brainpy.math.surrogate.log_tailed_relu#

brainpy.math.surrogate.log_tailed_relu(x, alpha=0.0, origin=False)[source]#

Judge spiking state with the Log-tailed ReLU 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:

\[\begin{split}\begin{split}g(x) = \begin{cases} \alpha x, & x \leq 0 \\ x, & 0 < x \leq 0 \\ log(x), x > 1 \\ \end{cases}\end{split}\end{split}\]

Backward function:

\[\begin{split}\begin{split}g'(x) = \begin{cases} \alpha, & x \leq 0 \\ 1, & 0 < x \leq 0 \\ \frac{1}{x}, x > 1 \\ \end{cases}\end{split}\end{split}\]
>>> 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)
>>> grads = bm.vector_grad(bm.surrogate.leaky_relu)(xs, 0., 1.)
>>> plt.plot(bm.as_numpy(xs), bm.as_numpy(grads), label=r'$\alpha=0., \beta=1.$')
>>> plt.legend()
>>> plt.show()

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

../../_images/brainpy-math-surrogate-log_tailed_relu-1.png
Parameters:

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

  • alpha (float) – The parameter to control the gradient.

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

Returns:

out – The spiking state.

Return type:

jax.Array

References