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Memory Network Maintenance Using
Spike-Timing Dependent Plasticity
David Jangraw, ELE ’07
Advisor: John Hopfield, Department of Molecular Biology
category
i(mA)
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• Each neuron is modeled as a parallel RC circuit with a
firing threshold
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Br
Bl
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Gr
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property
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time(s)
output voltage
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• The firing frequency ‘f’ is our measure of activity.
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Each black square in this grid represents an
active neuron encoding something about a
person. For example, if the bottom row of
neurons encodes eye color, and the ‘green’
neuron is active, this person has green eyes.
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time(s)
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frequency (Hz)
Synaptic Drift (δT):
Small, random changes in synaptic strength due to “noisy”
cellular processes
• This will make the neuron fire more quickly than the
neurons connected to it (-δt)
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• STDP would transform this spike timing delay into
negative changes in synaptic strength (-δT)
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• This would produce a proportional negative change in
input current (+δI) that could stabilize the memory!
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Normal memories have equal activity in each participating
neuron, but synaptic drift causes unequal activity (a
corrupted memory) or even memory loss.
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Io = DC input current (mA)
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Non-Memory
+δT  +δI  –δt  –δT  –δI
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• STDP applied based on average delay
after 50 spikes of each neuron
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• STDP successfully used to
synchronize firing of many neurons
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applications of STDP rule (x50 spikes)
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• Slope of STDP rule affects speed and
stability of synchronization
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Synchronization of two neurons
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m=5
m=30
m=50
m=80
m=100
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applications of STDP rule (x50 spikes)
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delta T
- Neuron Activity
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Io (mA)
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Changes in input current (while still on the f-I plateau)
lead to changes in spike timing.
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applications of STDP
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Future Directions
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current through active neurons
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Drift Correction
• This indicates that spiking neurons could
correct for synaptic drift using STDP
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Two neurons with slightly different input currents are synchronized using STDP rules with
different slopes (m). Low m produced slow convergence; high m produced damped
oscillation; extremely high m (not shown) produced instability.
• Each drifted memory did converge
to an ideal memory
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time of spike relative to input max (ms)
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• Applied random synaptic drift (≤5%) to
each active connection in a memory.
A Simple STDP Rule
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final timing of spikes: A=5, w=30
Figure (except titles) from J. J. Hopfield (2006). “Searching for memories, Sudoku, implicit check-bits,
and the iterative use of not-always-correct rapid neural computation.” arXiv.org, 19 Sep 2006.
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• Simplified memory network using
continuous-variable neurons with spiking
neuron’s f-I curve and spike timing patterns
AC input produces a plateau on the neuron’s f-I curve.
…Can the system correct itself?
Drifted Memory
IAC
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The Problem:
Ideal Memory
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Stability Analysis:
• A small positive change in T (synaptic drift, +δT) will
produce a proportional positive change in the input
current (+δI) to the receiving neuron
frequency response of neuron: A=5mA
w=30Hz
I = Io + 0.05
sin(2π wt)
Synaptic Strength (matrix T):
T21 is proportional to the size of the electrical response in
neuron 2 evoked by an electrical spike in neuron 1
T12
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Spike-Timing Dependent Plasticity
Synapse:
A connection between two neurons
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• If we feed an AC input of the form:
I=Io + A sin(2π wt)
into a neuron, a large range of DC offsets (Io) will drive
the cell to fire at a frequency w, creating a plateau on
the f-I curve (below left).
• Modeled disconnected neurons given
slightly different input currents, causing
varying delays in spike timing
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• When the membrane voltage exceeds threshold, the
cell fires.
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Synaptic Drift
T21
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…
v (mV)
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t
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Eyes:
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Synchronization of 51 neurons, m=0.1
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input current (mA)
• We will model the activity of these neurons
using MATLAB
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• Each property of the person or thing being
remembered is represented by the activity of
one neuron
• All neurons active in a memory are
connected, so thinking of one thing about a
memory (i.e. a name) will recall other things
(i.e. height, eye color)
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• Associative memory is not fully understood;
here we refine a simplified model of it
Spike-Timing Dependent Plasticity (STDP):
Experimentally observed phenomenon by which relative
spike timing changes synaptic strength
input current
Sample Memory
Synchronization
average delay (t2-t1), in ms
Associative Memory:
Learned connections between ideas one
remembers as being associated
Stabilization of Firing
average delay (t2-t1), in ms
Associative Memory
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• Load multiple, overlapping memories into network and test performance
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delay (ms)
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Changes in spike timing are converted to
proportional changes in synaptic strength.
Spikes too far separated are ignored.
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• Create converging memory network of spiking neurons
• Use more realistic STDP rule
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