brainpy.rates.QIF

class brainpy.rates.QIF(size, keep_size=False, tau=1.0, eta=-5.0, delta=1.0, J=15.0, x_ou_mean=0.0, x_ou_sigma=0.0, x_ou_tau=5.0, y_ou_mean=0.0, y_ou_sigma=0.0, y_ou_tau=5.0, x_initializer=Uniform(min_val=0, max_val=0.05, rng=[ 575320324 2599701768]), y_initializer=Uniform(min_val=0, max_val=0.05, rng=[ 575320324 2599701768]), method='exp_auto', name=None, input_var=True, mode=None)

A mean-field model of a quadratic integrate-and-fire neuron population.

Model Descriptions

The QIF population mean-field model, which has been derived from a population of all-to-all coupled QIF neurons in [5]. The model equations are given by:

\[\begin{split}\begin{aligned} \tau \dot{r} &=\frac{\Delta}{\pi \tau}+2 r v \\ \tau \dot{v} &=v^{2}+\bar{\eta}+I(t)+J r \tau-(\pi r \tau)^{2} \end{aligned}\end{split}\]

where \(r\) is the average firing rate and \(v\) is the average membrane potential of the QIF population [5].

This mean-field model is an exact representation of the macroscopic firing rate and membrane potential dynamics of a spiking neural network consisting of QIF neurons with Lorentzian distributed background excitabilities. While the mean-field derivation is mathematically only valid for all-to-all coupled populations of infinite size, it has been shown that there is a close correspondence between the mean-field model and neural populations with sparse coupling and population sizes of a few thousand neurons [6].

Model Parameters

Parameter	Init Value	Unit	Explanation
tau	1	ms	the population time constant
eta	-5.		the mean of a Lorenzian distribution over the neural excitability in the population
delta	1.0		the half-width at half maximum of the Lorenzian distribution over the neural excitability
J	15		the strength of the recurrent coupling inside the population

Parameters:

• x_ou_mean (Parameter) – The noise mean of the \(x\) variable, [mV/ms]

• y_ou_mean (Parameter) – The noise mean of the \(y\) variable, [mV/ms].

• x_ou_sigma (Parameter) – The noise intensity of the \(x\) variable, [mV/ms/sqrt(ms)].

• y_ou_sigma (Parameter) – The noise intensity of the \(y\) variable, [mV/ms/sqrt(ms)].

• x_ou_tau (Parameter) – The timescale of the Ornstein-Uhlenbeck noise process of \(x\) variable, [ms].

• y_ou_tau (Parameter) – The timescale of the Ornstein-Uhlenbeck noise process of \(y\) variable, [ms].

References

[5] (1,2)

E. Montbrió, D. Pazó, A. Roxin (2015) Macroscopic description for networks of spiking neurons. Physical Review X, 5:021028, https://doi.org/10.1103/PhysRevX.5.021028.

[6]

R. Gast, H. Schmidt, T.R. Knösche (2020) A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation. Neural Computation 32.9 (2020): 1615-1634.

__init__(size, keep_size=False, tau=1.0, eta=-5.0, delta=1.0, J=15.0, x_ou_mean=0.0, x_ou_sigma=0.0, x_ou_tau=5.0, y_ou_mean=0.0, y_ou_sigma=0.0, y_ou_tau=5.0, x_initializer=Uniform(min_val=0, max_val=0.05, rng=[ 575320324 2599701768]), y_initializer=Uniform(min_val=0, max_val=0.05, rng=[ 575320324 2599701768]), method='exp_auto', name=None, input_var=True, mode=None)

Methods

__init__(size[, keep_size, tau, eta, delta, ...])
clear_input()	Function to clear inputs in the neuron group.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
dx(x, t, y, x_ext)
dy(y, t, x, y_ext)
get_batch_shape([batch_size])
get_delay_data(identifier, delay_step, *indices)	Get delay data according to the provided delay steps.
load_state_dict(state_dict[, warn, compatible])	Copy parameters and buffers from state_dict into this module and its descendants.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
reset(*args, **kwargs)	Reset function which reset the whole variables in the model.
reset_local_delays([nodes])	Reset local delay variables.
reset_state([batch_size])	Reset function which reset the states in the model.
save_states(filename[, variables])	Save the model states.
state_dict()	Returns a dictionary containing a whole state of the module.
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	Unflatten the data to construct an object of this class.
unique_name([name, type_])	Get the unique name for this object.
update([x1, x2])	The function to specify the updating rule.
update_local_delays([nodes])	Update local delay variables.
vars([method, level, include_self, ...])	Collect all variables in this node and the children nodes.

Attributes

global_delay_data	Global delay data, which stores the delay variables and corresponding delay targets.
mode	Mode of the model, which is useful to control the multiple behaviors of the model.
name	Name of the model.
varshape	The shape of variables in the neuron group.