that global inhibition in a rate-based

network model is sufficient to stabilize plasticity at excit-

atory synapses with a sliding presynaptic and fixed post-

synaptic plasticity threshold. Finally, using a model-based

approach, Wilmes et al. [76] have proposed that dendritic

inhibition could exert binary switch-like control over

plasticity by gating back-propagating action potentials.

Other modeling studies have suggested a role for

inhibitory synaptic plasticity (ISP) [77,78], instead of

Current Opinion in Neurobiology 2017, 43:166–176

170 Neurobiology of learning and plasticity

Figure 4

Current Opinion in Neurobiology

Stimulation times:

Pop

ulat

ion

rate

(H

z) 60

0

400

units

3736.8 37.2 37.4 37.6

Time (min)

Spikes:

active cell assembly

(a) (b)

neuronal-levelheterosynaptic

branch-specificsingle

synapselevel

Inhibitoryplasticity

(a) Schematic representation of the many potential loci of rapid compensatory processes. (b) Example of a plastic network model displaying

attractor dynamics in three distinct cell assemblies. Because these dynamics outlast the stimulus that triggers them they have been considered as

neural substrate for working memory. The top panel shows a spike raster, whereas the bottom panel shows the population firing rates of the three

cell assemblies. This particular model uses an augmented triplet STDP learning rule (cf. Figure 3) in which heterosynaptic plasticity and single-

synapse-level plasticity have been added as stabilizing RCPs. Moreover, this model relies on a slow form of inhibitory plasticity which normalizes

the overall network activity and ensures that cell assemblies do not grow indefinitely over time by recruiting additional neurons. This provides a

proof of principle that a biologically inspired learning rule can indeed be stabilized by a sensible combination of RCPs, whereas the same learning

rule endowed with slow compensatory mechanisms leads to run-away dynamics (cf. Figure 3b–d). Figure adapted from Zenke et al. [73].

non-plastic inhibition, in stabilizing Hebbian plasticity. It

has been suggested, for instance, that ISP in conjunction

with a fixed plasticity threshold at the excitatory synapse

could have a similar effect as the sliding threshold in the

BCM model [79]. Finally, in some experiments excitatory

and inhibitory plasticity are not integrated as indepen-

dent events, but can influence each other. For instance,

there are cases in which induction of ISP alone can flip the

sign of subsequent plasticity at excitatory synapses [80].

While inhibition and ISP may act as RCPs, a clear picture

of how these elements tie together has not yet emerged.

Further experimental and theoretical work is required to

understand their potential for acting as RCPs.

Neuromodulation may also play an important role in

stabilizing plasticity. Neuromodulators have been impli-

cated in both homeostatic signalling [21] and in gating the

expression of synaptic plasticity [81–84]. However, to

successfully serve as RCP, neuromodulatory mechanisms

have to either drive rapid compensatory changes directly,

or substantially reduce the average rate of Hebbian plas-

ticity in vivo to enable slower forms of homeostatic

plasticity to preserve stability. While a detailed account

of the role of neuromodulators goes beyond the scope of

this article (but see [84,85] for reviews), here we note that

Current Opinion in Neurobiology 2017, 43:166–176

several neuromodulators at least partially meet one of

these core requirements for RCPs. For example, nitric

oxide (NO), which is involved in synaptic homeostasis

and plasticity [86], is released in response to increased

NMDA activity and decays within some tens of seconds

[87]. Because cell membranes are permeable to NO, the

molecule diffuses rapidly and thus could potentially act

as a fast proxy of bulk neuronal activity that can be read

out locally [88]. Similarly, dopaminergic transmission can

be fast [89] and is known to affect induction, consolida-

tion and possibly maintenance of synaptic long-term

plasticity [82,84,90–92]. A sensible gating strategy imple-

mented by dopamine or other neuromodulators could

result in a drastically reduced and more manageable

average rate of plasticity in vivo. In contrast, in vitro such

neuromodulatory mechanisms might be disengaged,

thus potentially creating less natural and much faster

plasticity rates compared to in vivo. Apart from the

neuromodulatory system, recent work has highlighted

the complexity of the local interactions between astro-

cytes and synaptic plasticity which may also act as RCPs

[93–95]. However, to unequivocally answer which

aspects of neuromodulation and glial interactions consti-

tute suitable RCPs will require further experimental and

theoretical work.

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The temporal paradox of Hebb and homeostatic plasticity Zenke, Gerstner and Ganguli 171

A more well studied possibility for an RCP is hetero-

synaptic plasticity, which operates at the level of indi-

vidual neurons or potentially dendritic branches.

