ginzburg_neuron – Binary stochastic neuron with sigmoidal activation function
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Description
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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 used here is :math:`g(h) = c_1 h + c_2 (1 +
\tanh(c_3 (h-\theta)))/2` (output clipped to :math:`[0, 1]`). This permits
affine-linear (:math:`c_1\neq0, c_2\neq0, c_3=0`) or sigmoidally shaped
(:math:`c_1=0, c_2=1, c_3\neq0`) gain functions. The latter choice
corresponds to the definition in [1]_, giving the name to this
neuron model.
The choice :math:`c_1=0, c_2=1, c_3=\beta/2` corresponds to the Glauber
dynamics [2]_, :math:`g(h) = 1 / (1 + \exp(-\beta (h-\theta)))`.
The time constant :math:`\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 :math:`\tau_m = dt \times N`, where :math:`dt` is the simulation time
step and :math:`N` the number of neurons in the original simulation with
asynchronous update. This ensures that a neuron is updated on
average every :math:`\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 :math:`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 :math:`d`, the user has to specify the
delay :math:`d+h` upon connection, where :math:`h` is the simulation time step.
Parameters
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====== ============= ===========================================================
tau_m ms Membrane time constant (mean inter-update-interval)
theta mV Threshold for sigmoidal activation function
c_1 probability/ Linear gain factor
mV
c_2 probability Prefactor of sigmoidal gain
c_3 1/mV Slope factor of sigmoidal gain
====== ============= ===========================================================
.. admonition:: Special requirements for binary neurons
As the ``ginzburg_neuron`` is a binary neuron, the user must
ensure that the following requirements are observed. NEST does not
enforce them. Breaching the requirements can lead to meaningless
results.
1. Binary neurons must only be connected to other binary neurons.
#. No more than connection must be created between any pair of
binary neurons. When using probabilistic connection rules, specify
``'allow_autapses': False`` to avoid accidental creation of
multiple connections between a pair of neurons.
#. Binary neurons can be driven by current-injecting devices, but
*not* by spike generators.
#. Activity of binary neurons can only be recored using a ``spin_detector``
or ``correlospinmatrix_detector``.
References
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.. [1] 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
Receives
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CurrentEvent
See also
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:doc:`Neuron `, :doc:`Binary `