Memory Retention and Retrieval
E-mail address: fusi@cns.unibe.ch (S. Fusi).
Neurocomputing 38}40 (2001) 1223}1228
Long term memory:
Encoding and storing strategies of the brain
Stefano Fusi
Institute of Physiology, University of Bern, Bu( hlplatz 5, 3012 Bern, Switzerland
Abstract
Plastic material devices, either arti”cial or biological, should be capable of rapidly modifying
their internal state to acquire information and, at the same time, preserve it for long periods (the
stability}plasticity dilemma). Here we compare, in a simple and intuitive way, memory stability
against noise of two di!erent strategies based, respectively, on fully analog devices that
accumulate linearly small changes and on systems with a limited number of stable states and
threshold mechanisms. We show that the discrete systems are more stable, even with short
inherent time constants, and can easily exploit the noise in the input to control the learning rate.
We “nally demonstrate the strategy by discussing a model of a biologically plausible spike-
driven synapse. � 2001 Elsevier Science B.V. All rights reserved.
Keywords: Synaptic plasticity; Long term memory; Learning
1. Introduction
Material (arti”cial or biological) learning devices, like the synapses, have the
capability of changing their internal states in order to acquire (learn) and store
(memorize) information about the statistics of the incoming #ux of stimulations. In
a realistic situation, the stimulations carrying relevant information are separated
by long time intervals of noisy input which tends to erase the memory of the
previously acquired information.Moreover the interference of novel stimulations with
already acquired older &memories’ may give rise to memory loss (e.g. the oldest
stimulations are forgotten to make room for the new ones). This is also known as the
0925-2312/01/$ – see front matter � 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 – 2 3 1 2 ( 0 1 ) 0 0 5 7 1 – 9
stability}plasticity dilemma: the memory should be stable against irrelevant inputs
(e.g. noise) for long periods and, at the same time, the internal state should be rapidly
modi”ed to acquire the information conveyed by the relevant inputs. This dilemm
a
becomes particularly arduous when dealing with material memory devices that do not
allow arbitrarily large time constants or parameters “ne tuning, especially if the
devices are small (e.g. it is reasonable to assume that permanent changes can not be
arbitrarily small).
Here we show one possible encoding and storing strategy that solves this dilemma
and we exemplify it by discussing a model of a spike-driven learning synapse. The
strategy is based on the assumption that information to be coded is redundant: e.g. for
the synapses this means that many cells on the dendritic tree carry similar informa-
tion.We compare two possible scenarios: in the “rst each synapse is described in terms
of one continuous internal variable x. In the absence of any stimulation, the value
encoded by x is preserved forever. In the second, the synapse is discrete on long time
scales: it has only a limited number of attracting stable states: when x drifts away from
one of them, a recalling force drives it back to the closest stable state. To make
a change permanent, the internal variable should cross some threshold, to be then
attracted towards a di!erent stable state. Let K be the number of stable states and �x
the minimal distance between two stable states.
2. Preserving information: The stability problem
We now consider the current generated by the synaptic inputs as the relevant
variable. We assume that it is approximately the linear sum of many input neuronal
activities a
�
multiplied by the corresponding weights J
�
, which, in turn, depend on the
internal state of the synapses. Let
I
�
be the current induced by N neurons that encode
the same information, i.e. that are activated in the same way by a generic stimulus
(a
�
“a for i”1,2,N):
I
�
”
1
N
�
�
���
J
�
a
�
”
a
N
�
�
���
J
�
.
If we start from the fully analog synaptic values and we clamp them to the closest
stable states (see Fig. 1), the error on I
�
goes as &1/(K�N). If N is large enough (the
code is redundant), the error becomes negligible and there is no relevant loss of
information, which would be the only disadvantage of the discrete code. This is
a known property of some neural networks (see e.g. [6]).