Heterosynaptic plasticity refers to a non input-specific

change at other synapses onto a neuron that are not

directly activated [30,96,97,98�,99�]. Its viability as

putative RCP arises from the fact that some forms of

heterosynaptic plasticity can be induced rapidly, and

moreover, similar to synaptic scaling, can show aspects

of weight normalization [97]. For instance, a rapid form

of heterosynaptic plasticity, in which neuronal bursting

causes bi-directional weight-dependent changes in af-

ferent synapses, has been observed recently [98�,100�].While the observed weight-dependence is reminiscent

of Oja’s rule [8], as strong synapses weaken, it is not

identical because weak synapses can also strengthen.

Nevertheless, this form of heterosynaptic plasticity has

been shown to prevent runaway of LTP in models

of feedforward circuits [30] and has been demonstrated

to co-occur with Hebbian plasticity in experiments

[100�].

Recently, the utility in stabilizing runaway LTP has also

been demonstrated in a recurrent network model of

spiking neurons [73], in which a similarly burst depen-

dent form of heterosynaptic plasticity is crucial to ensure

stable formation and recall of Hebbian cell assemblies

(Figure 4b). Moreover, the work suggests a potential role

of heterosynaptic plasticity in triggering the reversal of

LTP and LTD [101].

At the level of dendritic branches, a recently described

form of structural heterosynaptic plasticity [99�],involves local dendritic competition between synapses.

Specifically, glutamate induced structural synaptic

potentiation of a set of clustered dendritic spines causes

shrinkage of nearby, but unstimulated spines. Interest-

ingly, even when structural potentiation was switched

off through inhibition of Ca2+/calmodulin dependent

protein kinase II (CaMKII), the heterosynaptic effect

persists, suggesting a model in which spines send and

receive shrinkage signals instead of competing for

limited resources. Moreover, the observed dendritic

locality is consistent with work on local or branch

specific conservation of total synaptic conductance

[97,102].

Finally, in some cases heterosynaptic plasticity might not

actually be heterosynaptic, as it may still depend on low

levels of spontaneous synaptic activity in unstimulated

synapses [103]. A recent biophysical model derived from

synaptic plasticity data [104�] actually requires such low-

levels of activity to match the data. Interestingly, this

model suggests such ‘heterosynaptic’ plasticity could

arise as a consequence of a rapid (timescale �12 s) ho-

meostatic sliding threshold possibly related to autopho-

sphorylation of CaMKII.

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While heterosynaptic plasticity, like synaptic scaling, can

have a stabilizing effect, it is distinct from synaptic scaling

in two ways. First, heterosynaptic plasticity need not

multiplicatively scale all weights in the same manner.

Second, it is unclear whether heterosynaptic plasticity in

general drives neuronal activity variables to a specific set

point, like synaptic scaling does [24�]. Thus, while het-

erosynaptic plasticity has the rapidity to act as a putative

RCP, its functional utility in storing memories requires

further empirical and theoretical study, as it may lack the

ability to precisely preserve ratios of synaptic strengths.

However, its clear functional utility in preventing insta-

bility (Figure 3d), along with even an approximate pres-

ervation in ratios of strengths, could potentially endow

the interaction of heterosynaptic plasticity and Hebbian

learning with the ability to stably learn and remember

memories. Further network modeling, building on prom-

ising heterosynaptic plasticity models [30,73�,104�], could

be highly instructive in elucidating the precise properties,

beyond rapidity, a putative RCP must obey in order to

provide appropriate competition and stability to Hebbian

plasticity.

ConclusionThe trinity of Hebbian plasticity, competition and stabil-

ity are presumed to be crucial for effective learning and

memory. However, a detailed theoretical and empirical

understanding of how these diverse elements conspire to

functionally shape neurobiological circuits is still missing.

Here we have focused on one striking difference between

existing models and neurobiology: the paradoxical sepa-

ration of timescales between Hebbian and homeostatic

plasticity. In models, such a separation of timescales

typically leads to instability, unless plasticity is con-

strained by RCPs that act much faster than observed

forms of homeostatic plasticity. In principle, RCPs could

be implemented at various spatial scales. Here we have

primarily discussed different forms of heterosynaptic

plasticity and processes involving synaptic inhibition as

possible candidates. However, rapid processes involving

neuromodulation, glial interactions, or intrinsic plasticity

[105–108] could also constitute RCPs. Thus, identifying

the key neurobiological processes that provide stability

and competition to Hebbian learning rules remains an

important direction for future research.

Conflict of interest statementNothing declared.

Acknowledgements

FZ was supported by the SNSF (Swiss National Science Foundation). SGwas supported by the Burroughs Wellcome, Sloan, McKnight, Simons andJames S. McDonnell Foundations and the Office of Naval Research. WGwas supported for this work by the European Research Council under grantagreement number 268689 (MultiRules) and by the European Community’sSeventh Framework Program under grant no. 604102 (Human BrainProject).

Current Opinion in Neurobiology 2017, 43:166–176

172 Neurobiology of learning and plasticity

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have been highlighted as:

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