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使用 NumPy 和 SciPy 创建扩展¶
创建于：2017 年 3 月 24 日 | 最后更新：2023 年 4 月 25 日 | 最后验证：未验证
作者：Adam Paszke
更新者：Adam Dziedzic
在本教程中，我们将完成两个任务
创建一个没有参数的神经网络层。
这调用了 numpy 作为其实现的一部分
创建一个具有可学习权重的神经网络层
这调用了 SciPy 作为其实现的一部分
import torch
from torch.autograd import Function
无参数示例¶
此层并没有特别做任何有用的或数学上正确的事情。
它被恰当地命名为 BadFFTFunction
层实现
from numpy.fft import rfft2, irfft2
class BadFFTFunction(Function):
@staticmethod
def forward(ctx, input):
numpy_input = input.detach().numpy()
result = abs(rfft2(numpy_input))
return input.new(result)
@staticmethod
def backward(ctx, grad_output):
numpy_go = grad_output.numpy()
result = irfft2(numpy_go)
return grad_output.new(result)
# since this layer does not have any parameters, we can
# simply declare this as a function, rather than as an ``nn.Module`` class
def incorrect_fft(input):
return BadFFTFunction.apply(input)
创建层的示例用法
input = torch.randn(8, 8, requires_grad=True)
result = incorrect_fft(input)
print(result)
result.backward(torch.randn(result.size()))
print(input)
tensor([[ 2.1007, 2.6758, 6.1699, 3.5140, 16.9024],
[ 9.2379, 13.8331, 9.7708, 9.5670, 9.6625],
[11.8466, 8.2359, 6.3284, 5.9224, 10.6756],
[ 4.5172, 3.8650, 8.0120, 1.7539, 9.6564],
[ 0.0610, 2.5647, 3.8037, 7.6060, 20.8580],
[ 4.5172, 13.6494, 8.3293, 4.8767, 9.6564],
[11.8466, 4.2204, 8.4846, 8.4208, 10.6756],
[ 9.2379, 12.2773, 3.2013, 2.4911, 9.6625]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[ 1.9269, 1.4873, 0.9007, -2.1055, 0.6784, -1.2345, -0.0431, -1.6047],
[-0.7521, 1.6487, -0.3925, -1.4036, -0.7279, -0.5594, -0.7688, 0.7624],
[ 1.6423, -0.1596, -0.4974, 0.4396, -0.7581, 1.0783, 0.8008, 1.6806],
[ 1.2791, 1.2964, 0.6105, 1.3347, -0.2316, 0.0418, -0.2516, 0.8599],
[-1.3847, -0.8712, -0.2234, 1.7174, 0.3189, -0.4245, 0.3057, -0.7746],
[-1.5576, 0.9956, -0.8798, -0.6011, -1.2742, 2.1228, -1.2347, -0.4879],
[-0.9138, -0.6581, 0.0780, 0.5258, -0.4880, 1.1914, -0.8140, -0.7360],
[-1.4032, 0.0360, -0.0635, 0.6756, -0.0978, 1.8446, -1.1845, 1.3835]],
requires_grad=True)
参数化示例¶
在深度学习文献中，此层容易与卷积混淆，而实际操作是互相关（唯一的区别是卷积的滤波器被翻转，而互相关则不然）。
具有可学习权重的层的实现，其中互相关具有代表权重的滤波器（内核）。
反向传播计算 wrt 输入的梯度和 wrt 滤波器的梯度。
from numpy import flip
import numpy as np
from scipy.signal import convolve2d, correlate2d
from torch.nn.modules.module import Module
from torch.nn.parameter import Parameter
class ScipyConv2dFunction(Function):
@staticmethod
def forward(ctx, input, filter, bias):
# detach so we can cast to NumPy
input, filter, bias = input.detach(), filter.detach(), bias.detach()
result = correlate2d(input.numpy(), filter.numpy(), mode='valid')
result += bias.numpy()
ctx.save_for_backward(input, filter, bias)
return torch.as_tensor(result, dtype=input.dtype)
@staticmethod
def backward(ctx, grad_output):
grad_output = grad_output.detach()
input, filter, bias = ctx.saved_tensors
grad_output = grad_output.numpy()
grad_bias = np.sum(grad_output, keepdims=True)
grad_input = convolve2d(grad_output, filter.numpy(), mode='full')
