# brainpy.math.surrogate.q_pseudo_spike#

brainpy.math.surrogate.q_pseudo_spike(x, alpha=2.0)[source]#

Judge spiking state with the q-PseudoSpike surrogate function [1].

If origin=False, computes the forward function:

$\begin{split}g(x) = \begin{cases} 1, & x \geq 0 \\ 0, & x < 0 \\ \end{cases}\end{split}$

If origin=True, computes the original function:

$\begin{split}\begin{split}g(x) = \begin{cases} \frac{1}{2}(1-\frac{2x}{\alpha-1})^{1-\alpha}, & x < 0 \\ 1 - \frac{1}{2}(1+\frac{2x}{\alpha-1})^{1-\alpha}, & x \geq 0. \end{cases}\end{split}\end{split}$

Backward function:

$g'(x) = (1+\frac{2|x|}{\alpha-1})^{-\alpha}$
>>> import brainpy as bp
>>> import brainpy.math as bm
>>> import matplotlib.pyplot as plt
>>> xs = bm.linspace(-3, 3, 1000)
>>> bp.visualize.get_figure(1, 1, 4, 6)
>>> for alpha in [0.5, 1., 2., 4.]:
>>>   plt.plot(bm.as_numpy(xs), bm.as_numpy(grads), label=r'$\alpha=$' + str(alpha))
>>> plt.legend()
>>> plt.show()

Parameters:
• x (jax.Array, Array) – The input data.

• alpha (float) – The parameter to control tail fatness of gradient.

Returns:

out – The spiking state.

Return type:

jax.Array

References