import torch
import torch.nn as nn
import torch.nn.functional as F
import math
tab4_str = '\t\t\t\t' # used for aligning code
curly_bracket_l = '{'
curly_bracket_r = '}'
[文档]def heaviside(x: torch.Tensor):
'''
* :ref:`API in English <heaviside.__init__-en>`
.. _heaviside.__init__-cn:
:param x: 输入tensor
:return: 输出tensor
heaviside阶跃函数，定义为
.. math::
g(x) =
\\begin{cases}
1, & x \\geq 0 \\\\
0, & x < 0 \\\\
\\end{cases}
阅读 `HeavisideStepFunction <https://mathworld.wolfram.com/HeavisideStepFunction.html>`_ 以获得更多信息。
* :ref:`中文API <heaviside.__init__-cn>`
.. _heaviside.__init__-en:
:param x: the input tensor
:return: the output tensor
The heaviside function, which is defined by
.. math::
g(x) =
\\begin{cases}
1, & x \\geq 0 \\\\
0, & x < 0 \\\\
\\end{cases}
For more information, see `HeavisideStepFunction <https://mathworld.wolfram.com/HeavisideStepFunction.html>`_.
'''
return (x >= 0).to(x)
[文档]def check_manual_grad(primitive_function, spiking_function, *args, **kwargs):
'''
:param primitive_function: 梯度替代函数的原函数
:type primitive_function: callable
:param spiking_function: 梯度替代函数
:type spiking_function: callable
梯度替代函数的反向传播一般是手写的，可以用此函数去检查手写梯度是否正确。
此函数检查梯度替代函数spiking_function的反向传播，与原函数primitive_function的反向传播结果是否一致。“一致”被定义为，两者的误差不超过eps。
示例代码：
.. code-block:: python
def s2nn_apply(x, alpha, beta):
return surrogate.s2nn.apply(x, alpha, beta)
surrogate.check_manual_grad(surrogate.S2NN.primitive_function, s2nn_apply, alpha=4., beta=1.)
'''
x = torch.arange(-2, 2, 32 / 8192)
# x = torch.as_tensor([-1., 0., 1.])
x.requires_grad_(True)
primitive_function(x, *args, **kwargs).sum().backward()
x_grad_auto = x.grad.clone()
x.grad.zero_()
spiking_function(x, *args, **kwargs).sum().backward()
x_grad_manual = x.grad.clone()
print('auto grad', x_grad_auto)
print('manual grad', x_grad_manual)
abs_error = (x_grad_manual - x_grad_auto).abs()
idx = abs_error.argmax()
print('max error', abs_error[idx], 'occurs at')
print(f'x[{idx}] = {x[idx]}')
print('auto grad', x_grad_auto[idx])
print('manual grad', x_grad_manual[idx])
[文档]def check_cuda_grad(neu: nn.Module, surrogate_function, device, *args, **kwargs):
# check_cuda_grad(neuron.MultiStepIFNode, surrogate.S2NN, device='cuda:1', alpha=4., beta=1.)
for dtype in [torch.float, torch.half]:
print(dtype)
net = neu(surrogate_function=surrogate_function(*args, **kwargs))
net.to(device)
x = torch.arange(-2, 2, 32 / 8192, device=device, dtype=dtype)
x = x.unsqueeze(-1)
x.requires_grad_(True)
net.backend = 'torch'
net(x).sum().backward()
x_grad_py = x.grad.clone()
x.grad.zero_()
net.reset()
net.backend = 'cupy'
net(x).sum().backward()
x_grad_cp = x.grad.clone()
# print('python grad', x_grad_py)
# print('cupy grad', x_grad_cp)
abs_error = (x_grad_cp - x_grad_py).abs()
idx = abs_error.argmax()
print('max error', abs_error[idx], 'occurs at')
print(f'x[{idx}] = {x[idx]}')
print('python grad', x_grad_py[idx])
print('cupy grad', x_grad_cp[idx])
[文档]class SurrogateFunctionBase(nn.Module):
def __init__(self, alpha, spiking=True):
super().__init__()
self.spiking = spiking
self.alpha = alpha
[文档] def set_spiking_mode(self, spiking: bool):
self.spiking = spiking
[文档] @staticmethod
def spiking_function(x, alpha):
raise NotImplementedError
[文档] @staticmethod
def primitive_function(x, alpha):
raise NotImplementedError
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
raise NotImplementedError
[文档] def forward(self, x: torch.Tensor):
if self.spiking:
return self.spiking_function(x, self.alpha)
else:
return self.primitive_function(x, self.alpha)
[文档]class MultiArgsSurrogateFunctionBase(nn.Module):
def __init__(self, spiking: bool, *args, **kwargs):
super().__init__()
self.spiking = spiking
[文档] def set_spiking_mode(self, spiking: bool):
self.spiking = spiking
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
raise NotImplementedError
[文档]class piecewise_quadratic(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
x_abs = ctx.saved_tensors[0].abs()
mask = (x_abs > (1 / ctx.alpha))
grad_x = (grad_output * (- (ctx.alpha ** 2) * x_abs + ctx.alpha)).masked_fill_(mask, 0)
return grad_x, None
[文档]class PiecewiseQuadratic(SurrogateFunctionBase):
def __init__(self, alpha=1.0, spiking=True):
'''
* :ref:`API in English <PiecewiseQuadratic.__init__-en>`
.. _PiecewiseQuadratic.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
反向传播时使用分段二次函数的梯度（三角形函数）的脉冲发放函数。反向传播为
.. math::
g'(x) =
\\begin{cases}
0, & |x| > \\frac{1}{\\alpha} \\\\
-\\alpha^2|x|+\\alpha, & |x| \\leq \\frac{1}{\\alpha}
\\end{cases}
对应的原函数为
.. math::
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}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseQuadratic.*
