Ctrl+K

braincore.surrogate.piecewise_exp

Contents

braincore.surrogate.piecewise_exp#

braincore.surrogate.piecewise_exp(x, alpha=1.0)[source]#

Judge spiking state with a piecewise exponential 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:

\[\begin{split}g(x) = \begin{cases} \frac{1}{2}e^{\alpha x}, & x < 0 \\ 1 - \frac{1}{2}e^{-\alpha x}, & x \geq 0 \end{cases}\end{split}\]

Backward function:

\[g'(x) = \frac{\alpha}{2}e^{-\alpha |x|}\]
>>> import braincore as bc
>>> import matplotlib.pyplot as plt
>>> xs = jax.numpy.linspace(-3, 3, 1000)
>>> for alpha in [0.5, 1., 2., 4.]:
>>>   grads = bc.vector_grad(bc.surrogate.piecewise_exp)(xs, alpha)
>>>   plt.plot(xs, grads, label=r'$\alpha$=' + str(alpha))
>>> plt.legend()
>>> plt.show()

(Source code)

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

References

Contents