Skip to content

Latest commit

 

History

History
211 lines (172 loc) · 7.76 KB

neurons.md

File metadata and controls

211 lines (172 loc) · 7.76 KB
Raw

Neuronal Cells

The neuron (or neuronal cell) represents one of the fundamental building blocks of a biomimetic neural system. These particular objects are meant to perform, per simulated time step, a calculation of output activity values given an internal arrangement of compartments (or sources where signals from other neuronal cell(s) are to be deposited). Typically, a neuron integrates an (ordinary) differential equation, which depends on the type of neuronal cell and dynamics under consideration.

Graded, Real-valued Neurons

This family of neuronal cells adheres to dynamics or performs calculations utilizing graded (real-valued/continuous) values; in other words, they do not produce any discrete signals or action potential values.

The Rate Cell

This cell evolves one set of dynamics over state z (a sort of real-valued continuous membrane potential). The "electrical" inputs that drive it include j (non-modulated signals) and j_td (modulated signals), which can be mapped to bottom-up and top-down pressures (such as those produced by error neurons) if one is building a strictly hierarchical neural model. Note that the "spikes" zF emitted are real-valued for the rate-cell and are represented via the application of a nonlinear activation function (default is the identity) configured by the user.

.. autoclass:: ngclearn.components.RateCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

The Error Cell

This cell is (currently) a stateless neuron, i.e., it is not driven by an underlying differential equation, thus emulating a "fixed-point" error or mismatch calculation. Variations of the fixed-point error cell depend on the local distribution assumed over mismatch activities, e.g., Gaussian distribution yields a Gaussian error cell, which will also change the form of their internal compartments (typically a target, mu, dtarget, and dmu).

Gaussian Error Cell

This cell is (currently) fixed to be a Gaussian cell that assumes an identity covariance. Note that this neuronal cell has several important compartments: in terms of input compartments, target is for placing the desired target activity level while mu is for placing an externally produced mean prediction value, while in terms of output compartments, dtarget is the first derivative with respect to the target (sometimes used to emulate a top-down pressure/expectation in predictive coding) and dmu is the first derivative with respect to the mean parameter.

.. autoclass:: ngclearn.components.GaussianErrorCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

Laplacian Error Cell

This cell is (currently) fixed to be a Laplacian cell that assumes an identity scale. Note that this neuronal cell has several important compartments: in terms of input compartments, target is for placing the desired target activity level while mu is for placing an externally produced mean prediction value, while in terms of output compartments, dtarget is the first derivative with respect to the target (sometimes used to emulate a top-down pressure/expectation in predictive coding) and dmu is the first derivative with respect to the mean parameter.

.. autoclass:: ngclearn.components.LaplacianErrorCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

Spiking Neurons

These neuronal cells exhibit dynamics that involve emission of discrete action potentials (or spikes). Typically, such neurons are modeled with multiple compartments, including at least one for the electrical current j, the membrane potential v, the voltage threshold thr, and action potential s. Note that the interactions or dynamics underlying each component might itself be complex and nonlinear, depending on the neuronal cell simulated (i.e., some neurons might be running multiple differential equations under the hood).

The Simplified LIF (sLIF) Cell

This cell, which is a simplified version of the leaky integrator (i.e., model described later below), models dynamics over voltage v and threshold thr (note that j is further treated as a point-wise current for simplicity). Importantly, an optional fast form of lateral inhibition can be emulated with this cell by setting the inhibitory resistance inhibit_R > 0 -- this will mean that the dynamics over v include a term that is equal to a negative hollow matrix product with the spikes emitted at time t-1 (yielding a recurrent negative pressure on the membrane potential values at t).

.. autoclass:: ngclearn.components.SLIFCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

The LIF (Leaky Integrate-and-Fire) Cell

This cell (the "leaky integrator") models dynamics over the voltage v and threshold shift thrTheta (a homeostatic variable). Note that thr is used as a baseline level for the membrane potential threshold while thrTheta is treated as a form of short-term plasticity (full threshold is: thr + thrTheta(t)).

.. autoclass:: ngclearn.components.LIFCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

The Quadratic LIF (Leaky Integrate-and-Fire) Cell

This cell (the quadratic "leaky integrator") models dynamics over the voltage v and threshold shift thrTheta (a homeostatic variable). Note that thr is used as a baseline level for the membrane potential threshold while thrTheta is treated as a form of short-term plasticity (full threshold is: thr + thrTheta(t)). The dynamics are driven by a critical voltage value as well as a voltage scaling factor for membrane potential accumulation over time.

.. autoclass:: ngclearn.components.QuadLIFCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

The FitzHugh–Nagumo Cell

This cell models dynamics over voltage v and a recover variable w (where w governs the behavior of the action potential of a spiking neuronal cell). In effect, the FitzHugh-Nagumo model is a set of two coupled differential equations that simplify the four differential equation Hodgkin-Huxley (squid axon) model. A voltage v_thr can be used to extract binary spike pulses. (Note that this cell supports either Euler or midpoint method / RK-2 integration.)

.. autoclass:: ngclearn.components.FitzhughNagumoCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex:

The Izhikevich Cell

This cell models dynamics over voltage v and a recover variable w (where w governs the behavior of the action potential of a spiking neuronal cell). In effect, the Izhikevich model is a set of two coupled differential equations that simplify the more complex dynamics of the Hodgkin-Huxley model. Note that this Izhikevich model can be configured to model particular classes of neurons, including regular spiking (RS), intrinsically bursting (IB), chattering (CH), fast spiking (FS), low-threshold spiking (LTS), and resonator (RZ) neurons. (Note that this cell supports either Euler or midpoint method / RK-2 integration.)

.. autoclass:: ngclearn.components.IzhikevichCell
  :noindex:

  .. automethod:: advance_state
    :noindex:
  .. automethod:: verify_connections
    :noindex:
  .. automethod:: reset
    :noindex: