Comment by scheme271
Neurons don't just work on electrical potentials, they also have a multiple whole systems of neurotransmitters that affect their operation. So I don't think their activation is a continuous function. Although I suppose we could use non-continuous functions for activations in a NN, I don't think there's an easy way to train a NN that does that.
Sure, a real neuron activates by outputting a train of spikes after some input threshold has been crossed (a complex matter of synapse operation - not just a summation of inputs), while in ANNs we use "continuous" activation functions like ReLU... But note that the output of a ReLu, while continuous, is basically on or off, equivalent to a real neuron having crossed it's activation threshold or not.
If you really wanted to train artificial spiking neural networks in biologically plausible fashion then you'd first need to discover/guess what that learning algorithm is, which is something that has escaped us so far. Hebbian "fire together, wire together" may be part of it, but we certainly don't have the full picture.
OTOH, it's not yet apparent whether an ANN design that more closely follows real neurons has any benefit in terms of overall function, although an async dataflow design would be a lot more efficient in terms of power usage.