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Temporal decoding principle

fig6

A temporal neuron like in C can detect specific spatio-temporal spike
patterns. On the top, an example of a spatio-temporal spike pattern based on three neurons N1 to N3 and 6 spikes. On the bottom, the specific organization of synapses along the dendrite corresponding to the detected spike pattern given above.

A neuron for which the behavior can be described by eq. 4
(hereafter named temporal neuron) is able to detect a
specific spatio-temporal pattern of spikes. The general idea
of this form of detection is that all the EPSPs created by the
different spikes in the spike train will converge at the same
moment at the soma using the different propagation times to
counter-balance the different spike arrival times at each
synapse; all this creating a maximal depolarization in the
soma. A different version of the same general idea was
suggested by Gerstner et al. ([7] page 144) with the notable
difference that instead of using different propagation times,
they implemented different rise times.

Effect of a dendrite on the EPSP

Location of a synapse on a dendrite will modulate the
arrival time of the EPSP at the soma level due to the
propagation time of the EPSP in the dendrite [8] and will
also modulate the shape of the alpha function. Fig 1B.

The soma arrival time depends logically on the
propagation velocity v within the dendrite, on the spike
arrival time at the synapse and on the distance to be
traversed by the EPSP to the soma: lambda_s, or synapse position.
Accounting for this dendritic effect, equation 1 then
becomes u(t ,p,lambda_s) with p relating to the position on the
dendrite relative to the soma:

eq2

 

 

μ represents the maximum value of u expressed without
considering the synaptic weight w. It is only used to
normalize u, making u equal the synaptic weight w at the
EPSP peak. μ is expressed by the following equation:eq3

 

The amplitude of the EPSP is also attenuated during its
somatopetal propagation (from the synapse to the soma) [8],
[9], [10]. This attenuation at a particular position p on the
dendrite depends on the distance to the synapse:( ) and
on a chosen attenuation rate α. We used the following
attenuation function:

eq4

 

 

 

delay line neural network as precise spikes sequence detector

delay line I&F neural network
delay line I&F neural network

This neural network has been done with the Animatlab software using only firing realistic neurons.

Here, to simplify, there is only one input neuron, in red. But the principle is the same with several input neurons. Each input neuron has to project to the delay line neurons, in orange. The last neuron of the delay line, in orange, has to project to the output neuron with a conduction weight depending on the number of spikes in the pattern to be recognize.

With this specific connectivity, the input neuron creates 3 links to the conduction delay neurons, hence the pattern to be recognize will contain 3 spikes. I have used a conduction delay of 10ms. This network will then recognize a spike pattern of 3 spikes with the following arrival time t1=0, t2=30ms and t3=40ms.

Composite EPSP

Everytime a spike input the delay line neural network, it creates a particular composite EPSP in the output neuron.

composite EPSP
the particular network architecture creates a predictable composite EPSP

This particular shape of the membrane potential is created by the propagation times the different spikes take to go through the conduction line neural network. Because the propagation time are predictable  as well as the axonic connections, the composite EPSP in the output neuron is hence predictable.

temporal decoding : precise spike sequence detection.

when a specific spike pattern arrives with a particular timing the output neuron integrates the composite EPSPs and fire.
when a specific spike pattern arrives with a particular timing the output neuron integrates the composite EPSPs and fire.

when the input have the particular timing of the network:  t1=0, t2=30ms and t3=40ms, the output neuron recognize the sequence and fire.

the precise spike timing is also important even in the case of 3 input spikes.

Even with 3 spikes, the precise spike timing is important to make the output neuron fire.
Even with 3 spikes, the precise spike timing is important to make the output neuron fire.

if the timing is not good, the composite EPSPs do not combine well in the output neuron that cannot reach the membrane potential threshold to fire.

The precision of the timing can be modulated by tuning the decay time of each EPSP. With a longer duration of the EPSP it is possible to be less exigent on the precision of the timing.

We have seen here that with a conduction line neural network and only realistic neurons it is possible to make a temporal decoder: the output neuron can fire only when a precise spatio-temporal spike pattern is in input.

EPSP on a point neuron

What is the relation between the morphology of a neuron and its function? Neurons mostly present large dendritic extensions, the exact role of which largely remains unknown. It could be, as has already been suggested, that dendrites are simply there to increase the membrane surface area of the neurons to enable the binding of 10- or 20 fold more synapses (Mel WB in [2] p421). This being the case, the shape of the dendritic tree and the particular position of the synapses would have only little influence on the computation performed by the neurons. The best model for approximating this dendritic function would be the point neuron. A: the arrival of an action potential at a synapse triggers an EPSP in the post-synaptic neuron. [6] Pages 75-76.

eq1

This function supposes an incoming firing time at t=0 of the presynaptic neuron. In this equation, u is the membrane potential of the dendrite and soma, w is the synaptic weight, delta_ax is the transmission delay between the time the pre-synaptic neuron is active and the time the synapse s becomes active. t is the time constant, t_r is the rising time constant and H is the Heaviside function.

One of the most obvious functions that the point neuron model can perform is coincidence detection: when two neurons are synchronized and both have the same point neuron as output, then the simultaneous arrival of the spikes triggers a summed EPSP that overshoots the spike threshold. This target point neuron then emits an action potential that indicates its coincidence detection. Thus, for a point neuron, the variation of the membrane potential depends exclusively on the synaptic weights and the arrival times of the incoming spikes.

What is less clear however is how this type of neuron, except when integrated in large networks, could detect many spike arrival times, i.e. a specific spike train. To investigate this, we modified the point neuron equation to incorporate a
propagation function along a dendrite.

Perception : spatio-temporal spikes patterns

http://neuroxidence.com/

All our perceptions from the world are coded in our brain by spatio-temporal patterns of spikes : In a mathematical word there are binary matrices. Those data look like the raster plot figure on the left.

When we recognize an object the brain recognize in fact a specific spatio-temporal spikes pattern (STSP) or a sequence of STSPs or a set of STSPs.

If the brain is not able to recognize any memorized STSP, our actions manipulate the object in all directions in order to enter a specific configuration of stimuli which in turn create a specific STSP that can be recognized.

The TempUnit model showed in this website will demonstrate that it can:

  • detect (recognize) a specific STSP
  • detect a noisy STSP
  • detect an incomplete STSP

What Artificial Intelligence would look like when it is only about manipulation of STSPs ?