ginzburg_neuron – Binary stochastic neuron with sigmoidal activation function¶

Description¶

The ginzburg_neuron is an implementation of a binary neuron that is irregularly updated as Poisson time points. At each update point, the total synaptic input h into the neuron is summed up, passed through a gain function g whose output is interpreted as the probability of the neuron to be in the active (1) state.

The gain function g used here is \(g(h) = c_1*h + c_2 * 0.5*(1 + \tanh(c_3*(h-\theta)))\) (output clipped to [0,1]). This allows to obtain affine-linear (\(c_1\neq0, c_2\neq0, c_3=0\)) or sigmoidal (\(c_1=0, c_2=1, c_3\neq0\)) shaped gain functions. The latter choice corresponds to the definition in 1, giving the name to this neuron model. The choice \(c_1=0, c_2=1, c_3=\beta/2\) corresponds to the Glauber dynamics 2, \(g(h) = 1 / (1 + \exp(-\beta (h-\theta)))\). The time constant \(\tau_m\) is defined as the mean inter-update-interval that is drawn from an exponential distribution with this parameter. Using this neuron to reproduce simulations with asynchronous update 1, the time constant needs to be chosen as \(\tau_m = dt*N\), where dt is the simulation time step and N the number of neurons in the original simulation with asynchronous update. This ensures that a neuron is updated on average every \(\tau_m\) ms. Since in the original paper 1 neurons are coupled with zero delay, this implementation follows this definition. It uses the update scheme described in 3 to maintain causality: The incoming events in time step \(t_i\) are taken into account at the beginning of the time step to calculate the gain function and to decide upon a transition. In order to obtain delayed coupling with delay d, the user has to specify the delay d+h upon connection, where h is the simulation time step.

Remarks:

This neuron has a special use for spike events to convey the binary state of the neuron to the target. The neuron model only sends a spike if a transition of its state occurs. If the state makes an up-transition it sends a spike with multiplicity 2, if a down transition occurs, it sends a spike with multiplicity 1. The decoding scheme relies on the feature that spikes with multiplicity larger 1 are delivered consecutively, also in a parallel setting. The creation of double connections between binary neurons will destroy the deconding scheme, as this effectively duplicates every event. Using random connection routines it is therefore advisable to set the property ‘allow_multapses’ to false. The neuron accepts several sources of currents, e.g. from a noise_generator.

Parameters¶

tau_m	ms	Membrane time constant (mean inter-update-interval)
theta	mV	Threshold for sigmoidal activation function
c_1	probability/ mV	Linear gain factor
c_2	probability	Prefactor of sigmoidal gain
c_3	1/mV	Slope factor of sigmoidal gain

References¶

1(1,2,3): Ginzburg I, Sompolinsky H (1994). Theory of correlations in stochastic neural networks. PRE 50(4) p. 3171 DOI: https://doi.org/10.1103/PhysRevE.50.3171
2: Hertz J, Krogh A, Palmer R (1991). Introduction to the theory of neural computation. Addison-Wesley Publishing Conmpany.
3: Morrison A, Diesmann M (2007). Maintaining causality in discrete time neuronal simulations. In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben, Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer. DOI: https://doi.org/10.1007/978-3-540-73159-7_10

Sends¶

SpikeEvent

Receives¶

SpikeEvent, PotentialRequest