# brainpy.math.surrogate.sigmoid#

brainpy.math.surrogate.sigmoid = <brainpy._src.math.surrogate._utils.VJPCustom object>#

Spike function with the sigmoid-shaped surrogate gradient.

If origin=False, return 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:

$g(x) = \mathrm{sigmoid}(\alpha x) = \frac{1}{1+e^{-\alpha x}}$

Backward function:

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

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

• alpha (float) – Parameter to control smoothness of gradient

• origin (bool) – Whether to compute the original function as the feedfoward output.

Returns:

out – The spiking state.

Return type:

jax.Array