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13th December

Computing with spike timing and delays
Types of neuronal pattern recognition
Scale-invariant recognition
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E
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in speech recognition, loudness is not a variant in recognition
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g
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The size of x doesn’t matter
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The scale factor shouldn’t come into
play, they are the same input pattern, and the relative firing rate of the neurons will be same
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A strong input neuron would usually have a strong connection and
a weak input neuron would have a weak connection and make less of a difference
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However if the network is pattern
based, then the weak input would be crucial in identifying the identity of the input
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Hopfield’s 1995 time-advance coding network
Described a computational model in which the sizes of variables are represented by the explicit
times at which action potentials occur, rather than by the more usual ‘firing rate’ of neurons
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Olfactory bulb has theta oscillation
frequency (10 Hz) due to inhibitory input from medial septum
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When an input current is added, the cell potential (neglecting
currents which flow during an action potential) will cross threshold, as shown by the broken curve
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The cell potential
never again exceeds the threshold for spike generation until the next cycle of the periodic oscillation
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13th December
The pattern is coded by the timing of spikes relative to a sub-threshold membrane potential oscillation
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If there is a big input current, then the shift of cell potential oscillation upwards will
occur relatively early in the oscillation wave
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So small
inputs must fire near the peak of the sub-threshold membrane potential oscillation for it to be able to bring
it to firing threshold
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“The action potential of 5 different neurons drive with different input currents (analogue signal strengths)
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The firing frequency remains f over a greater input current if the refractory
period is long
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The input neurons are coded by the strength of a
smell they’ve detected and their inputs are one spike each, but the timing of that input is crucial instead
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So neuron
one fires early in the oscillation wave because it has a large current and brings the cell’s oscillation above
firing threshold
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So all the neurons fire once per cycle at slightly differently points in the cycle
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So all the
input neurons’ spikes will arrive simultaneously at the output neuron, and that will make a big impact on the
output cell, especially if the cell does coincidence detection
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If there is a different pattern, the conduction delays will not fit and the firing will not
summate
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Adding scaling-invariant to this network

13th December
If the time advance (Ti) is proportional to the log of the input current, log(xi), then the network will do scaleinvariant recognition, if the input current strength is doubled: log(2xi)= log(2) + log(xi)
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By doubling, the output neuron will respond earlier by log(2)
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Consider the shape of the oscillatory curve, it is roughly sinusoidal so it could produce something like a log
coding of stimulus intensity
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So the shape of this membrane oscillation curve over
time means small increases in inputs are actually magnified in giving a big time advance than big inputs
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Olfactory bulb, hippocampus have this oscillation so this might be how information is coded in them
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Here input values = time
advance, processing via delay-lines
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There are some implausibility to this model, how to vary conduction delay? Some axons maybe myelinated
for faster transmission, but there is no differential myelination for different conduction speeds
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Conduction delays have to match these time delays, i
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they have to vary between
10, 20 msec too
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Although the olfactory bulb does contain unmyelinated axons, so the delay may be longer
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(People don’t really know what they are doing)
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A pruning mechanism might be possible where there are lots of pre-existing axons available, and the
ones that are useful for recognition remain, and other ones gets degraded by astrocytes
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