Dynamic delays during a run

[KarimHabashy]

Dynamic delays during a run

[mstimberg]

It took me a moment to get a hand on that book in order to make sure I understand what you are referring to. This is quite a different situation, since the equations in that chapter do not refer to spiking networks, but to continuous interactions between non-spiking neurons (the same methods could also be applied to population dynamics). Such interactions can be simulated in Brian, but you cannot have delays for continuous interactions (see #1098 and #467). However, you can easily implement what he calls a "multistage delay", i.e. an approximation of a delayed connection by one or more additional variables.
E.g., the equations 4.15 from the book

$$ \begin{align*} \frac{dE}{dt} &= \frac{1}{10}(-E - 2\Delta) \\ \frac{dI}{dt} &= \frac{1}{50}(-I + 8E) \\ \frac{d\Delta}{dt} &= \frac{1}{\delta}(-\Delta + I) \end{align*} $$

Can be written as:

eqs = '''
dE/dt = 1/(10*ms) * (-E - 2*Delta)  : 1
dI/dt = 1/(50*ms) * (-I + 8*E) : 1
dDelta/dt = 1/delta * (-Delta + I) : 1
'''

You can run this directly like this, to show that there is oscillation for some values of $\delta$

from brian2 import *
eqs = '...#see above'
delta = 7.61*ms
group = NeuronGroup(1, eqs, method='euler')
group.E = 1  # initial activity
mon = StateMonitor(group, ['E', 'I'], record=True)
run(200*ms)
plt.plot(mon.t/ms, mon.E[0], label='E')
plt.plot(mon.t/ms, mon.I[0], label='I')
plt.legend()
plt.show()

This is not a good way of doing things in general, though, since here the connection between the E and I neurons is hardcoded into the equations, i.e. you cannot have several E and I neurons that are connected this way. Instead, a more general approach would be to separate the E and I populations into two separate NeuronGroups and then connect them either using a "linked variable" (if you only have 1-to-1 connections), or via a "summed variable" (for the general case). We don't have many examples of this kind, but see Tetzlaff et al. (2015) for a (quite complex) example of non-spiking interactions via summed variables.

If you have more questions about this, I'd suggest asking over at https://brian.discourse.group.

[mstimberg]

Indeed, here is the original issue: #355 – nothing has fundamentally changed since then, unfortunately we still don't have a mechanism for it.

I can see possible workarounds:

• Instead of changing the delays, have multiple synapses between each source/target pair with different delays and switch between them (i.e. adapt the weights instead of the delays). Approaches like this have been used to model plasticity in the auditory system: https://direct.mit.edu/neco/article-abstract/24/9/2251/7800/Frequency-Selectivity-Emerging-from-Spike-Timing
• Instead of changing the delays during the run, change another variable. At regular intervals, stop the simulation and apply the changes accumulated in the other variable to the actual delays. If you did this at every time step, this would be perfectly equivalent to changing the delays dynamically, but… it would also be terribly slow and not useful in practice. But if it is ok to only apply the changes in delays, say, every 100ms or so, then it could be feasibly – I don't know what kind of plasticity to have in mind, but I'd expect changes in dynamic delays to be rather slow.

[KarimHabashy]

Thanks for your quick reply! If you need me to continue this discussion in the other post let me know! However, I have another question before that, if you don't mind. Was it considered to use multistage delays in the neuron's dynamic equations to simulate delays? I am referring to the method mentioned in the book "https://www.amazon.com/Spikes-Decisions-Actions-Foundations-Neuroscience/dp/0198524307" by Wilson, Page "56". If it was considered what were the difficulties in implementation? I am asking this because I was thinking of using this method to learn delays.