:width: 100%
该函数在文章 [#esser2016convolutional]_ [#STBP]_ [#LSNN]_ [#neftci2019surrogate]_ [#panda2020toward]_ 中使用。
* :ref:`中文API <PiecewiseQuadratic.__init__-cn>`
.. _PiecewiseQuadratic.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The piecewise quadratic surrogate spiking function. The gradient is defined by
.. math::
g'(x) =
\\begin{cases}
0, & |x| > \\frac{1}{\\alpha} \\\\
-\\alpha^2|x|+\\alpha, & |x| \\leq \\frac{1}{\\alpha}
\\end{cases}
The primitive function is defined by
.. math::
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}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseQuadratic.*
:width: 100%
The function is used in [#esser2016convolutional]_ [#STBP]_ [#LSNN]_ [#neftci2019surrogate]_ [#panda2020toward]_.
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return piecewise_quadratic.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
mask0 = (x > (1.0 / alpha)).to(x)
mask1 = (x.abs() <= (1.0 / alpha)).to(x)
return mask0 + mask1 * (-(alpha ** 2) / 2 * x.square() * x.sign() + alpha * x + 0.5)
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.PiecewiseQuadratic(alpha=1.5, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=1.5$')
# surrogate_function = surrogate.PiecewiseQuadratic(alpha=1.5, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=1.5$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('Piecewise quadratic surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class piecewise_exp(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
grad_x = ctx.alpha / 2 * (- ctx.alpha * ctx.saved_tensors[0].abs()).exp_() * grad_output
return grad_x, None
[文档]class PiecewiseExp(SurrogateFunctionBase):
def __init__(self, alpha=1.0, spiking=True):
'''
* :ref:`API in English <PiecewiseExp.__init__-en>`
.. _PiecewiseExp.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
反向传播时使用分段指数函数的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\frac{\\alpha}{2}e^{-\\alpha |x|}
对应的原函数为
.. math::
g(x) =
\\begin{cases}
\\frac{1}{2}e^{\\alpha x}, & x < 0 \\\\
1 - \\frac{1}{2}e^{-\\alpha x}, & x \\geq 0
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseExp.*
:width: 100%
该函数在文章 [#SLAYER]_ [#neftci2019surrogate]_ 中使用。
* :ref:`中文API <PiecewiseExp.__init__-cn>`
.. _PiecewiseExp.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The piecewise exponential surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\frac{\\alpha}{2}e^{-\\alpha |x|}
The primitive function is defined by
.. math::
g(x) =
\\begin{cases}
\\frac{1}{2}e^{\\alpha x}, & x < 0 \\\\
1 - \\frac{1}{2}e^{-\\alpha x}, & x \\geq 0
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseExp.*
:width: 100%
The function is used in [#SLAYER]_ [#neftci2019surrogate]_ .
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return piecewise_exp.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
mask_nonnegative = heaviside(x)
mask_sign = mask_nonnegative * 2 - 1
exp_x = (mask_sign * x * -alpha).exp_() / 2
return mask_nonnegative - exp_x * mask_sign
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.PiecewiseExp(alpha=2, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=2$')
# surrogate_function = surrogate.PiecewiseExp(alpha=2, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=2$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('Piecewise exponential surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class sigmoid(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
sgax = (ctx.saved_tensors[0] * ctx.alpha).sigmoid_()
grad_x = grad_output * (1. - sgax) * sgax * ctx.alpha
return grad_x, None
[文档]class Sigmoid(SurrogateFunctionBase):
def __init__(self, alpha=4.0, spiking=True):
'''
* :ref:`API in English <Sigmoid.__init__-en>`
.. _Sigmoid.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
反向传播时使用sigmoid的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\alpha * (1 - \\mathrm{sigmoid} (\\alpha x)) \\mathrm{sigmoid} (\\alpha x)
对应的原函数为
.. math::
g(x) = \\mathrm{sigmoid}(\\alpha x) = \\frac{1}{1+e^{-\\alpha x}}
.. image:: ./_static/API/clock_driven/surrogate/Sigmoid.*
:width: 100%
该函数在文章 [#STBP]_ [#roy2019scaling]_ [#SNNLSTM]_ [#SNU]_ 中使用。
* :ref:`中文API <Sigmoid.__init__-cn>`
.. _Sigmoid.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The sigmoid surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\alpha * (1 - \\mathrm{sigmoid} (\\alpha x)) \\mathrm{sigmoid} (\\alpha x)
The primitive function is defined by
.. math::
g(x) = \\mathrm{sigmoid}(\\alpha x) = \\frac{1}{1+e^{-\\alpha x}}
.. image:: ./_static/API/clock_driven/surrogate/Sigmoid.*
:width: 100%
The function is used in [#STBP]_ [#roy2019scaling]_ [#SNNLSTM]_ [#SNU]_ .
