4 Jun
2020
4 Jun
'20
9:03 p.m.
Hello everyone,
I would like to ask how to normalize synaptic weights during STDP learning.
What I want to do is keeping the total amount of synaptic weights to/from
each neuron constant.
I try to describe my goal a bit more precisely:
i: The index of a pre-synaptic neuron.
j: The index of a post-synaptic neuron.
w_ij(t): The synaptic weight from i-th neuron to j-th neuron at time=t.
s_i(t): the sum of all incoming synaptic weights to i-th neuron at time=t.
i.e. the sum of w_ij(t) over j.
The goal is to set the sum of incoming weights (s_i(*)) to 1 by
normalization (1 is just for simplicity).
By STDP, we can get updated synaptic weight matrix w_ij(t+1), and the sum
s_i(t+1) is not necessarily 1. So, I want to set
w_ij(t+1) <- w_ij(t+1) / s_i(t+1)
I briefly read the documentation for synaptic models(
https://nest-simulator.readthedocs.io/en/stable/models/synapses.html).
I am not very confident if my understanding is correct, but it seems that
existing synaptic models handle only one synaptic weight.
How can I gather data of all incoming(or outgoing as well) weights to a
neuron and use the summation value inside of the STDP synapse model?
Best regards,
Keiko Fujii
29 Jun
29 Jun
2:03 a.m.
Dear Keiko,
Thank you for writing in and addressing this issue. Because of the way that the data
structures are laid out in NEST, normalising the weights per neuron is a costly operation
(in terms of time spent). One has to iterate over all the neurons, then for each neuron
fetch all of its connections, calculate the vector norm and perform the actual
normalisation, and finally to write back the new weights.
This would look something like:
for neur in neurons_to_be_normalised:
connect = nest.GetConnections(target=[neur]], synapse_model="stdp_synapse")
w = nest.GetStatus(connect, "weight")
nest.SetStatus(connect, "weight", np.array(w/np.sum(w)))
The next question is then, how often should this normalisation be carried out? To be
formally correct, it should be done at each simulation timestep, but weights typically
evolve on a much longer timescale than the network is simulated at, so this would be very
inefficient. Depending on how fast your weights change, you may want to perform this
update, say, every 100 ms of simulated time, or every 1 s (or even less frequently).
So, the basic strategy is to divide your total simulation time into chunks of, say, 100
ms. You simulate for 100 ms, then you stop simulating and update the weights (using the
code above), and then continue simulating the next chunk.
Please let us know in case you have any remaining questions.
With kind regards,
Charl
On Thu, Jun 4, 2020, at 21:03, Keiko Fujii wrote:
Hello everyone,
I would like to ask how to normalize synaptic weights
during STDP learning.
What I want to do is keeping the total amount of
synaptic weights to/from each neuron constant.
I try to describe my goal a bit more precisely:
i: The index of a pre-synaptic neuron.
j: The index of a post-synaptic neuron.
w_ij(t): The synaptic weight from i-th neuron to j-th
neuron at time=t.
s_i(t): the sum of all incoming synaptic weights to
i-th neuron at time=t. i.e. the sum of w_ij(t) over j.
The goal is to set the sum of incoming weights
(s_i(*)) to 1 by normalization (1 is just for simplicity).
By STDP, we can get updated synaptic weight matrix
w_ij(t+1), and the sum s_i(t+1) is not necessarily 1. So, I want to set
w_ij(t+1) <- w_ij(t+1) / s_i(t+1)
I briefly read the documentation for synaptic
models(https://nest-simulator.readthedocs.io/en/stable/models/synapses.html).
I am not very confident if my understanding is
correct, but it seems that existing synaptic models handle only one synaptic weight.
How can I gather data of all incoming(or outgoing as
well) weights to a neuron and use the summation value inside of the STDP synapse model?
Best regards,
Keiko Fujii
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participants (2)
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Charl Linssen -
Keiko Fujii