# the previous line can be expressed equivalently as:
# grad_input = correlate2d(grad_output, flip(flip(filter.numpy(), axis=0), axis=1), mode='full')
grad_filter = correlate2d(input.numpy(), grad_output, mode='valid')
return torch.from_numpy(grad_input), torch.from_numpy(grad_filter).to(torch.float), torch.from_numpy(grad_bias).to(torch.float)
class ScipyConv2d(Module):
def __init__(self, filter_width, filter_height):
super(ScipyConv2d, self).__init__()
self.filter = Parameter(torch.randn(filter_width, filter_height))
self.bias = Parameter(torch.randn(1, 1))
def forward(self, input):
return ScipyConv2dFunction.apply(input, self.filter, self.bias)
示例用法
module = ScipyConv2d(3, 3)
print("Filter and bias: ", list(module.parameters()))
input = torch.randn(10, 10, requires_grad=True)
output = module(input)
print("Output from the convolution: ", output)
output.backward(torch.randn(8, 8))
print("Gradient for the input map: ", input.grad)
Filter and bias: [Parameter containing:
tensor([[ 1.5980, 0.1115, -0.0392],
[ 1.4112, -0.6556, 0.8576],
[-1.6270, -1.3951, -0.2387]], requires_grad=True), Parameter containing:
tensor([[-0.5050]], requires_grad=True)]
Output from the convolution: tensor([[ 2.6490, 0.9049, -2.4603, 4.9172, -2.6995, -0.5259, 0.8084, 2.9712],
[-7.4314, 2.0491, 1.1998, 2.9348, -1.0925, 2.3583, -0.4701, 0.0620],
[ 0.4747, 2.7422, -3.1890, -1.3733, -0.2700, 5.3886, 4.3234, 0.7127],
[ 1.9092, -2.2850, -5.8786, -0.0514, -3.9709, -1.3217, -4.1159, 0.1144],
[-5.2757, -7.3949, 4.8335, -1.4541, -1.7630, -2.9781, -3.6742, 0.6746],
[-1.3930, 1.5531, 1.3611, -5.1453, 1.4953, 0.2460, -2.6832, 0.3069],
[-2.9077, -2.0569, -2.8977, -1.1425, 2.6128, 1.0830, -3.7180, 4.4202],
[-3.3766, -2.4025, -1.3721, 2.2309, -4.1819, -1.2281, -4.5500, 0.4863]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[-1.0954, 0.8242, -2.3188, -2.7640, -2.4841, 0.5890, -0.0936, 1.2190,
0.0921, -0.0307],
[-3.5222, 0.8920, -1.8908, -0.6549, -0.2606, 0.7365, -4.9122, 1.3548,
-0.5405, 0.6700],
[-3.3450, 1.7799, -2.4677, 3.7305, 7.3472, 0.0637, 0.7740, 0.6444,
-2.8296, -0.1736],
[ 2.5613, 7.4243, -4.5369, 2.7349, -3.9802, -1.3710, 5.9015, 0.9176,
1.8604, 0.0468],
[ 5.4830, 1.3442, 3.4260, 5.3385, 0.8872, 3.3689, -2.8774, -1.6875,
-0.2114, -0.0434],
[ 2.6617, -6.2559, -1.9922, -2.9800, -2.8432, -2.9184, -1.1842, 0.9845,
-0.5682, -0.0600],
[ 1.9133, -1.7688, 6.1904, 0.9140, 2.1316, 3.6076, -0.3446, -1.0438,
0.8684, 0.6735],
[-2.4305, -7.8832, -0.8278, -6.6322, -0.5148, 0.2151, -4.0533, -3.7276,
-2.6069, -1.2354],
[-0.4031, -2.5208, 0.9026, -2.6378, -0.1116, -2.9007, 2.9866, 2.7905,
4.0234, -0.5354],
[-0.2927, 3.2093, 3.1423, 2.3881, 2.7282, 1.4053, -1.7006, -0.0692,
1.0831, 0.2345]])
检查梯度
from torch.autograd.gradcheck import gradcheck
moduleConv = ScipyConv2d(3, 3)
input = [torch.randn(20, 20, dtype=torch.double, requires_grad=True)]
test = gradcheck(moduleConv, input, eps=1e-6, atol=1e-4)
print("Are the gradients correct: ", test)
Are the gradients correct: True
脚本总运行时间： ( 0 分钟 0.585 秒)
