# brainpy.math.surrogate.piecewise_leaky_relu#

brainpy.math.surrogate.piecewise_leaky_relu(x, c=0.01, w=1.0)[source]#

Judge spiking state with a piecewise leaky relu function [1] [2] [3] [4] [5] [6] [7] [8].

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:

$\begin{split}\begin{split}g(x) = \begin{cases} cx + cw, & x < -w \\ \frac{1}{2w}x + \frac{1}{2}, & -w \leq x \leq w \\ cx - cw + 1, & x > w \\ \end{cases}\end{split}\end{split}$

Backward function:

$\begin{split}\begin{split}g'(x) = \begin{cases} \frac{1}{w}, & |x| \leq w \\ c, & |x| > w \end{cases}\end{split}\end{split}$
>>> 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(-3, 3, 1000)
>>> for c in [0.01, 0.05, 0.1]:
>>>   for w in [1., 2.]:
>>> plt.legend()
>>> plt.show()

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

• c (float) – When $$|x| > w$$ the gradient is c.

• w (float) – When $$|x| <= w$$ the gradient is 1 / w.

Returns:

out – The spiking state.

Return type:

jax.Array

References