Neural Networks: Spiking Neural Networks
8 important questions on Neural Networks: Spiking Neural Networks
What are the 3 generations of neural networks that Maass (1997) identifies?
- Networks based on McCulloch-Pitts neurons.
- Networks based on neurons with continuous activation function.
- Networks based on spiking neurons.
What is the biological inspiration for spiking neural networks?
- neurons have a firing rate.
- Activation level of second generation represents firing rate.
- It can however not explain fast cortical computations.
- More evidence has been found that the timing of action potentials is used to encode information.
How does the spiking neural network work?
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What are the basics of a general spiking neural network?
v fires once its potential P is above threshold Theta.
P is the sum of excitatory and inhibitory postsynaptic potentials (EPSP/ISPS) from connected neurons u.
How much u which fired at time s contributes at time t depends on:
- w ≥ 0, the weight between u and v.
- epsilon(t-s), the response function.
Why two response functions and not just negative weights?
This is caused by the biological plausibility. neurons do not change from inhibitory to excitatory and vice versa.
Does the Threshold Θ stay constant?
- Neurons do not fire for a few msec after they have fired at t' (absolute refractory period).
- After this period, neurons are more reluctant to fire (i.e. require a higher P).
- Select an appropriate threshold function.
What is the full formalisation of the spiking neural?
- Let V be a finite set of spiking neurons
- Let E ⊆ V x V be the set of synapses, where each synapse <u,v> ∈ E has a
Weight w ≥ 0
Response function ε: R+ → R
- For every v ∈ V
- Let F ⊆ R+ be the set of firing times of neuron u
What are some properties of spiking neural networks?
- Spiking NNs can simulate arbitrary feed forward sigmoidal neural networks.
- Hence, can approximate any continuous function.
- Spiking neurons are computationally more powerful than neurons with sigmoidal activation functions.
- Biologically more plausible.
- Can act as reservoir in the reservoir computing approaches.
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