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return sigmoid.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
return (x * alpha).sigmoid()
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
alpha = str(self.alpha) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
code += f'''
{tab4_str}const float {sg_name}_sigmoid_ax = 1.0f / (1.0f + expf(- {alpha} * {x}));
{tab4_str}const float {y} = (1.0f - {sg_name}_sigmoid_ax) * {sg_name}_sigmoid_ax * {alpha};
'''
elif dtype == 'fp16':
code += f'''
{tab4_str}const half2 {sg_name}_alpha = __float2half2_rn({alpha});
{tab4_str}const half2 {sg_name}_sigmoid_ax = __h2div(__float2half2_rn(1.0f), __hadd2(h2exp(__hneg2(__hmul2({sg_name}_alpha, {x}))), __float2half2_rn(1.0f)));
{tab4_str}const half2 {y} = __hmul2(__hmul2(__hsub2(__float2half2_rn(1.0f), {sg_name}_sigmoid_ax), {sg_name}_sigmoid_ax), {sg_name}_alpha);
'''
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.Sigmoid(alpha=5, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=5$')
# surrogate_function = surrogate.Sigmoid(alpha=5, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=5$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('Sigmoid surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class soft_sign(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
grad_x = grad_output / (2 * ctx.alpha * (1 / ctx.alpha + ctx.saved_tensors[0].abs()).pow_(2))
return grad_x, None
[文档]class SoftSign(SurrogateFunctionBase):
def __init__(self, alpha=2.0, spiking=True):
'''
* :ref:`API in English <SoftSign.__init__-en>`
.. _SoftSign.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
反向传播时使用soft sign的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\frac{\\alpha}{2(1 + |\\alpha x|)^{2}} = \\frac{1}{2\\alpha(\\frac{1}{\\alpha} + |x|)^{2}}
对应的原函数为
.. math::
g(x) = \\frac{1}{2} (\\frac{\\alpha x}{1 + |\\alpha x|} + 1)
= \\frac{1}{2} (\\frac{x}{\\frac{1}{\\alpha} + |x|} + 1)
.. image:: ./_static/API/clock_driven/surrogate/SoftSign.*
:width: 100%
该函数在文章 [#SuperSpike]_ [#neftci2019surrogate]_ 中使用。
* :ref:`中文API <SoftSign.__init__-cn>`
.. _SoftSign.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The soft sign surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\frac{\\alpha}{2(1 + |\\alpha x|)^{2}}
The primitive function is defined by
.. math::
g(x) = \\frac{1}{2} (\\frac{\\alpha x}{1 + |\\alpha x|} + 1)
.. image:: ./_static/API/clock_driven/surrogate/SoftSign.*
:width: 100%
The function is used in [#SuperSpike]_ [#neftci2019surrogate]_ .
'''
super().__init__(alpha, spiking)
assert alpha > 0, 'alpha must be lager than 0'
[文档] @staticmethod
def spiking_function(x, alpha):
return soft_sign.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
return (F.softsign(x * alpha) + 1) / 2
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.SoftSign(alpha=3, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=3$')
# surrogate_function = surrogate.SoftSign(alpha=3, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=3$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('SoftSign surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class atan(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
grad_x = ctx.alpha / 2 / (1 + (math.pi / 2 * ctx.alpha * ctx.saved_tensors[0]).pow_(2)) * grad_output
return grad_x, None
[文档]class ATan(SurrogateFunctionBase):
def __init__(self, alpha=2.0, spiking=True):
'''
* :ref:`API in English <ATan.__init__-en>`
.. _ATan.__init__-cn:
反向传播时使用反正切函数arc tangent的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\frac{\\alpha}{2(1 + (\\frac{\\pi}{2}\\alpha x)^2)}
对应的原函数为
.. math::
g(x) = \\frac{1}{\\pi} \\arctan(\\frac{\\pi}{2}\\alpha x) + \\frac{1}{2}
.. image:: ./_static/API/clock_driven/surrogate/ATan.*
:width: 100%
* :ref:`中文API <ATan.__init__-cn>`
.. _ATan.__init__-en:
The arc tangent surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\frac{\\alpha}{2(1 + (\\frac{\\pi}{2}\\alpha x)^2)}
The primitive function is defined by
.. math::
g(x) = \\frac{1}{\\pi} \\arctan(\\frac{\\pi}{2}\\alpha x) + \\frac{1}{2}
.. image:: ./_static/API/clock_driven/surrogate/ATan.*
:width: 100%
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return atan.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
return (math.pi / 2 * alpha * x).atan_() / math.pi + 0.5
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
alpha = str(self.alpha) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
code += f'''
{tab4_str}const float {sg_name}_M_PI_2__alpha__x = ((float) 1.57079632679489661923) * {alpha} * {x};
{tab4_str}const float {y} = {alpha} / 2.0f / (1.0f + {sg_name}_M_PI_2__alpha__x * {sg_name}_M_PI_2__alpha__x);