However, memory preservation is much more stable in the case of discrete synapses
since the e!ects of noise do not accumulate. Let �t be the typical `responsea time of the
synaptic device, i.e. the time interval during which any change of an internal variable
is established: the noise induces small jumps �x with probability p, either upwards or
downwards, once every �t. The ratio p/�t can also be seen as the rate of events that can
induce permanent changes (e.g. the spikes). Let � be the time constant of the recalling
force: no matter how far x gets from one stable state, in a time of the order of �, it is
1224 S. Fusi / Neurocomputing 38}40 (2001) 1223}1228
Fig. 1. Clipping synaptic e$cacies: passing from fully analog synapses (left) to three-state synaptic e$cacies
(right) does not degrade much of the memory. The input neurons (below) are arranged in such a way that
the “rst N neurons are driven by a generic stimulus to the same activity level. These neurons carry the same
information (redundancy) for that speci”c stimulus. The e$cacies are di!erent because other uncorrelated
stimuli, activating di!erent subsets of neurons, had been previously encoded. When clipped to the closest
stable state, the synapses are pushed up and down and the “nal `errora on the a!erent current I
�
, generated
by N neurons, is equivalent to a noise whose amplitude scales as 1/�N.
driven back to the closest stable state. For the fully analog synapse, after time ¹, the
mean displacement is of the order of �x�p¹/�t. Hence, to have an error of �x, one
has to wait a time of the order of:
¹��&�t�
�x
�x�
�
p��.
If the internal variable x hits one of the boundaries, this time is even shorter [4]. For
the discrete synapse, the same error �x is produced when a #uctuation drives the
internal variable across the threshold. This happens with a probability &(p�/�t)� per
� where h”�/�x is the number of jumps required to reach �. Hence
¹��
&�t
�
�t�
p�
�t�
��
, (1)
which can be much longer than the time of the fully analog synapse, especially if p is
small. It can be so long, that x practically never hits the boundaries (see Section 4). The
best case is when h is maximal, i.e. when the synapse is binary. The same behavior
could be obtained in the analog case by adding an extra device that triggers perma-
nent modi”cations only if some threshold is crossed. However, there is accumulating
experimental evidence that the single synaptic contacts are actually binary on long
time scales [5].
3. Acquiring information: The plasticity problem
It was rather intuitive and well known that discreteness can increase stability
without necessarily degrading memory performance. What was less clear is whether
this is still true in case of on-line learning, when discrete synapses are updated after
every stimulus presentation. Actually discreteness can be advantageous also in this
S. Fusi / Neurocomputing 38}40 (2001) 1223}1228 1225
Fig. 2. Updating synaptic e$cacies. The scheme is described in Fig. 1. Upon the presentation of a generic
stimulus, the analog synapses (left) are potentiated by �”�x/4. Since theN synapses see the same pre- and
post-synaptic activity they are all updated in the same way. The same change in I
�
can be obtained in the
discrete case by modifying only a fourth of the N synapses (synapse �2 in the “gure). This can be obtained
with a stochastic selection mechanism that updates each synapse with probability q”1/4. Interestingly the
presentation of a generic pattern interferes with the memory of other uncorrelated patterns in the same way
in the two scenarios. Indeed, if f is the fraction of neurons activated by a di!erent stimulus, the “nal change
in its current would be fN� in the analog case and fqN�x in the discrete case. For a more general analytical
study see [1].
case. Since the code is redundant, there is no need to modify all the synapses. If the
fraction of synapses that are changed following each stimulation is small (slow
learning), it is possible to better redistribute the synaptic &memory’ resources among
the di!erent patterns of stimulation and actually recover the optimal storage capacity
even with binary synapses [1]. Slow learning is usually di$cult because it is rather
unlikely that the minimal change � inducible by the input is arbitrarily small. After
M repetitions of the same signal, the minimal change of I
�
would be M�. In the
discrete case, the noise superposed to the stimulations can turn in our favor by
providing a triggering signal which selects in a local and unbiased way a small fraction
of synapses to be changed. With the threshold mechanism of the discrete case, the
input, at parity of signal, can induce or not a permanent change, i.e. a transition to
a di!erent stable state. In this case the minimal change in Iwould beMq�x, where q is
the transition probability for each synapse. q�x can be much smaller than � and the
average number of synapses changed after each repetition can be even(1 (see Fig. 2).
This scheme has the very attractive feature that it transfers part of the updating
process outside the device (e.g. embedded in the input): q is not necessarily related to
the intrinsic dynamics of the system. This can be a much better strategy, especially for
small devices with short time constants.
4. Spike-driven synaptic plasticity
To demonstrate how the load of generating low probability events can be transfer-
red outside the device, we discuss a model of a bistable (K”2) spike-driven learning
synapse which has been recently introduced [3]. The transitions between the two
states are activity dependent and stochastic, even without any intrinsic noise source in
the synaptic device. The synapse exploits the #uctuations in the inter-spike intervals,
1226 S. Fusi / Neurocomputing 38}40 (2001) 1223}1228
Fig. 3. Simulation of stochastic LTP. Pre- and post-synaptic neurons have the same mean rate and the
synapse starts from the same initial value. At parity of activity (signal), the “nal state is di!erent in the two
cases.
