Creating extensions using numpy and scipy¶
Author: Adam Paszke
In this tutorial, we shall go through two tasks:
Create a neural network layer with no parameters.
- This calls into numpy as part of it’s implementation
Create a neural network layer that has learnable weights
- This calls into SciPy as part of it’s implementation
import torch
from torch.autograd import Function
from torch.autograd import Variable
Parameter-less example¶
This layer doesn’t particularly do anything useful or mathematically correct.
It is aptly named BadFFTFunction
Layer Implementation
from numpy.fft import rfft2, irfft2
class BadFFTFunction(Function):
def forward(self, input):
numpy_input = input.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)
# 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()(input)
Example usage of the created layer:
input = Variable(torch.randn(8, 8), requires_grad=True)
result = incorrect_fft(input)
print(result.data)
result.backward(torch.randn(result.size()))
print(input.grad)
Out:
9.3850 3.7278 12.1252 4.7440 0.1007
8.7267 10.0111 7.8526 3.9947 5.8996
2.2608 6.1943 4.1151 4.2829 1.9711
13.3399 1.4309 3.4576 6.0777 2.9095
2.2723 5.1269 1.0994 6.9922 0.8258
13.3399 11.7054 3.6514 7.9590 2.9095
2.2608 10.0309 1.3558 2.1418 1.9711
8.7267 7.2774 10.2759 6.5953 5.8996
[torch.FloatTensor of size 8x5]
Variable containing:
-0.1448 -0.2484 -0.0526 0.0304 -0.2208 0.0304 -0.0526 -0.2484
-0.0952 0.1012 -0.1489 -0.2706 -0.1588 -0.0548 -0.1102 -0.0034
-0.1208 0.1651 0.0928 -0.0030 -0.1559 -0.1216 0.1992 -0.0146
-0.2294 -0.0393 -0.1855 0.0452 -0.0132 -0.2218 0.2052 0.0554
-0.2641 0.0647 0.0580 0.0371 0.0597 0.0371 0.0580 0.0647
-0.2294 0.0554 0.2052 -0.2218 -0.0132 0.0452 -0.1855 -0.0393
-0.1208 -0.0146 0.1992 -0.1216 -0.1559 -0.0030 0.0928 0.1651
-0.0952 -0.0034 -0.1102 -0.0548 -0.1588 -0.2706 -0.1489 0.1012
[torch.FloatTensor of size 8x8]
Parametrized example¶
This implements a layer with learnable weights.
It implements the Cross-correlation with a learnable kernel.
In deep learning literature, it’s confusingly referred to as Convolution.
The backward computes the gradients wrt the input and gradients wrt the filter.
Implementation:
Please Note that the implementation serves as an illustration, and we did not verify it’s correctness
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):
result = correlate2d(input.numpy(), filter.numpy(), mode='valid')
ctx.save_for_backward(input, filter)
return input.new(result)
@staticmethod
def backward(ctx, grad_output):
input, filter = ctx.saved_tensors
grad_output = grad_output.data
grad_input = convolve2d(grad_output.numpy(), filter.t().numpy(), mode='full')
grad_filter = convolve2d(input.numpy(), grad_output.numpy(), mode='valid')
return Variable(grad_output.new(grad_input)), \
Variable(grad_output.new(grad_filter))
class ScipyConv2d(Module):
def __init__(self, kh, kw):
super(ScipyConv2d, self).__init__()
self.filter = Parameter(torch.randn(kh, kw))
def forward(self, input):
return ScipyConv2dFunction.apply(input, self.filter)
Example usage:
module = ScipyConv2d(3, 3)
print(list(module.parameters()))
input = Variable(torch.randn(10, 10), requires_grad=True)
output = module(input)
print(output)
output.backward(torch.randn(8, 8))
print(input.grad)
Out:
[Parameter containing:
1.0754 -0.8066 0.3304
-1.2231 -0.2035 0.4939
-0.7975 -0.5881 -0.4792
[torch.FloatTensor of size 3x3]
]
Variable containing:
0.7439 0.2808 -0.5860 -2.8316 -0.2953 -3.6276 -0.2887 -2.4730
-0.5076 4.2934 -1.0637 2.4279 -3.4973 1.7451 -1.5061 -0.4581
-1.5620 -2.0292 -0.6322 -0.7476 1.3275 -1.3496 -4.6143 -0.3132
1.1628 0.2356 0.7270 -1.8374 2.3684 -0.8792 1.6460 -3.7633
-1.3106 0.1731 4.7157 1.4189 -0.4938 0.1348 -1.0437 -4.3917
0.0328 3.8527 0.3729 -0.3629 1.0639 -1.6496 -2.5545 -0.6386
1.0335 3.0539 -1.2026 0.1993 -2.2277 0.9936 -1.1667 -3.0316
-0.0735 2.0411 -0.1119 -1.1178 0.9447 -2.3621 1.1529 -0.5529
[torch.FloatTensor of size 8x8]
Variable containing:
-0.8229 0.2347 1.2491 2.3353 -3.1271 0.7935 0.7964 -1.6882 1.0310 0.7973
-0.9049 2.5531 -0.9611 2.5009 1.8931 -1.4156 1.4328 -1.0260 2.3507 2.0734
1.2155 -0.7011 3.0197 0.7824 1.0602 -2.9660 2.6185 1.9948 0.1988 1.8599
-1.6361 1.1401 1.0264 -6.7814 2.7394 -0.2772 -2.1926 2.6752 0.8478 1.3467
2.1865 -1.7675 -3.1038 1.3559 -0.4572 3.3876 -3.6443 1.0721 2.3393 0.6073
-1.1338 -2.0506 3.8598 -0.1274 -0.6803 -1.5970 -1.0469 -1.5129 4.6992 1.8922
1.1923 -0.4203 0.1477 -1.6515 -1.7188 3.3253 1.6627 0.0663 0.5617 0.9708
-2.0164 1.7991 -1.1626 2.6752 -0.2630 0.5074 0.2911 -1.7214 -0.0022 1.3144
1.3249 0.4139 0.8088 1.1148 -0.2780 1.1887 1.0866 1.2730 0.0558 0.2604
-0.4282 -0.6577 0.3834 -0.3729 -0.0176 -0.4416 -0.0738 0.1783 -0.4358 0.3744
[torch.FloatTensor of size 10x10]
Total running time of the script: ( 0 minutes 0.003 seconds)