brainpy.math.surrogate.inv_square_grad

brainpy.math.surrogate.inv_square_grad(x, alpha=100.0)

Spike function with the inverse-square surrogate gradient.

Forward function:

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

Backward function:

\[g'(x) = \frac{1}{(\alpha * |x| + 1.) ^ 2}\]

>>> import brainpy as bp
>>> import brainpy.math as bm
>>> import matplotlib.pyplot as plt
>>> xs = bm.linspace(-1, 1, 1000)
>>> for alpha in [1., 10., 100.]:
>>>   grads = bm.vector_grad(bm.surrogate.inv_square_grad)(xs, alpha)
>>>   plt.plot(xs, grads, label=r'$\alpha$=' + str(alpha))
>>> plt.legend()
>>> plt.show()

(Source code, png, hires.png, pdf)

Parameters:

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

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

Returns:

out – The spiking state.

Return type:

jax.Array