Fig. 4. Contour plots of LTP and LTD probabilities (q) on log scale vs pre- and post-synaptic neuron rates
for a 500 ms stimulation. LTP occurs when pre- and post-synaptic rates are both high. Around the white
plateau, P
���
drops sharply and becomes negligible for spontaneous rates. The strong non-linearity allows
to discriminate easily between relevant signals and background noise.
which are the results of the collective dynamics of the network. This noise is always
superposed to the signal (pre- and post-synaptic mean frequencies) during the stimula-
tion and is di!erent from synapse to synapse. Each pre-synaptic spike drives the
internal state x either up or down depending on whether the post-synaptic depolariz-
ation is above or below the threhsold �
�
. LTP/LTD might occur or not at parity of
mean pre-synaptic and post-synaptic activities (see Fig. 3). In this case p (see Eq. (1)) is
the probability of coincidence of two events (e.g. a pre-synaptic spike and high
depolarization) and hence can be very small. In Fig. 4 we show that the stochastic
transitions between stable states are easily manipulable. In the presence of noise (low,
spontaneous activity), the time to wait for a transition can be of the order of years,
even if the longest time constant � is of the order of 100 ms, whereas under stimulation
(higher frequencies) the transition probabilities are easily controllable in the range
S. Fusi / Neurocomputing 38}40 (2001) 1223}1228 1227
10��}10��, as expected from Eq. (1). Extensive simulations of the learning process in
networks of integrate-and-“re neurons connected by the proposed synapse are pre-
sented in [2].
We believe that this strategy based on the combination of discreteness and external
stochasticity is a good general strategy for storing variables on long time scales and it
is likely to underlie the basic mechanisms of many other biological small systems.
Moreover this analysis shows that synaptic models in which single events (e.g. single
spikes) modify permanently the synaptic e$cacy can be hardly used as long term
memory devices since the information acquired during the stimulation would be
erased in a short time by the spontaneous activity.
References
[1] D.J. Amit, S. Fusi, Learning in neural networks with material synapses, Neural Comput. 6 (1994)
957}982.
[2] P. Del Giudice, M. Mattia, Long and short term synaptic plasticity and the formation of working
memory: a case study, Neurocomputing 38}40 (2001) 1175}1180, this issue.
[3] S. Fusi, M. Annunziato, D. Badoni, A. Salamon, D.J. Amit, Spike-driven synaptic plasticity: theory,
simulation, VLSI implementation, Neural Comput. 12 (2000) 2227}2258.
[4] G. Parisi, A memory which forgets, J. Phys. A 19 (1986) L617.
[5] C.C.H. Petersen, R.C. Malenka, R.A. Nicoll, J.J. Hop”eld, All-or-none potentiation at CA3-CA1
synapses, Proc.Natl.Acad.Sci. 95 (1998) 4732.
[6] H. Sompolinsky, The theory of neural networks: the Hebb rule and beyond, in: L. van Hemmen, I.
Morgenstern (Eds.), Heidelberg Colloquium on Glassy Dynamics, Springer, 1987.
Stefano Fusi was born in 1968 in Florence, Italy. He received his master degree in
physics from the university of Roma in 1992. He had been working as a researcher
in the National Institute of Nuclear Physics (INFN, Roma) from 1993 to 1999 and
received a Ph.D. in physics from the HebrewUniversity of Jerusalem in 1999. He is
currently working in the Institute of Physiology of Bern. His research interests
include long-term synaptic plasticity, in vivo experiments on behaving monkeys,
neuromorphic VLSI hardware and analytical studies of networks of spiking
neurons.
1228 S. Fusi / Neurocomputing 38}40 (2001) 1223}1228
PSYC 575
Journal Article Summary Template
Answer the following 8 questions and submit the completed
Journal Article Summary Template as well as a PDF of the article being reviewed to Canvas.
1. Current APA reference of article being reviewed:
2. What is the research problem that is being investigated? What is the purpose of the research being conducted?
3. What is the research question?
4. What are 2 or more theories that are discussed in the Introduction? How are they used to motivate (or set up) the research question? Do the authors agree or disagree with these theories?