'''
elif dtype == 'fp16':
code += f'''
{tab4_str}const half2 {sg_name}_alpha = __float2half2_rn({alpha});
{tab4_str}const half2 {sg_name}_M_PI_2__alpha__x = __hmul2(__hmul2(__float2half2_rn((float) 1.57079632679489661923), {sg_name}_alpha), {x});
{tab4_str}const half2 {y} = __h2div(__h2div({sg_name}_alpha, __float2half2_rn(2.0f)), __hfma2({sg_name}_M_PI_2__alpha__x, {sg_name}_M_PI_2__alpha__x, __float2half2_rn(1.0f)));
'''
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.ATan(alpha=3, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=3$')
# surrogate_function = surrogate.ATan(alpha=3, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=3$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('ATan surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class nonzero_sign_log_abs(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
grad_x = grad_output / (1 / ctx.alpha + ctx.saved_tensors[0].abs())
return grad_x, None
[文档]class NonzeroSignLogAbs(SurrogateFunctionBase):
def __init__(self, alpha=1.0, spiking=True):
'''
* :ref:`API in English <LogAbs.__init__-en>`
.. _LogAbs.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
.. warning::
原函数的输出范围并不是(0, 1)。它的优势是反向传播的计算量特别小。
反向传播时使用NonzeroSignLogAbs的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\frac{\\alpha}{1 + |\\alpha x|} = \\frac{1}{\\frac{1}{\\alpha} + |x|}
对应的原函数为
.. math::
g(x) = \\mathrm{NonzeroSign}(x) \\log (|\\alpha x| + 1)
其中
.. math::
\\mathrm{NonzeroSign}(x) =
\\begin{cases}
1, & x \\geq 0 \\\\
-1, & x < 0 \\\\
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/NonzeroSignLogAbs.*
:width: 100%
该函数在文章 中使用。
* :ref:`中文API <LogAbs.__init__-cn>`
.. _LogAbs.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
.. admonition:: Warning
:class: warning
The output range the primitive function is not (0, 1). The advantage of this function is that computation
cost is small when backward.
The NonzeroSignLogAbs surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\frac{\\alpha}{1 + |\\alpha x|} = \\frac{1}{\\frac{1}{\\alpha} + |x|}
The primitive function is defined by
.. math::
g(x) = \\mathrm{NonzeroSign}(x) \\log (|\\alpha x| + 1)
where
.. math::
\\mathrm{NonzeroSign}(x) =
\\begin{cases}
1, & x \\geq 0 \\\\
-1, & x < 0 \\\\
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/NonzeroSignLogAbs.*
:width: 100%
The function is used in .
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return nonzero_sign_log_abs.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
# the gradient of ``(heaviside(x) * 2 - 1) * (alpha * x.abs() + 1).log()`` by autograd is wrong at ``x==0``
mask_p = heaviside(x) * 2 - 1
return mask_p * (alpha * mask_p * x + 1).log()
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.NonzeroSignLogAbs(alpha=1, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=1$')
# surrogate_function = surrogate.NonzeroSignLogAbs(alpha=1, spiking=False)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=1$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('NonzeroSignLogAbs surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class erf(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
grad_x = grad_output * (- (ctx.saved_tensors[0] * ctx.alpha).pow_(2)).exp_() * (ctx.alpha / math.sqrt(math.pi))
return grad_x, None
[文档]class Erf(SurrogateFunctionBase):
def __init__(self, alpha=2.0, spiking=True):
'''
* :ref:`API in English <Erf.__init__-en>`
.. _Erf.__init__-cn:
:param alpha: 控制反向传播时梯度的平滑程度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
反向传播时使用高斯误差函数(erf)的梯度的脉冲发放函数。反向传播为
.. math::
g'(x) = \\frac{\\alpha}{\\sqrt{\pi}}e^{-\\alpha^2x^2}
对应的原函数为
.. math::
:nowrap:
\\begin{split}
g(x) &= \\frac{1}{2}(1-\\text{erf}(-\\alpha x)) \\\\
&= \\frac{1}{2} \\text{erfc}(-\\alpha x) \\\\
&= \\frac{1}{\\sqrt{\\pi}}\int_{-\\infty}^{\\alpha x}e^{-t^2}dt
\\end{split}
.. image:: ./_static/API/clock_driven/surrogate/Erf.*
:width: 100%
该函数在文章 [#esser2015backpropagation]_ [#STBP]_ [#SRNN]_ 中使用。
* :ref:`中文API <Erf.__init__-cn>`
.. _Erf.__init__-en:
:param alpha: parameter to control smoothness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The Gaussian error (erf) surrogate spiking function. The gradient is defined by
.. math::
g'(x) = \\frac{\\alpha}{\\sqrt{\pi}}e^{-\\alpha^2x^2}
The primitive function is defined by
.. math::
:nowrap:
\\begin{split}
g(x) &= \\frac{1}{2}(1-\\text{erf}(-\\alpha x)) \\\\
&= \\frac{1}{2} \\text{erfc}(-\\alpha x) \\\\
&= \\frac{1}{\\sqrt{\\pi}}\int_{-\\infty}^{\\alpha x}e^{-t^2}dt
\\end{split}
.. image:: ./_static/API/clock_driven/surrogate/Erf.*
:width: 100%
The function is used in [#esser2015backpropagation]_ [#STBP]_ [#SRNN]_.
