Convolutions for Images

English Version pytorch
1

http://d2l.ai/chapter_convolutional-neural-networks/conv-layer.html

2

Hey @anirudh in section 6.2.4 Learning A Kernel
when printing this at the bottom of our for loop:

if (i+1) % 2 == 0:
print(f'batch {i+1}, loss {l.sum():.3f}')

should it be batch or epoch? I thought it was epoch, could you explain why its batch instead?

1 Like
3
  1. When you try to automatically find the gradient for the Conv2D class we created, what kind of error message do you see?

Got Error Message: Inplace operations are not supported using autograd .

  1. How do you represent a cross-correlation operation as a matrix multiplication by changing the input and kernel tensors?

–> flip the two-dimensional kernel tensor both horizontally and vertically, and then perform the cross-correlation operation with the input tensor

K = torch.tensor([[1.0, -1.0]]) # filter shape: (1, 2)
# flip horizontally
K = torch.flip(K, [1])
# flip vertically
K = torch.flip(K, [0])
print(K)
print(K)

 Y = corr2d(X, K)
 plt.imshow(Y, cmap="gray")

What is the minimum size of a kernel to obtain a derivative of degree d?
–> I have no idea about this. Can someone clarify?

1 Like
4

For Exercise 2, l.sum().backward() is already computing the gradient, is it not?

5

how did you automatically try to find gradient?

6

yes through backpropagation the leaf tensor gradient is stored in net.grad

7

Exercises

  1. Construct an image X with diagonal edges.

    1. What happens if you apply the kernel K in this section to it?

      • zero matrix.

    2. What happens if you transpose X?

      • No change

    3. What happens if you transpose K?

      • zero matrix.

  2. When you try to automatically find the gradient for the Conv2D class we created, what kind

of error message do you see?

* I am able to do `net.weights.grad`, when I try `net.grad` I get the error `'Conv2d' object has no attribute 'grad'`
  1. How do you represent a cross-correlation operation as a matrix multiplication by changing

the input and kernel tensors?

* cross correlation is basically matrix multiplication between slices of tensorfrom X of the shape of kernel and summing.

* It can be done by padding Kand X based on what is needed to multiply

  1. Design some kernels manually.

    1. What is the form of a kernel for the second derivative?

    2. What is the kernel for an integral?

      • how do you actually make it manually

  2. What is the minimum size of a kernel to obtain a derivative of degree d

     * dont know.
8

I think so，epoch is batter than batch.

9

Thanks, @jimmiemunyi @tiger_st for bringing this up. Makes sense to me. Raised a PR for the fix.

10

Construct an image X with diagonal edges.

  1. What happens if you apply the kernel K in this section to it?
    it detects the diagonal edges

  2. What happens if you transpose X ?
    same

  3. What happens if you transpose K ?
    same also

  4. How do you represent a cross-correlation operation as a matrix multiplication by changing the input and kernel tensors?
    transforming the kernal in a matrix
    Km = torch.zeros((9,5))
    kv = torch.tensor([0.0,1.0,0.0,2.0,3.0])
    for i in range(4):
    Km[i:i+5,i] = kv
    Km = Km.t()
    Km = Km[torch.arange(Km.size(0))!=2]
    Km = Km.t()

Km = tensor([[0., 0., 0., 0.],
[1., 0., 0., 0.],
[0., 1., 0., 0.],
[2., 0., 0., 0.],
[3., 2., 1., 0.],
[0., 3., 0., 0.],
[0., 0., 2., 0.],
[0., 0., 3., 0.],
[0., 0., 0., 0.]])

transforming the input X in a vector
X = torch.tensor([[float(i) for i in range(9)]])

X = tensor([[0., 1., 2., 3., 4., 5., 6., 7., 8.]])

X @ Km #matrix multiplication
result : tensor([[19., 25., 37., 0.]])

11

My solutions to the exs: 7.2

1 Like
12

We reprint a key figure in Fig. 7.2.2 to illustrate the striking similarities.

What similarities is Fig. 7.2.2 trying to illustrate? I mean, what is being compared to what?