官方教程链接: CREATING EXTENSIONS USING NUMPY AND SCIPY
该教程主要有两个任务：
- 使用 NumPy 实现无参数的网络
- 使用 SciPy 实现有参数的网络
使用 NumPy 实现无参数的网络
下面使用的这层网络没有做任何有用的或者数学上正确的计算，所以被称为 BadFFTFunction。
# layer implementation
from numpy.fft import rfft2, irfft2
class BadFFTFunction(Function):
def forward(self, input):
numpy_input = input.detach().numpy()
result = abs(rfft2(numpy_input))
return input.new(result)
def backward(self, grad_output):
numpy_go = grad_output.numpy()
result = irfft2(numpy_go)
return grad_output.new(result)
因为这一层没有任何参数，我们可以简单地将其声明为一个函数，而不是 nn.Module 类。
def incorrect_fft(input):
return BadFFTFunction()(input)
下面是使用该网络层的例子：
inputs = torch.randn(8, 8, requires_grad=True)
result = incorrect_fft(inputs)
print(result)
result.backward(torch.randn(result.size()))
print(inputs)
-------------------------------------------------------------------------
tensor([[ 3.5953, 2.3891, 2.8538, 6.3056, 7.1890],
[ 6.0135, 10.8107, 4.2032, 9.4689, 10.2098],
[ 4.6084, 4.5200, 7.8461, 5.3306, 16.6947],
[ 1.1328, 3.6691, 5.6570, 10.1536, 1.2553],
[ 4.9080, 3.0635, 4.9613, 5.5422, 10.7650],
[ 1.1328, 10.7622, 11.3006, 12.5434, 1.2553],
[ 4.6084, 9.3826, 6.1878, 3.6052, 16.6947],
[ 6.0135, 2.6298, 4.7681, 0.3978, 10.2098]],
grad_fn=<BadFFTFunction>)
tensor([[ 1.8835, 0.4974, -1.0209, 0.1234, 0.3349, -2.1377, 0.1967, -1.2438],
[-0.6187, -1.3692, 1.9919, -0.6665, -0.4790, -1.1658, -1.0086, 0.0427],
[-0.9035, 0.5733, -1.9797, 0.3805, -0.4385, 1.7815, 0.2453, 0.3710],
[-0.5477, 0.9553, -0.7232, -0.9086, -0.7948, 0.9149, 0.4236, -0.2123],
[-1.4582, -0.9862, 0.6265, -0.5989, 0.7842, 0.7988, -0.3591, 0.8035],
[-0.1081, 0.4932, -0.2232, 0.5371, 0.7379, -0.5363, -0.6724, -0.0632],
[-1.7535, 2.3054, 0.0435, 1.2096, -0.0145, 0.5476, -0.3470, 0.3916],
[-0.5269, -0.5503, 0.2355, -0.2890, 0.0305, -0.4156, 1.0513, 0.2139]],
requires_grad=True)
使用 SciPy 实现有参数的网络
在深度学习文献中，这一层被混淆地称为卷积，而实际操作是 cross-correlation (唯一的区别是卷积时会翻转滤波器，而 cross-correlation 不翻转)。
cross-correction 也有一个表示权值的 filter (kernel)，该层也是一个具有可学习权值的层。其反向传播会计算相对于输入的梯度和相对于 filter 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 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)
使用类来实现该层网络的操作：
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)
下面是使用该网络层的例子：
module = ScipyConv2d(3, 3)
print("Filter and bais: ", 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 bais: [Parameter containing:
tensor([[ 1.0172, -0.7830, -1.9644],
[-1.7501, -0.3380, 1.0851],
[-0.6086, 0.5211, -0.1384]], requires_grad=True), Parameter containing:
tensor([[0.8491]], requires_grad=True)]
Output from the convolution: tensor([[-3.3643, -1.6414, 3.8635, 5.7214, 4.2812, -0.1469, 2.2956, 4.6972],
[ 1.0405, 5.4137, -0.2289, 3.7867, -0.8485, 1.0467, 5.0971, 0.6170],
[ 0.3865, 7.9669, 4.7172, -5.9195, 2.6202, 4.1359, -1.2188, 4.6258],
[-4.0765, -1.9985, 3.0376, 3.7519, 4.8408, -0.5378, 0.9233, 2.9950],
[ 7.2145, -0.1482, 1.9535, 2.1877, -0.5471, 6.3192, 6.6404, 4.5604],
[ 2.6525, 1.4568, 8.2622, 2.1857, -4.5970, -0.7388, -1.2843, 3.0592],
[ 3.2907, 4.0466, -2.7943, -2.3269, -0.5543, 7.4176, 2.9281, 0.6315],
[ 5.6153, 1.4405, -8.2649, -3.6808, 7.4088, 4.8308, 0.6125, 0.2748]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[ 8.4448e-01, -4.6131e-01, -1.2356e+00, -2.3001e-01, -2.7439e+00,
-9.6755e-01, 3.9761e+00, 3.8412e-01, -1.0720e+00, 1.3304e+00],
[-2.0427e+00, 5.0312e-01, -1.3896e-01, -9.8333e-01, 3.3517e+00,
1.8381e+00, -2.5191e+00, -1.6409e+00, 5.2481e-01, -4.0503e-01],
[-3.4304e-03, 9.7143e-01, 8.0939e-01, -2.3209e+00, -2.4818e+00,
-2.2358e+00, 3.3594e-01, 9.6761e-01, -8.7727e-01, 1.7346e+00],
[ 1.2670e+00, -3.0389e+00, -1.3391e+00, 1.4903e-01, 1.7144e+00,
-2.2407e-01, 5.4215e-01, 2.1312e+00, -2.2236e+00, -2.2285e+00],
[ 6.0892e-01, -1.5455e+00, 3.4901e+00, -3.1687e+00, -3.5638e+00,
5.3970e+00, -4.1608e+00, -7.5911e-01, 5.0879e+00, 2.5559e+00],
[ 4.9064e-01, 3.2317e+00, -6.9631e+00, -4.6371e+00, 4.4206e+00,
-6.6388e-02, 1.6657e+00, 8.6398e-01, -4.3631e+00, -6.9194e-01],
[-1.7784e+00, -1.9765e+00, -5.0315e+00, 3.8658e+00, 1.1239e+00,
-3.7742e+00, -2.5467e+00, -1.1219e+00, -3.4360e-01, 1.1228e+00],
[ 4.4786e-01, -4.6717e+00, -5.5782e-01, -1.5868e-01, -8.8934e+00,
2.3656e+00, 2.7402e+00, 4.5009e+00, 2.4637e+00, -1.5834e+00],
[-3.2312e+00, -1.3407e+00, 2.0052e-01, -1.1472e-02, 4.3446e+00,
3.0356e+00, -1.3052e+00, -7.6964e-01, -1.5648e+00, 6.0754e-01],
[-1.0473e+00, 8.7615e-01, -1.1456e+00, 1.1731e+00, 5.9753e-01,
-1.8710e-01, 1.7740e-01, -5.7756e-01, 3.6896e-01, -6.6725e-02]])
最后进行一下梯度校验：
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
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