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return erf.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
return torch.erfc_(-alpha * x) / 2
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.Erf(alpha=2, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=2$')
# surrogate_function = surrogate.Erf(alpha=2, spiking=False)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=2$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('Gaussian error surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class piecewise_leaky_relu(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x: torch.Tensor, w=1, c=0.01):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.w = w
ctx.c = c
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
if ctx.needs_input_grad[0]:
mask_width = (ctx.saved_tensors[0].abs() < ctx.w)
mask_c = mask_width.logical_not()
grad_x = grad_output * ctx.saved_tensors[0].masked_fill(mask_width, 1 / ctx.w).masked_fill(mask_c, ctx.c)
return grad_x, None, None
[文档]class PiecewiseLeakyReLU(MultiArgsSurrogateFunctionBase):
def __init__(self, w=1., c=0.01, spiking=True):
'''
* :ref:`API in English <PiecewiseLeakyReLU.__init__-en>`
.. _PiecewiseLeakyReLU.__init__-cn:
:param w: ``-w <= x <= w`` 时反向传播的梯度为 ``1 / 2w``
:param c: ``x > w`` 或 ``x < -w`` 时反向传播的梯度为 ``c``
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
分段线性的近似脉冲发放函数。梯度为
.. math::
g'(x) =
\\begin{cases}
\\frac{1}{w}, & -w \\leq x \\leq w \\\\
c, & x < -w ~or~ x > w
\\end{cases}
对应的原函数为
.. math::
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}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseLeakyReLU.*
:width: 100%
该函数在文章 [#yin2017algorithm]_ [#STBP]_ [#huh2018gradient]_ [#wu2019direct]_ [#STCA]_ [#roy2019scaling]_ [#LISNN]_ [#DECOLLE]_ 中使用。
* :ref:`中文API <PiecewiseLeakyReLU.__init__-cn>`
.. _PiecewiseLeakyReLU.__init__-en:
:param w: when ``-w <= x <= w`` the gradient is ``1 / 2w``
:param c: when ``x > w`` or ``x < -w`` the gradient is ``c``
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The piecewise surrogate spiking function. The gradient is defined by
.. math::
g'(x) =
\\begin{cases}
\\frac{1}{w}, & -w \\leq x \\leq w \\\\
c, & x < -w ~or~ x > w
\\end{cases}
The primitive function is defined by
.. math::
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}
.. image:: ./_static/API/clock_driven/surrogate/PiecewiseLeakyReLU.*
:width: 100%
The function is used in [#yin2017algorithm]_ [#STBP]_ [#huh2018gradient]_ [#wu2019direct]_ [#STCA]_ [#roy2019scaling]_ [#LISNN]_ [#DECOLLE]_.
'''
super().__init__(spiking)
assert w > 0.
self.w = w
self.c = c
self.spiking = spiking
if spiking:
self.f = self.spiking_function
else:
self.f = self.primitive_function
[文档] def forward(self, x):
return self.f(x, self.w, self.c)
[文档] @staticmethod
def spiking_function(x: torch.Tensor, w, c):
return piecewise_leaky_relu.apply(x, w, c)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, w, c):
mask0 = (x < -w).to(x)
mask1 = (x > w).to(x)
mask2 = torch.ones_like(x.data) - mask0 - mask1
if c == 0:
return mask2 * (x / (2 * w) + 1 / 2) + mask1
else:
cw = c * w
return mask0 * (c * x + cw) + mask1 * (c * x + (- cw + 1)) \
+ mask2 * (x / (2 * w) + 1 / 2)
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
w = str(self.w) + 'f'
w_inv = str(1. / self.w) + 'f'
c = str(self.c) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
code += f'''
{tab4_str}const float {sg_name}_x_abs = fabsf({x});
float {y};
if ({sg_name}_x_abs > {w})
{curly_bracket_l}
{y} = {c};
{curly_bracket_r}
else
{curly_bracket_l}
{y} = {w_inv};
{curly_bracket_r}
'''
elif dtype == 'fp16':
code += f'''
{tab4_str}const half2 {sg_name}_x_abs = __habs2({x});
{tab4_str}const half2 {sg_name}_x_abs_ge_w = __hge2({sg_name}_x_abs, __float2half2_rn({w}));
{tab4_str}half2 {y} = __hadd2(__hmul2(__float2half2_rn({c}), {sg_name}_x_abs_ge_w), __hmul2(__hsub2(__float2half2_rn(1.0f), {sg_name}_x_abs_ge_w), __float2half2_rn({w_inv})));
'''
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200)
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.PiecewiseLeakyReLU(w=1, c=0.1, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $w=1, c=0.1$')
# surrogate_function = surrogate.PiecewiseLeakyReLU(w=1, c=0.1, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $w=1, c=0.1$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('PiecewiseLeakyReLU surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# plt.show()
[文档]class squarewave_fourier_series(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x: torch.Tensor, n: int, T_period: float):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.n = n
ctx.T_period = T_period
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = 0.
