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In common ANN, nodes are based on a activation function, like a sigmoid or tanh or ReLU. Updates of synaptic weight are based on the derivative of this function.

When node are represented with spiking neurons, what does activation function become ? how updates of synaptic weight are done ?

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The activation function would be inherent to the spiking model used.

Each model have a different dynamic which will depend on the proper model and parameters used.

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