# 2.8. Projections¶

## 2.8.1. Declaring the projections¶

Once the populations are created, one can connect them by creating Projection instances:

 proj = Projection(
pre = pop1,
post = pop2,
target = "exc",
synapse = BCM
)

• pre is either the name of the pre-synaptic population or the corresponding Population object.
• post is either the name of the post-synaptic population or the corresponding Population object.
• target is the type of the connection.
• synapse is an optional argument requiring a Synapse instance.

The post-synaptic neuron type must use sum(exc) in the rate-coded case respectively g_exc in the spiking case, otherwise the projection will be useless.

If the synapse argument is omitted, the default synapse will be used:

• the default rate-coded synapse defines psp = w * pre.r,
• the default spiking synapse defines g_target += w.

## 2.8.2. Building the projections¶

Creating the Projection objects only defines the information that two populations are connected. The synapses must be explicitely created by applying a connector method on the Projection object.

To this end, ANNarchy already provides a set of predefined connector methods, but the user has also the possibility to define his own (see Connectivity).

The pattern can be applied either directly at the creation of the Projection:

proj = Projection(
pre = pop1,
post = pop2,
target = "exc",
synapse = BCM
).connect_all_to_all( weights = 1.0 )


or afterwards:

proj = Projection(
pre = pop1,
post = pop2,
target = "exc",
synapse = BCM
)
proj.connect_all_to_all( weights = 1.0 )


The connector method must be called before the network is compiled.

## 2.8.3. Projection attributes¶

Let’s suppose the BCM synapse is used to create the Projection proj (spiking synapses are accessed similarly):

BCM = Synapse(
parameters = """
eta = 0.01 : projection
tau = 100. : projection
""",
equations = """
tau * dtheta/dt + theta = post.r^2 : postsynaptic
dw/dt = eta * post.r * (post.r - theta) * pre.r : min=0.0
"""
)


### 2.8.3.1. Global attributes¶

The global parameters and variables of a projection (i.e. defined with the postsynaptic or projection flags) can be accessed directly through attributes. Attributes defined with projection have a single value for the whole population:

>>> proj.tau
100


Attributes defined with postsynaptic have one value per post-synaptic neuron, so the result is a vector:

>>> proj.theta
[3.575, 15.987, ... , 4.620]


Post-synaptic variables can be modified by passing:

• a single value, which will be the same for all post-synaptic neurons.
• a list of values, with the same size as the number of neurons receiving synapses (for some sparse connectivity patterns, it may not be the same as the size of the population, so no multidimensional array is accepted).

After compilation (and therefore creation of the synapses), you can access how many post-synaptic neurons receive actual synapses with:

>>> proj.size
4


The list of ranks of the post-synaptic neurons receiving synapses is obtained with:

>>> proj.post_ranks
[0, 1, 2, 3]


### 2.8.3.2. Local attributes¶

At the projection level

Local attributes can also be accessed globally through attributes. It will return a list of lists containing the synapse-specific values.

The first index represents the post-synaptic neurons. It has the same length as proj.post_ranks. Beware that if some post-synaptic neurons do not receive any connection, this index will not correspond to the ranksof the post-synaptic population.

The second index addresses the pre-synaptic neurons. If the connection is sparse, it also is unrelated to the ranks of the pre-synaptic neurons in their populations.

Warning

Modifying these lists of lists is error-prone, so this method should be avoided if possible.

At the post-synaptic level

The local parameters and variables of a projection (synapse-specific) should better be accessed through the Dendrite object, which gathers for a single post-synaptic neuron all synapses belonging to the projection.

Beware: As projections are only instantiated after the call to compile(), local attributes of a Projection are only available then. Trying to access them before compilation will lead to an error!