x = ctx.saved_tensors[0]
w = math.pi * 2. / ctx.T_period
for i in range(1, ctx.n):
grad_x += torch.cos_((2 * i - 1.) * w * x)
grad_x *= 4. / ctx.T_period
grad_x *= grad_output
return grad_x, None, None
[文档]class SquarewaveFourierSeries(MultiArgsSurrogateFunctionBase):
def __init__(self, n: int = 2, T_period: float = 8, spiking=True):
super().__init__(spiking)
assert isinstance(n, int) and T_period > 0.
self.n = n
self.T_period = T_period
self.spiking = spiking
if spiking:
self.f = self.spiking_function
else:
self.f = self.primitive_function
[文档] def forward(self, x):
return self.f(x, self.n, self.T_period)
[文档] @staticmethod
def spiking_function(x: torch.Tensor, w, c):
return squarewave_fourier_series.apply(x, w, c)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, n: int, T_period: float):
w = math.pi * 2. / T_period
ret = torch.zeros_like(x.data)
for i in range(1, n):
c = (2 * i - 1.)
ret += torch.sin(c * w * x) / c
return 0.5 + 2. / math.pi * ret
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
w = str(self.w) + 'f'
w_inv = str(1. / self.w) + 'f'
c = str(self.c) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
raise NotImplementedError
elif dtype == 'fp16':
raise NotImplementedError
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# import torch
# from spikingjelly.clock_driven import surrogate
# from matplotlib import pyplot as plt
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200, figsize=(6, 4))
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
#
# c_list = []
# for n in [2, 4, 8]:
# surrogate_function = surrogate.SquarewaveFourierSeries(n=n, T_period=8, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label=f'Primitive, $n={n}$')
# c_list.append(plt.gca().lines[-1].get_color())
#
# plt.xlim(-2, 2)
# plt.legend()
# plt.title(f'SquarewaveFourierSeries surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# # plt.grid(linestyle='--')
# plt.savefig('./docs/source/_static/API/clock_driven/surrogate/SquarewaveFourierSeries1.pdf')
# plt.savefig('./docs/source/_static/API/clock_driven/surrogate/SquarewaveFourierSeries1.svg')
# plt.clf()
# for i, n in enumerate([2, 4, 8]):
# surrogate_function = surrogate.SquarewaveFourierSeries(n=n, T_period=8, spiking=True)
# x = x.detach()
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label=f'Gradient, $n={n}$', c=c_list[i])
# x.grad.zero_()
#
# plt.xlim(-2, 2)
# plt.legend()
# plt.title(f'SquarewaveFourierSeries surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# # plt.grid(linestyle='--')
# plt.savefig('./docs/source/_static/API/clock_driven/surrogate/SquarewaveFourierSeries2.pdf')
# plt.savefig('./docs/source/_static/API/clock_driven/surrogate/SquarewaveFourierSeries2.svg')
[文档]class s2nn(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x: torch.Tensor, alpha: float, beta: float):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
ctx.beta = beta
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
x = ctx.saved_tensors[0]
sgax = torch.sigmoid(ctx.alpha * x)
grad_x = torch.where(x < 0., ctx.alpha * sgax * (1. - sgax), ctx.beta / (x + 1.))
