Symposium "Memory: from neuron to cognition"
Académie des Sciences, Paris, April 17-18, 1997
Nicolas BRUNEL and
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure
Laboratoire associé au C.N.R.S. (URA1306), à l'ENS, et aux universités Paris VI et Paris VII
Ecole Normale Supérieure
24, rue Lhomond - 75231 Paris Cedex 05
The variety of theoretical approaches to the modeling of memory is
as wide as the variety of experimental approaches.
Modelers explore many different levels,
from molecular and single cell models to very high level models.
In this short contribution we will comment on one intermediate family of
models, namely single networks with working memory properties.
These networks can be built with more or less complex `formal neurons',
from the binary neuron of the Hopfield model (Hopfield 1982) to
spiking neurons like the integrate-and-fire neuron (as in the models by Amit et al, to be presented below).
These networks can in turn be used
as building blocks for models with more complex functions, as
the models presented in this symposium by S. Dehaene.
Attractor neural networks
The common property of these models is the formation during learning
of `memory states'. A stimulus, when shown to the neural network (assembly),
elicits a configuration of
activity specific to that stimulus. This configuration of activity is then
learned via Hebbian synaptic modifications. These synaptic
modifications in turn enable the neural assembly to sustain an active
representation of the stimulus (i.e. the ensemble of neural activities
specific to that stimulus), in the absence of it: a `memory state'.
It was Hopfield who introduced the general
concept of attractor neural network, in which this behaviour
is generically observed. More specifically, in his paper of 1982
he defines an associative memory model
based on formal neurons which represents
the first full mathematical formalisation of Hebb
ideas and proposals on the neural assembly,
the learning rule, the role of the connectivity in the
assembly and the neural dynamics.
Synaptic plasticity: Hebbian rules
Most associative memory models are based
on Hebbian learning rules.
In fact, after the basic proposals of Stent and Hebb,
remarkable progresses have been made in both
the experimental studies of synaptic plasticity
(see talks given
at this symposium)
and the theoretical analysis of Hebbian type learning rules.
In many cases
the so called covariance rule (Sejnowski 1977)
and other closely related rules (such as the BCM rule)
are compatible with experimental data, and on the theoretical side
can be shown to be efficient
in models of formal neurons (in particular the
Hopfield model uses a covariance rule).
Optimal and generic properties
In the late 80's, a new theoretical approach
has led to the study of the optimal and typical
(generic) properties of
formal neural networks. A practical consequence was that it
was possible to compare the performances of a given model with the
best possible ones. An unexpected and interesting result was
that, in the limit of sparse coding (that is in the limit
when a given memory state activates a very low fraction of neurons),
a simple Hebbian learning rule
reaches the theoretical maximal storage
capacity (see Meunier and Nadal 1995 and ref. therein).
In addition, near to optimality performance
is reached with the Hebbian rule proposed in the sixties
by Willshaw et al, where synaptic efficacies
can take only two values.
This is an encouraging result since neurophysiological experiments
indicate that the fraction of neurons participating to a given
`memory state' in the observed area is indeed very low (of order 0.01,
see e.g. Miyashita).
Models and psychology
Short term memory models (Nadal et al 1986),
obtained as simple variants of
the original Hopfield model, allow
for a comparison with psychological data.
These models reproduce basic properties of human working memory as
studied by psychologists -
forgetting of old memories which are erased by new ones, but also more
elaborate phenomena, such as primacy effects and
proactive interference (Nadal et al 1988).
It is not clear, however,
whether such simple models can account for more complex phenomena
as described by A. Baddeley.
Another succesful domain is the modeling of the effect of lesions in the cortex. In particular, a phenomenon similar to prosopagnosia is generically observed in neural networks (Virasoro 1988): information relative to individual memories is lost before the information which characterizes the class.
Models and neurophysiology
From the very definition of the first Hopfield type models, it was obvious
that no direct comparison with data at the neurophysiological level could be possible.
Quite recently, it has been understood how to build
a new generation of models (Amit et al 1994),
as a compromise between the need for
preserving simple systems, exhibiting the same collective properties as in the
Hopfield model, and the need for
incorporating more realistic details which would allow for a direct comparison
with the phenomenology of recordings during memory tasks.
Very encouraging results have been obtained:
selective neural activity exhibited in these models is in nice
correspondence with the phenomenology of single unit recordings in
monkeys during delayed response tasks, for example in inferior temporal
(IT) cortex (Miyashita 1988)
or in prefrontal (PF) cortex (Fuster 1995).
In addition to the ability to form memory states, new properties appear that cannot be present in the simpler models. In particular, due to a strong recurrent inhibition, in each memory state only a small subset of neurons fires at more elevated frequencies, and, in the absence of external stimulation, the network stabilizes in a state of low spontaneous activity (Amit and Brunel 1997).
Towards a test of the attractor neural network paradigm
An interesting development of these models
concerns learning of temporal context: the hypothesis is that when
two stimuli are often shown one after the other, synaptic modifications
will occur in such a way as, when one of the stimuli is shown,
neurons selective to the other also tend to be activated. Thus
memory states corresponding to two stimuli which often appear one after
the other become correlated. Models implementing such type of
learning (Amit et al 1994)
have been shown to reproduce quantitatively the results
of the experiment of Miyashita,
in which precisely these
correlations were measured in IT cortex.
The availability of a detailed learning dynamics
enables to predict these correlations as a function
of the temporal correlations existing in the sequence of stimuli.
The ability of these models to analyse experimental data
and to make new predictions has made
possible a collaboration between physicists (namely the group of D.J. Amit)
and neurobiologists (the group of S. Hochstein and V. Yakovlev in
Jerusalem), in order to set
experiments which will test these predictions.
To our knowledge this is the first serious attempt to test the hypothesis
that a collective phenomenon is at the origin of a memory function.
The field of memory neural networks
has experienced a lot of progress during the last 10 years.
For the first time memory models can be confronted with experimental
data from both psychology and neurophysiology.
These models are composed of more realistic elements, however
they remain simple enough to be analyzed and simulated.
A lot of research remains to be done, notably concerning the
dynamical properties of such systems, and learning of spatio-temporal
These models may help to obtain a better understanding of specific systems
(hippocampus, higher sensory cortices, prefrontal cortex), but
also to understand the interactions between systems such as
the cortico-hippocampal interactions.
A major challenge is to build realistic multi-module models
serving specific functions, as pioneered by Dehaene and Changeux.
Another major challenge is to understand how the sensory
systems build efficient representations to be stored in memory:
despite important progresses made in the
analysis of sensory coding (see e.g. Atick 1992), only few attempts have
been made to combine the coding and storing stages.
The proceedings of this symposium "Memory: from neuron to cognition" are published as a special issue of the Comptes Rendus de l'Académie des Sciences, série III (Sciences de la Vie/Life Sciences), vol. 321 No 2-3 ( Feb-March 1998). This texte: pages 249-252.
(back to text)