如何使用PyTorch优化一个边缘检测器

import torch
import torch.nn as nn

X = torch.tensor([[10,10,10,0,0,0],[10,10,10,0,0,0],[10,10,10,0,0,0],[10,10,10,0,0,0],[10,10,10,0,0,0],[10,10,10,0,0,0]], dtype=float)
Y = torch.tensor([[0,30,30,0],[0,30,30,0],[0,30,30,0],[0,30,30,0]], dtype=float)

conv2d = nn.Conv2d(1,1,kernel_size=(3,3), bias=False, dtype=float)

X = X.reshape((1,1,6,6))
Y = Y.reshape((1,1,4,4))
lr = 0.0005

optim = torch.optim.RMSprop(conv2d.parameters(), lr=lr)
loss_fn = torch.nn.MSELoss()
for i in range(4000):
    Y_pred = conv2d(X)
    loss = loss_fn(Y_pred, Y)
    # 更新参数
    if 0: # 手动更新
        conv2d.zero_grad()
        loss.backward()
        conv2d.weight.data[:] -= lr * conv2d.weight.grad
    if 10: # 使用优化器更新
        optim.zero_grad()
        loss.backward()
        optim.step()
    if(i + 1) % 100 == 0:
        print(f'epoch {i+1}, loss {loss.sum():.4f}')

# 打印训练的参数
print(conv2d.weight.data.reshape(3,3))

输出：

epoch 100, loss 331.4604
epoch 200, loss 284.8803
epoch 300, loss 248.8032
epoch 400, loss 218.8007
epoch 500, loss 193.1186
epoch 600, loss 170.4061
epoch 700, loss 149.4530
epoch 800, loss 129.7580
epoch 900, loss 111.4134
epoch 1000, loss 94.5393
epoch 1100, loss 79.1782
epoch 1200, loss 65.3312
epoch 1300, loss 52.9822
epoch 1400, loss 42.1062
epoch 1500, loss 32.6718
epoch 1600, loss 24.6388
epoch 1700, loss 17.9555
epoch 1800, loss 12.5522
epoch 1900, loss 8.3332
epoch 2000, loss 5.1700
epoch 2100, loss 2.9096
epoch 2200, loss 1.4077
epoch 2300, loss 0.5341
epoch 2400, loss 0.1348
epoch 2500, loss 0.0166
epoch 2600, loss 0.0006
epoch 2700, loss 0.0000
epoch 2800, loss 0.0001
epoch 2900, loss 0.0001
epoch 3000, loss 0.0001
epoch 3100, loss 0.0001
epoch 3200, loss 0.0002
epoch 3300, loss 0.0002
epoch 3400, loss 0.0002
epoch 3500, loss 0.0002
epoch 3600, loss 0.0002
epoch 3700, loss 0.0002
epoch 3800, loss 0.0002
epoch 3900, loss 0.0002
epoch 4000, loss 0.0002
tensor([[ 1.3123, -0.0050, -1.0276],
        [ 0.8334,  0.0677, -0.8868],
        [ 0.8551, -0.0619, -1.0849]], dtype=torch.float64)

由训练出的结果可以看出卷积核参数与实际的卷积核挺接近了。

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