status: being updated.
The original title is: ‘Neuronal Dynamics, the Basics’ but now that I think of it’s too big a topic to be covered in one article, so I should probably start a series, on neuronal dynamical issues pertaining to SNNs.
This series will only cover relevant issues(that I deem them to be) about SNNs so it’s by no mean comprehensive(something you really shouldn’t expect from a amateur blogger) nor even correct/applicable.
The main ideas are extracted from a great textbook on neuronal dynamics, with some supplement information from several papers. Personal hunches and wild guesses will be marked out.
1 Integrate and Fire Models
A more formal description of IF neuron models should be included in my previous post about SNNs, to avoid redundancy let’s get to the business real quick.
IF models are very simplified regarding the complexity of actual neurons, basically they treat neuron as Shishiodoshi:
- Integration: Synaptic inputs to the neuron are treated as injected current into the neuron. The input current can be arbitrary complex time dependent function, but they are added linearly and integrated.
- Leakiness: If the reservoir does not leak, then it’s vanilla IF model: the neuron doesn’t have memory of the timing of past synaptic inputs. If you drill a hole on the reservoir, then it becomes Leaky-IF model: postsynaptic potential will fade if not repeatedly reinforced by synaptic inputs in a short time frame to reach threshold.
- Refractoriness: A fired neuron will need some time to recover before it can fire another action potential, no matter how big the injected current is.
- Fire: If the accumulated PSP(postsynaptic potential) reached the threshold, it releases an action potential down the axon.
We can already see some problem with this model:
- Linearity is not our friend: Inputs were linearly integrated regardless of presynaptic neurons while synaptic inputs in real neurons exhibit all sorts of non-linear interactions, as we’ll see.
- No adaptation for vanilla LIF: The reset potential and firing threshold is uniform which is inaccurate in real neurons.
- Unrealistic potential reset: Spiking of IF models are Markovian in the sense it doesn’t have memory of previous spikes.
Let’s examine some neuroscientific facts to appreciate the oversimplification of IF models.
2 Neuroscientific Intricacies not Respected by IF models
3 Shunting Inhibition, an Example
4 Not So Bad Afterall?
 2014 – book – Neuronal Dynamics, From Single Neurons to Networks and Models of Cognition – Wulfram Gerstner, et al. – A really good textbook for neuronal dynamics, highly recommended if you’re interested in neuroscientific principles behind thinking brain but not really care about a whole lot mumbo jumbo about anatomy jargons, subsidiary systems and peripheral neural systems which takes most of the space in normal neuroscience textbooks. But if you still insist in getting a better neurosci background please check reference below because I don’t want to be the only one have done this and regret later.
 2016 – book – Neuroscience: Exploring the Brain – Barry W. Connors, et al. – A good neuroscience text book.