spikingjelly.clock_driven.surrogate 源代码

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, eps=1e-5): ''' :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 :param eps: 最大误差 :type eps: float 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 surrogate.check_manual_grad(surrogate.ATan.primitive_function, surrogate.atan.apply) ''' alpha = torch.tensor(1.0, dtype=torch.float) x = torch.arange(-16, 16, 32 / 8192) x.requires_grad_(True) primitive_function(x, alpha).sum().backward() x_grad_auto = x.grad.clone() x.grad.zero_() spiking_function(x, alpha).sum().backward() x_grad_manual = x.grad.clone() assert (x_grad_manual - x_grad_auto).abs().max().item() <= eps, 'x.grad is wrong!' print('grad check pass')
[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] def extra_repr(self): return f'alpha={self.alpha}, spiking={self.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 cuda_code_start_comments(self): return f'// start: spikingjelly.clock_driven.surrogate.{self._get_name()}.cuda_code'
[文档] def cuda_code_end_comments(self): return f'// end: spikingjelly.clock_driven.surrogate.{self._get_name()}.cuda_code'
[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] def cuda_code_start_comments(self): return f'// start: spikingjelly.clock_driven.surrogate.{self._get_name()}.cuda_code'
[文档] def cuda_code_end_comments(self): return f'// end: spikingjelly.clock_driven.surrogate.{self._get_name()}.cuda_code'
[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, 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=1.0, 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')