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braincore.surrogate.multi_gaussian_grad

braincore.surrogate.multi_gaussian_grad#

braincore.surrogate.multi_gaussian_grad(x, h=0.15, s=6.0, sigma=0.5, scale=0.5)[source]#

Spike function with the multi-Gaussian gradient function [1].

The forward function:

\[\begin{split}g(x) = \begin{cases} 1, & x \geq 0 \\ 0, & x < 0 \\ \end{cases}\end{split}\]

Backward function:

\[\begin{array}{l} g'(x)=(1+h){{{\mathcal{N}}}}(x, 0, {\sigma }^{2}) -h{{{\mathcal{N}}}}(x, \sigma,{(s\sigma )}^{2})- h{{{\mathcal{N}}}}(x, -\sigma ,{(s\sigma )}^{2}) \end{array}\]
>>> import braincore as bc
>>> import matplotlib.pyplot as plt
>>> xs = jax.numpy.linspace(-3, 3, 1000)
>>> grads = bc.vector_grad(bc.surrogate.multi_gaussian_grad)(xs)
>>> plt.plot(xs, grads)
>>> plt.show()

(Source code)

Parameters:

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

  • h (float) – The hyper-parameters of approximate function

  • s (float) – The hyper-parameters of approximate function

  • sigma (float) – The gaussian sigma.

  • scale (float) – The gradient scale.

Returns:

out – The spiking state.

Return type:

jax.Array

References

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