brainpy.math.surrogate.log_tailed_relu#
- brainpy.math.surrogate.log_tailed_relu(x, alpha=0.0)[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()
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Source code,png,hires.png,pdf)
- Parameters:
- Returns:
out – The spiking state.
- Return type:
jax.Array
References