return grad_x * grad_output, None, None
[文档]class S2NN(MultiArgsSurrogateFunctionBase):
def __init__(self, alpha=4., beta=1., spiking=True):
"""
* :ref:`API in English <S2NN.__init__-en>`
.. _S2NN.__init__-cn:
:param alpha: 控制 ``x < 0`` 时梯度的参数
:param beta: 控制 ``x >= 0`` 时梯度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
`S2NN: Time Step Reduction of Spiking Surrogate Gradients for Training Energy Efficient Single-Step Neural Networks <https://arxiv.org/abs/2201.10879>`_ 提出的S2NN替代函数。反向传播为
.. math::
g'(x) = \\begin{cases}
\\alpha * (1 - \\mathrm{sigmoid} (\\alpha x)) \\mathrm{sigmoid} (\\alpha x), x < 0 \\\\
\\beta (x + 1), x \ge 0
\\end{cases}
对应的原函数为
.. math::
g(x) = \\begin{cases}
\\mathrm{sigmoid} (\\alpha x), x < 0 \\\\
\\beta \\mathrm{ln}(x + 1) + 1, x \ge 0
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/S2NN.*
:width: 100%
* :ref:`中文API <S2NN.__init__-cn>`
.. _S2NN.__init__-en:
:param alpha: the param that controls the gradient when ``x < 0``
:param beta: the param that controls the gradient when ``x >= 0``
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The S2NN surrogate spiking function, which is proposed by `S2NN: Time Step Reduction of Spiking Surrogate Gradients for Training Energy Efficient Single-Step Neural Networks <https://arxiv.org/abs/2201.10879>`_. The gradient is defined by
.. math::
g'(x) = \\begin{cases}
\\alpha * (1 - \\mathrm{sigmoid} (\\alpha x)) \\mathrm{sigmoid} (\\alpha x), x < 0 \\\\
\\beta (x + 1), x \ge 0
\\end{cases}
The primitive function is defined by
.. math::
g(x) = \\begin{cases}
\\mathrm{sigmoid} (\\alpha x), x < 0 \\\\
\\beta \\mathrm{ln}(x + 1) + 1, x \ge 0
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/S2NN.*
:width: 100%
"""
super().__init__(spiking)
self.alpha = alpha
self.beta = beta
self.spiking = spiking
if spiking:
self.f = self.spiking_function
else:
self.f = self.primitive_function
[文档] def forward(self, x):
return self.f(x, self.alpha, self.beta)
[文档] @staticmethod
def spiking_function(x: torch.Tensor, alpha, beta):
return s2nn.apply(x, alpha, beta)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha, beta):
return torch.where(x < 0., torch.sigmoid(x * alpha), beta * torch.log((x + 1.).abs_() + 1e-5) + 0.5)
# abs and 1e-5 are used to avoid nan
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
alpha = str(self.alpha) + 'f'
beta = str(self.beta) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
code += f'''
{tab4_str}const float {sg_name}_sigmoid_ax = 1.0f / (1.0f + expf(- {alpha} * {x}));
{tab4_str}const float {sg_name}_mask_l = (float)({x} < 0.0f);
{tab4_str}const float {y} = (1.0f - {sg_name}_sigmoid_ax) * {sg_name}_sigmoid_ax * {alpha} * {sg_name}_mask_l + {beta} / ({x} + 1.0f) * (1.0f - {sg_name}_mask_l);
'''
elif dtype == 'fp16':
code += f'''
{tab4_str}const half2 {sg_name}_alpha = __float2half2_rn({alpha});
{tab4_str}const half2 {sg_name}_sigmoid_ax = __h2div(__float2half2_rn(1.0f), __hadd2(h2exp(__hneg2(__hmul2({sg_name}_alpha, {x}))), __float2half2_rn(1.0f)));
{tab4_str}const half2 {sg_name}_mask_l = __hlt2({x}, __float2half2_rn(0.0f));
{tab4_str}const half2 {y} = __hadd2(__hmul2(__hmul2(__hmul2(__hsub2(__float2half2_rn(1.0f), {sg_name}_sigmoid_ax), {sg_name}_sigmoid_ax), {sg_name}_alpha), {sg_name}_mask_l), __hmul2(__h2div(__float2half2_rn({beta}), __hadd2({x}, __float2half2_rn(1.0f))), __hsub2(__float2half2_rn(1.0f), {sg_name}_mask_l)));
'''
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200, figsize=(6, 4))
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.S2NN(alpha=4., beta=1., spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=4, \\beta=1$')
#
# surrogate_function = surrogate.S2NN(alpha=4, beta=1., spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=4, \\beta=1$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('S2NN surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# # plt.show()
# plt.savefig('./S2NN.svg')
# plt.savefig('./S2NN.pdf')
[文档]class q_pseudo_spike(torch.autograd.Function):
[文档] @staticmethod
def forward(ctx, x, alpha):
if x.requires_grad:
ctx.save_for_backward(x)
ctx.alpha = alpha
return heaviside(x)
[文档] @staticmethod
def backward(ctx, grad_output):
grad_x = None
x = ctx.saved_tensors[0]
if ctx.needs_input_grad[0]:
grad_x = ((1 + 2 / (ctx.alpha - 1) * x.abs()).pow_(-ctx.alpha)) * grad_output
return grad_x, None
[文档]class QPseudoSpike(SurrogateFunctionBase):
def __init__(self, alpha=2.0, spiking=True):
'''
* :ref:`API in English <QPseudoSpike.__init__-en>`
.. _QPseudoSpike.__init__-cn:
:param alpha: 控制反向传播时梯度函数尾部厚度的参数
:param spiking: 是否输出脉冲，默认为 ``True``，在前向传播时使用 ``heaviside`` 而在反向传播使用替代梯度。若为 ``False``
则不使用替代梯度，前向传播时，使用反向传播时的梯度替代函数对应的原函数
`Surrogate Gradients Design <https://arxiv.org/abs/2202.00282>`_ 提出的 :math:`q`-PseudoSpike替代函数。反向传播为
.. math::
g'(x) = (1+\\frac{2|x|}{\\alpha-1})^{-\\alpha}
其中 :math:`\\alpha>1` 对应原文中的 :math:`q`。
对应的原函数为
.. math::
g(x) =
\\begin{cases}
\\frac{1}{2}(1-\\frac{2x}{\\alpha-1})^{1-\\alpha}, & x < 0 \\\\
1 - \\frac{1}{2}(1+\\frac{2x}{\\alpha-1})^{1-\\alpha}, & x \\geq 0.