5. How is the research question operationalized? First, identify the abstract constructs being studied. Next, identify the concrete way these are being observed or measured. This should include your IV and DV.
6. What is the research design (i.e. between or within subjects, what type of statistical tests were used, what were the levels of each variable)?
7. Describe the results (but not their broader implications). Were the results significant? Which ones? Do these support or not support the hypothesis?
8. What limitations are mentioned? Why are these limitations theoretically interesting?
Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.
PSYC 575
Journal Article Summary Assignment Instructions
Article review. You can select any article pertaining to cognitive psychology, but I suggest that you select an article that you could use in your paper on false memories. The article should be a peer reviewed journal article that discusses an experiment the authors actually conducted (i.e. a primary source). In other words, the article cannot be a review article, meta-analysis, editorial or something from the popular press. In all of these examples the author is discussing someone else’s work and you’re reading about it second-hand.
Overview
For each Journal Article Summary, you will choose an article to review and use the
Journal Article Summary Template to complete the assignment. The article you select must be a peer-reviewed journal article in the field of cognitive psychology. The article must also be a primary source, meaning that the authors are discussing their own research, not others’ research (e.g. review articles). Do not use an article that conducted a meta-analysis. It is ideal to select an article that you will be using in your paper; however, this is not a requirement. If you use an article that does not meet these criteria, you will not receive credit for this assignment. See the example below for detailed explanation of the required material for each question. Submit the completed form and a PDF of the article being reviewed. All material must be in current APA format.
Instructions
1. APA reference of article being reviewed
Write the reference for the article as if it were in the reference section of your paper.
2. What is the research problem that is being investigated? What is the purpose of the research being conducted?
Provide the “why” behind the paper. Why have they conducted this experiment? For example: “These experiments were designed to explore the role of second order conditioning in anxiety disorders.”
3. What is the research question?
The research question is more specific. What is the specific question or questions the article will answer as a result of the study or experiment? For example: “Are adolescents more sensitive to the memory imparting effects of alcohol?”
4. What are 2 or more theories that are discussed in the Introduction? How are they used to motivate (or set up) the research question? Do the authors agree or disagree with these theories?
Simply restate the theories discussed in the introduction in your own words. State how these theories are driving the research questions. If the authors’ hypothesis is correct, will it support the theory or be inconsistent with the theory? You should have good idea of where the authors stand based on the evidence presented and the arguments they are making.
5. How is the research question operationalized? First, identify the abstract constructs being studied. Next identify the concrete way these are being observed or measured. This should include your IV and DV.
A construct is an abstract explanatory variable that this not directly observable (e.g. memory). The concrete way the construct is measured will point you to the dependent variable (DV). For example, if the paper is concerned with memory, the DV may be the number of items recalled. The independent variable (IV) could be the amount of sleep each participant was allowed the night before the test. Remember that we cannot directly measure many of the constructs that are studied in psychology, so it is important that we identify how they are being operationalize in each research study.
6. What is the research design (i.e. between or within subjects, what type of statistical tests were used, what were the levels of each variable)?
This information will be in the methods section of your paper. Be sure to provide enough detail to describe how the study was designed.
7. Describe the results (but not their broader implications). Were the results significant? Which ones? Do these support or not support the hypothesis?
Describe the result in your own words. For example: Group X were able to recall significantly more words than Group Y. This finding supports the hypothesis that manipulation Y would reduce recall.
8. What limitations are mentioned? Why are these limitations theoretically interesting?
Limitations can be found in the discussion section of the paper. If a limitation is that they didn’t have X control group, then explain in your own words why that is important. Does it change the interpretation of the findings?
Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.
Page 2 of 2
Memory: Retention and Retrieval
DISCUSSION ASSIGNMENT INSTRUCTIONS
For each discussion, you are required to provide a discussion thread in response to the provided prompt for each discussion. Each discussion thread must be at
least 500 words, demonstrate course-related knowledge, and include at
least 3 scholarly sources,
not including the course text and/or Bible.
In addition to the discussion thread, you are required to reply to 2 other classmates’ discussion threads. Each discussion reply must be at least 200 words.
Using the principles cognitive psychologists have discovered about memory, write 3 ways in which you plan to either continue or change your study strategy. Remember to cite the studies you are using as evidence and include references for each point.
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