WongWangStep

WongWangStep#

class brainmass.WongWangStep(in_size, tau_S=Quantity(0.1, 's'), gamma=0.641, a=Quantity(270., 'Hz / nA'), theta=Quantity(0.31, 'nA'), J_N11=Quantity(0.2609, 'nA'), J_N22=Quantity(0.2609, 'nA'), J_N12=Quantity(0.0497, 'nA'), J_N21=Quantity(0.0497, 'nA'), J_A_ext=Quantity(0.0002243, 'nC'), mu_0=Quantity(30., 'Hz'), I_0=Quantity(0.3255, 'nA'), noise_s1=None, noise_s2=None)#

Wong-Wang reduced neural-mass model for perceptual decision-making.

Implements the reduced two-variable model of Wong & Wang (2006). It describes the competitive dynamics between two neural populations (e.g. left- vs right-motion detectors) through slow NMDA-mediated recurrent excitation, capturing the temporal integration of sensory evidence during perceptual decision-making.

Parameters:

  • in_size (int | Sequence[int] | integer | Sequence[integer]) – Shape of the population (number of independent decision units).

  • tau_S (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – NMDA receptor time constant.

  • gamma (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Saturation factor for the synaptic gating variables.

  • a (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Gain of the input-output (f-I) function.

  • theta (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Firing threshold of the input-output function.

  • J_N11 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Self-excitation strength of population 1.

  • J_N22 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Self-excitation strength of population 2.

  • J_N12 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Cross-inhibition strength from population 2 to population 1.

  • J_N21 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Cross-inhibition strength from population 1 to population 2.

  • J_A_ext (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – External input strength (AMPA).

  • mu_0 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Baseline external input rate.

  • I_0 (Callable | Array | ndarray | bool | number | bool | int | float | complex | Quantity | Param) – Background input current.

  • noise_s1 (Noise) – Noise process added to the input current of population 1. None disables noise on that population.

  • noise_s2 (Noise) – Noise process added to the input current of population 2. None disables noise on that population.

Return type:

Any

Notes

The model evolves the synaptic gating variables \(S_1\) and \(S_2\) of the two competing populations:

\[\frac{dS_1}{dt} = -\frac{S_1}{\tau_S} + (1-S_1)\gamma r_1 , \qquad \frac{dS_2}{dt} = -\frac{S_2}{\tau_S} + (1-S_2)\gamma r_2 ,\]

where the firing rates follow the threshold-linear f-I curve

\[\begin{split}r_i = \phi(I_i) = \begin{cases} a(I_i - \theta) & \text{if } I_i > \theta \\ 0 & \text{otherwise} , \end{cases}\end{split}\]

and the total input currents are

\[I_1 = J_{N,11}S_1 - J_{N,12}S_2 + J_{A,ext}\mu_0(1+c) + I_0 + I_{noise,1} ,\]
\[I_2 = J_{N,22}S_2 - J_{N,21}S_1 + J_{A,ext}\mu_0(1-c) + I_0 + I_{noise,2} ,\]

with motion coherence \(c \in [-1, 1]\).

The network exhibits a spontaneous (symmetric) state at \(c = 0\), a decision state in which one population wins for \(|c| > 0\), bistable attractor dynamics, and slow (\(\tau_S = 100\) ms) temporal integration of evidence over hundreds of milliseconds.

References

Examples

>>> import brainmass
>>> import brainstate
>>> import brainunit as u
>>> brainstate.environ.set(dt=0.1 * u.ms)
>>> model = brainmass.WongWangStep(in_size=2)
>>> _ = model.init_all_states()
>>> # one decision-making step with rightward motion coherence c=0.32
>>> r1, r2 = model.update(coherence=0.32)   # population firing rates (Hz)
>>> r1.shape
(2,)
>>> # S1 and S2 synaptic gating are accessible via model.S1.value / model.S2.value
__init__(in_size, tau_S=Quantity(0.1, 's'), gamma=0.641, a=Quantity(270., 'Hz / nA'), theta=Quantity(0.31, 'nA'), J_N11=Quantity(0.2609, 'nA'), J_N22=Quantity(0.2609, 'nA'), J_N12=Quantity(0.0497, 'nA'), J_N21=Quantity(0.0497, 'nA'), J_A_ext=Quantity(0.0002243, 'nC'), mu_0=Quantity(30., 'Hz'), I_0=Quantity(0.3255, 'nA'), noise_s1=None, noise_s2=None)[source]#
Parameters:
compute_inputs(coherence=0.0, noise_1_val=Quantity(0., 'nA'), noise_2_val=Quantity(0., 'nA'))[source]#

Compute the total input currents to both populations.

Parameters:

  • coherence (float, default 0.0) – Motion coherence level, c in [-1, 1].

  • noise_1_val (ArrayLike, default 0. * u.nA) – Noise input added to population 1.

  • noise_2_val (ArrayLike, default 0. * u.nA) – Noise input added to population 2.

Returns:

  • I1 (ArrayLike) – Total input current to population 1.

  • I2 (ArrayLike) – Total input current to population 2.

dS1_dt(S1, r1)[source]#

Differential equation for synaptic gating variable S1.

dS2_dt(S2, r2)[source]#

Differential equation for synaptic gating variable S2.

get_decision(threshold=Quantity(15., 'Hz'))[source]#

Return the current decision based on a firing-rate threshold.

Parameters:

threshold (ArrayLike, default 15. * u.Hz) – Firing-rate threshold a population must exceed to count as the winner.

Returns:

Decision code: 1 if population 1 wins, -1 if population 2 wins, and 0 if undecided.

Return type:

ArrayLike

init_state(batch_size=None, **kwargs)[source]#

Initialize the synaptic gating variables S1 and S2.

phi(I)[source]#

Threshold-linear input-output transfer function (f-I curve).

Parameters:

I (ArrayLike) – Input current (in units of nA).

Returns:

Firing rate (in units of Hz); a * (I - theta) above threshold and 0 otherwise.

Return type:

ArrayLike

update(coherence=0.0)[source]#

Advance the Wong-Wang model by one time step.

Parameters:

coherence (float, default 0.0) – Motion coherence level, c in [-1, 1]. Positive values favour population 1, negative values favour population 2.

Returns:

  • r1 (ArrayLike) – Firing rate of population 1 (in units of Hz).

  • r2 (ArrayLike) – Firing rate of population 2 (in units of Hz).