Each dendrite stores the parameters and variables of the corresponding synapses as attributes, as populations do for neurons. You can loop over all post-synaptic neurons receiving synapses with the dendrites iterator:

for dendrite in proj.dendrites:
print dendrite.rank
print dendrite.size
print dendrite.tau
print dendrite.alpha
print dendrite.w


dendrite.rank returns a list of pre-synaptic neuron ranks. dendrite.size returns the number of synapses for the considered post-synaptic neuron. Global parameters/variables return a single value (dendrite.tau) and local ones return a list (dendrite.w).

You can even omit the .dendrites part of the iterator:

for dendrite in proj:
print dendrite.rank
print dendrite.size
print dendrite.tau
print dendrite.alpha
print dendrite.w


You can also access the dendrites individually, either by specifying the rank of the post-synaptic neuron:

dendrite = proj.dendrite(13)
print dendrite.w


or its coordinates:

dendrite = proj.dendrite(5, 5)
print dendrite.w


When using ranks, you can also directly address the projection as an array:

dendrite = proj[13]
print dendrite.w


Warning

You should make sure that the dendrite actually exists before accessing it through its rank, because it is otherwise a None object.

### 2.8.3.3. Functions¶

If you have defined a function inside a Synapse definition:

BCM = Synapse(
parameters = """
eta = 0.01 : projection
tau = 100. : projection
""",
equations = """
tau * dtheta/dt + theta = post.r^2 : postsynaptic
dw/dt = eta * BCMRule(pre.r, post.r, theta) : min=0.0
""",
functions = """
BCMRule(pre, post, theta) = post * (post - theta) * pre
"""
)


you can use this function in Python as if it were a method of the corresponding object:

proj = Projection(pop1, pop2, 'exc', BCM).connect_xxx()

pre = np.linspace(0., 1., 100)
post = np.linspace(0., 1., 100)
theta = 0.01 * np.ones(100)

weight_change = proj.BCMRule(pre, post, theta)


You can pass either a list or a 1D Numpy array to each argument (not a single value, nor a multidimensional array!).

The size of the arrays passed for each argument is arbitrary (it must not match the projection’s size) but you have to make sure that they all have the same size. Errors are not catched, so be careful.

## 2.8.4. Connecting population views¶

Projections are usually understood as a connectivity pattern between two populations. Complex connectivity patterns have to specifically designed (see Connectivity).

In some cases, it can be much simpler to connect subsets of neurons directly, using built-in connector methods. To this end, the Projection object also accepts PopulationView objects (Populations) for the pre and post arguments.

Let’s suppose we want to connect the (8,8) populations pop1 and pop2 in a all-to-all manner, but only for the (4,4) neurons in the center of these populations. The first step is to create the PopulationView objects using the slice operator:

pop1_center = pop1[2:7, 2:7]
pop2_center = pop2[2:7, 2:7]


They can then be simply used to create a projection:

proj = Projection(
pre = pop1_center,
post = pop2_center,
target = "exc",
synapse = BCM
).connect_all_to_all( weights = 1.0 )


Each neuron of pop2_center will receive synapses from all neurons of pop1_center, and only them. Neurons of pop2 which are not in pop2_center will not receive any synapse.

Warning

If you define your own connector method (Connectivity) and want to use PopulationViews, you’ll need to iterate over the ranks attribute of the PopulationView object.

## 2.8.5. Specifying delays in synaptic transmission¶

By default, synaptic transmission is considered to be instantaneous (or more precisely, it takes one simulation step (dt) for a newly computed firing rate to be taken into account by post-synaptic neurons).

In order to take longer propagation times into account in the transmission of information between two populations, one has the possibility to define synaptic delays for a projection. All the built-in connector methods take an argument delays (default=dt), which can be a float (in milliseconds) or a random number generator.

proj.connect_all_to_all( weights = 1.0, delays = 10.0)
proj.connect_all_to_all( weights = 1.0, delays = Uniform(1.0, 10.0))


If the delay is not a multiple of the simulation time step (dt = 1.0 by default), it will be rounded to the closest multiple. The same is true for the values returned by a random number generator.

Note: Per design, the minimal possible delay is equal to dt: values smaller than dt will be replaced by dt. Negative values do not make any sense and are ignored.

Warning

Spiking projections accept non-uniform delays, but it is extremely slow (factor 100 at least).

Warning

Non-uniform delays are not available on CUDA.

## 2.8.6. Controlling projections¶

Synaptic transmission, update and plasticity

It is possible to selectively control synaptic transmission and plasticity at the projection level. The boolean flags transmission, update and plasticity can be set for that purpose:

proj.transmission = False
proj.update = False
proj.plasticity = False

• If transmission is False, the projection is totally shut down: it does not transmit any information to the post-synaptic population (the corresponding weighted sums or conductances are constantly 0) and all synaptic variables are frozen to their current value (including the synaptic weights w).
• If update is False, synaptic transmission occurs normally, but the synaptic variables are not updated. For spiking synapses, this includes traces when they are computed at each step, but not when they are integrated in an event-driven manner (flag event-driven). Beware: continous synaptic transmission as in NMDA synapses will not work in this mode, as internal variables are not updated.
• If only plasticity is False, synaptic transmission and synaptic variable updates occur normally, but changes to the synaptic weight w are ignored.

Disabling learning

Alternatively, one can use the enable_learning() and disable_learning() methods of Projection. The effect of disable_learning() depends on the type of the projection:

• for rate-coded projections, disable_learning() is equivalent to update=False: no synaptic variables is updated.
• for spiking projections, it is equivalent to plasticity=False: only the weights are blocked.

The reason of this difference is to allow continuous synaptic transmission and computation of traces. Calling enable_learning() without arguments resumes the default learning behaviour.

Periodic learning

enable_learning() also accepts two arguments period and offset. period defines the interval in ms between two evaluations of the synaptic variables. This can be useful when learning should only occur once at the end of a trial. It is recommended not to use ODEs in the equations in this case, as they are numerized according to a fixed time step. offset defines the time inside the period at which the evaluation should occur. By default, it is 0, so the variable updates will occur at the next step, then after period ms, and so on. Setting it to -1 will shift the update at the end of the period.

Note that spiking synapses using online evaluation will not be affected by these parameters, as they are event-driven.

## 2.8.7. Multiple targets¶

For spiking neurons, it may be desirable that a single synapses activates different currents (or conductances) in the post-synaptic neuron. One example are AMPA/NMDA synapses, where a single spike generates a “classical” AMPA current, plus a voltage-gated slower NMDA current. The following conductance-based Izhikevich is an example:

RSNeuron = Neuron(
parameters = """
a = 0.02
b = 0.2
c = -65.
d = 8.
tau_ampa = 5.
tau_nmda = 150.
vrev = 0.0
""" ,
equations="""
I = g_ampa * (vrev - v) + g_nmda * nmda(v, -80.0, 60.0) * (vrev -v)
dv/dt = 0.04 * v^2 + 5.0 * v + 140.0 - u + I : init=-65., midpoint
du/dt = a * (b*v - u) : init=-13.
tau_ampa * dg_ampa/dt = -g_ampa
tau_nmda * dg_nmda/dt = -g_nmda
""" ,
spike = """
v >= 30.
""",
reset = """
v = c
u += d
""",
functions = """
nmda(v, t, s) = ((v-t)/(s))^2 / (1.0 + ((v-t)/(s))^2)
"""
)


However, g_ampa and g_nmda collect by default spikes from different projections, so the weights will not be shared between the “ampa” projection and the “nmda” one. It is therefore possible to specify a list of targets when building a projection, meaning that a single pre-synaptic spike will increase both g_ampa and g_nmda from the same weight:

proj = Projection(pop1, pop2, ['ampa', 'nmda'], STDP)


An example is provided in examples/homeostatic_stdp/Ramp.py.

Warning

Multiple targets are not available on CUDA yet.