brainpy.math.surrogate.nonzero_sign_log#
- brainpy.math.surrogate.nonzero_sign_log(x, alpha=1.0, origin=False)[source]#
Judge spiking state with a nonzero sign log function.
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:
\[g(x) = \mathrm{NonzeroSign}(x) \log (|\alpha x| + 1)\]where
\[\begin{split}\begin{split}\mathrm{NonzeroSign}(x) = \begin{cases} 1, & x \geq 0 \\ -1, & x < 0 \\ \end{cases}\end{split}\end{split}\]Backward function:
\[g'(x) = \frac{\alpha}{1 + |\alpha x|} = \frac{1}{\frac{1}{\alpha} + |x|}\]This surrogate function has the advantage of low computation cost during the backward.
>>> 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 alpha in [0.5, 1., 2., 4.]: >>> grads = bm.vector_grad(bm.surrogate.nonzero_sign_log)(xs, alpha) >>> plt.plot(xs, grads, label=r'$\alpha$=' + str(alpha)) >>> plt.legend() >>> plt.show()
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