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/QPseudoSpike.*
:width: 100%
* :ref:`中文API <QPseudoSpike.__init__-cn>`
.. _QPseudoSpike.__init__-en:
:param alpha: parameter to control tail fatness of gradient
:param spiking: whether output spikes. The default is ``True`` which means that using ``heaviside`` in forward
propagation and using surrogate gradient in backward propagation. If ``False``, in forward propagation,
using the primitive function of the surrogate gradient function used in backward propagation
The :math:`q`-PseudoSpike surrogate spiking function, which is first proposed in `Surrogate Gradients Design <https://arxiv.org/abs/2202.00282>`_. The gradient is defined by
.. math::
g'(x) = (1+\\frac{2|x|}{\\alpha-1})^{-\\alpha}
where :math:`\\alpha>1` corresponds to :math:`q` in paper.
The primitive function is defined by
.. math::
g(x) =
\\begin{cases}
\\frac{1}{2}(1-\\frac{2x}{\\alpha-1})^{1-\\alpha}, & x < 0 \\\\
1 - \\frac{1}{2}(1+\\frac{2x}{\\alpha-1})^{1-\\alpha}, & x \\geq 0.
\\end{cases}
.. image:: ./_static/API/clock_driven/surrogate/QPseudoSpike.*
:width: 100%
'''
super().__init__(alpha, spiking)
[文档] @staticmethod
def spiking_function(x, alpha):
return q_pseudo_spike.apply(x, alpha)
[文档] @staticmethod
def primitive_function(x: torch.Tensor, alpha):
mask_nonnegative = heaviside(x)
mask_sign = mask_nonnegative * 2. - 1.
return mask_nonnegative - mask_sign * (0.5 * ((1. + 2. / (alpha - 1.) * x * mask_sign).pow_(1. - alpha)))
[文档] def cuda_code(self, x: str, y: str, dtype='fp32'):
sg_name = 'sg_' + self._get_name()
alpha = str(self.alpha) + 'f'
code = f'''
{tab4_str}{self.cuda_code_start_comments()}
'''
if dtype == 'fp32':
code += f'''
{tab4_str}const float {sg_name}_base = 1.0f + 2.0f / ({alpha} - 1.0f) * fabsf({x});
{tab4_str}const float {y} = powf({sg_name}_base, -{alpha});
'''
elif dtype == 'fp16':
code += f'''
{tab4_str}const half2 {sg_name}_alpha = __float2half2_rn({alpha});
{tab4_str}const half2 {sg_name}_base = __hadd2(__float2half2_rn(1.0f), __h2div(__hmul2(__float2half2_rn(2.0f), __habs2({x})), __hsub2({sg_name}_alpha, __float2half2_rn(1.0f))));
{tab4_str}const half2 {y} = h2exp2(__hmul2(h2log2({sg_name}_base), __hneg2({sg_name}_alpha))); // Replace power with combination of log and exp, since CUDA has no power function for FP16.
'''
else:
raise NotImplementedError
code += f'''
{tab4_str}{self.cuda_code_end_comments()}
'''
return code
# plt.style.use(['science', 'muted', 'grid'])
# fig = plt.figure(dpi=200, figsize=(6, 4))
# x = torch.arange(-2.5, 2.5, 0.001)
# plt.plot(x.data, surrogate.heaviside(x), label='Heaviside', linestyle='-.')
# surrogate_function = surrogate.QPseudoSpike(alpha=2, spiking=False)
# y = surrogate_function(x)
# plt.plot(x.data, y.data, label='Primitive, $\\alpha=2$')
# surrogate_function = surrogate.QPseudoSpike(alpha=2, spiking=True)
# x.requires_grad_(True)
# y = surrogate_function(x)
# z = y.sum()
# z.backward()
# plt.plot(x.data, x.grad, label='Gradient, $\\alpha=2$')
# plt.xlim(-2, 2)
# plt.legend()
# plt.title('QPseudoSpike surrogate function')
# plt.xlabel('Input')
# plt.ylabel('Output')
# plt.grid(linestyle='--')
# # plt.savefig('QPseudoSpike.svg')
# # plt.savefig('QPseudoSpike.pdf')
_has_cuda_ = [
ATan,
Sigmoid,
PiecewiseLeakyReLU,
S2NN,
QPseudoSpike
]