brainpy.math.surrogate.piecewise_quadratic
brainpy.math.surrogate.piecewise_quadratic#
- brainpy.math.surrogate.piecewise_quadratic = <brainpy._src.math.surrogate._utils.VJPCustom object>#
Judge spiking state with a piecewise quadratic function 1 2 3 4 5.
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:
\[\begin{split}g(x) = \begin{cases} 0, & x < -\frac{1}{\alpha} \\ -\frac{1}{2}\alpha^2|x|x + \alpha x + \frac{1}{2}, & |x| \leq \frac{1}{\alpha} \\ 1, & x > \frac{1}{\alpha} \\ \end{cases}\end{split}\]Backward function:
\[\begin{split}g'(x) = \begin{cases} 0, & |x| > \frac{1}{\alpha} \\ -\alpha^2|x|+\alpha, & |x| \leq \frac{1}{\alpha} \end{cases}\end{split}\]>>> 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.piecewise_quadratic)(xs, alpha) >>> plt.plot(xs, grads, label=r'$\alpha$=' + str(alpha)) >>> plt.legend() >>> plt.show()
(Source code, png, hires.png, pdf)
- Parameters
- Returns
out – The spiking state.
- Return type
jax.Array
References
- 1
Esser S K, Merolla P A, Arthur J V, et al. Convolutional networks for fast, energy-efficient neuromorphic computing[J]. Proceedings of the national academy of sciences, 2016, 113(41): 11441-11446.
- 2
Wu Y, Deng L, Li G, et al. Spatio-temporal backpropagation for training high-performance spiking neural networks[J]. Frontiers in neuroscience, 2018, 12: 331.
- 3
Bellec G, Salaj D, Subramoney A, et al. Long short-term memory and learning-to-learn in networks of spiking neurons[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems. 2018: 795-805.
- 4
Neftci E O, Mostafa H, Zenke F. Surrogate gradient learning in spiking neural networks: Bringing the power of gradient-based optimization to spiking neural networks[J]. IEEE Signal Processing Magazine, 2019, 36(6): 51-63.
- 5
Panda P, Aketi S A, Roy K. Toward scalable, efficient, and accurate deep spiking neural networks with backward residual connections, stochastic softmax, and hybridization[J]. Frontiers in Neuroscience, 2020, 14.
