brainpy.math.surrogate.piecewise_leaky_relu

brainpy.math.surrogate.piecewise_leaky_relu(x, c=0.01, w=1.0)

Judge spiking state with a piecewise leaky relu function [1] [2] [3] [4] [5] [6] [7] [8].

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:

\[\begin{split}\begin{split}g(x) = \begin{cases} cx + cw, & x < -w \\ \frac{1}{2w}x + \frac{1}{2}, & -w \leq x \leq w \\ cx - cw + 1, & x > w \\ \end{cases}\end{split}\end{split}\]

Backward function:

\[\begin{split}\begin{split}g'(x) = \begin{cases} \frac{1}{w}, & |x| \leq w \\ c, & |x| > w \end{cases}\end{split}\end{split}\]

>>> 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 c in [0.01, 0.05, 0.1]:
>>>   for w in [1., 2.]:
>>>     grads1 = bm.vector_grad(bm.surrogate.piecewise_leaky_relu)(xs, c=c, w=w)
>>>     plt.plot(bm.as_numpy(xs), bm.as_numpy(grads1), label=f'x={c}, w={w}')
>>> plt.legend()
>>> plt.show()

(Source code, png, hires.png, pdf)

Parameters:

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

• c (float) – When \(|x| > w\) the gradient is c.

• w (float) – When \(|x| <= w\) the gradient is 1 / w.

Returns:

out – The spiking state.

Return type:

jax.Array

References

[1]

Yin S, Venkataramanaiah S K, Chen G K, et al. Algorithm and hardware design of discrete-time spiking neural networks based on back propagation with binary activations[C]//2017 IEEE Biomedical Circuits and Systems Conference (BioCAS). IEEE, 2017: 1-5.

[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]

Huh D, Sejnowski T J. Gradient descent for spiking neural networks[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems. 2018: 1440-1450.

[4]

Wu Y, Deng L, Li G, et al. Direct training for spiking neural networks: Faster, larger, better[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2019, 33(01): 1311-1318.

[5]

Gu P, Xiao R, Pan G, et al. STCA: Spatio-Temporal Credit Assignment with Delayed Feedback in Deep Spiking Neural Networks[C]//IJCAI. 2019: 1366-1372.

[6]

Roy D, Chakraborty I, Roy K. Scaling deep spiking neural networks with binary stochastic activations[C]//2019 IEEE International Conference on Cognitive Computing (ICCC). IEEE, 2019: 50-58.

[7]

Cheng X, Hao Y, Xu J, et al. LISNN: Improving Spiking Neural Networks with Lateral Interactions for Robust Object Recognition[C]//IJCAI. 1519-1525.

[8]

Kaiser J, Mostafa H, Neftci E. Synaptic plasticity dynamics for deep continuous local learning (DECOLLE)[J]. Frontiers in Neuroscience, 2020, 14: 424.