對於神經網絡（火炬）中的每一層，應該有多少偏差？

Question

我在pytorch中有一個簡單的模型。

model = Network()

詳細信息是：

Network(
  (hidden): Linear(in_features=784, out_features=256, bias=True)
  (output): Linear(in_features=256, out_features=10, bias=True)
  (sigmoid): Sigmoid()
  (softmax): Softmax(dim=1)
)

總共有3個神經元層。 1個輸入（786個神經元），1個隱藏（256個神經元）和1個輸出（10個神經元）。 因此，將有兩個重量層。 所以兩個權重層都必須有兩個偏差（僅兩個浮點數），對嗎？ （糾正我，如果我錯了）。

現在，在初始化我的網絡后，我對這兩個偏差值感到好奇。 所以我想檢查隱藏層的偏差值，所以我寫道：

model.hidden.bias

結果是我沒有想到的！ 我實際上期望一個值！ 這就是我真正得到的：

tensor([-1.6868e-02, -3.5661e-02,  1.2489e-02, -2.7880e-02,  1.4025e-02,
        -2.6085e-02,  1.2625e-02, -3.1748e-02,  5.0335e-03,  3.8031e-03,
        -3.1648e-02, -3.4881e-02, -2.0026e-02,  1.9728e-02,  6.2461e-03,
         9.3936e-04, -5.9270e-03, -2.7183e-02, -1.9850e-02, -3.5693e-02,
        -1.9393e-02,  2.6555e-02,  2.3482e-02,  2.1230e-02, -2.2175e-02,
        -2.4386e-02,  3.4848e-02, -2.6044e-02,  1.3575e-02,  9.4125e-03,
         3.0012e-02, -2.6078e-02,  7.1615e-05, -1.7061e-02,  6.6355e-03,
        -3.4966e-02,  2.9311e-02,  1.4060e-02, -2.5763e-02, -1.4020e-02,
         2.9852e-02, -7.9176e-03, -1.8396e-02,  1.6927e-02, -1.1001e-03,
         1.5595e-02,  1.2169e-02, -1.2275e-02, -2.9270e-03, -6.5685e-04,
        -2.4297e-02,  3.0048e-02,  2.9692e-03, -2.5398e-02,  2.9955e-03,
        -9.3653e-04, -1.2932e-02,  2.4232e-02, -3.5182e-02, -1.6163e-02,
         3.0025e-02,  3.1227e-02, -8.2498e-04,  2.7102e-02, -2.3830e-02,
        -3.4958e-02, -1.1886e-02,  1.6097e-02,  1.4579e-02, -2.6744e-02,
         1.1900e-02, -3.4855e-02, -4.2208e-03, -5.2035e-03,  1.7055e-02,
        -4.8580e-03,  3.4088e-03,  1.6923e-02,  3.5570e-04, -3.0478e-02,
         8.4647e-03,  2.5704e-02, -2.3255e-02,  6.9396e-03, -1.2521e-03,
        -9.4101e-03, -2.5798e-02, -1.4438e-03, -7.2684e-03,  3.5417e-02,
        -3.4388e-02,  1.3706e-02, -5.1430e-03,  1.6174e-02,  1.8135e-03,
        -2.9018e-02, -2.9083e-02,  7.4100e-03, -2.7758e-02,  2.4367e-02,
        -3.8350e-03,  9.4390e-03, -1.0844e-02,  1.6381e-02, -2.5268e-02,
         1.3553e-02, -1.0545e-02, -1.3782e-02,  2.8519e-02,  2.3630e-02,
        -1.9703e-02, -2.0147e-02, -1.0485e-02,  2.4637e-02,  1.9989e-02,
         5.6601e-03,  1.9121e-02, -1.5286e-02,  2.5996e-02, -2.9833e-02,
        -2.9458e-02,  2.3944e-02, -3.0107e-02, -1.2307e-02, -1.8419e-02,
         3.3551e-02,  1.2396e-02,  2.9356e-02,  3.3274e-02,  5.4677e-03,
         3.1715e-02,  1.3361e-02,  3.3042e-02,  2.7843e-03,  2.2837e-02,
        -3.4981e-02,  3.2355e-02, -2.7658e-03,  2.2184e-02, -2.0203e-02,
        -3.3264e-02, -3.4858e-02,  1.0820e-03, -1.4279e-02, -2.8041e-02,
         4.1962e-03,  2.4266e-02, -3.5704e-02, -2.6172e-02,  2.3335e-02,
         2.0657e-02, -3.0387e-03, -5.7096e-03, -1.1062e-02,  1.3450e-02,
        -3.3965e-02,  1.9623e-03, -2.0067e-02, -3.3858e-02, -2.1931e-02,
        -1.5414e-02,  2.4454e-02,  2.5668e-02, -1.1932e-02,  5.7540e-04,
         1.5130e-02,  1.3916e-02, -2.1521e-02, -3.0575e-02,  1.8841e-02,
        -2.3240e-02, -2.7297e-02, -3.2668e-02, -1.5544e-02, -5.9408e-03,
         3.0241e-02,  2.2039e-02, -2.4389e-02,  3.1703e-02,  3.5305e-02,
        -2.7501e-03,  2.0154e-02, -5.3489e-03,  1.4177e-02,  1.6829e-02,
         3.3066e-02, -1.3425e-02, -3.2565e-02,  6.5624e-03, -1.5681e-02,
         2.3047e-02,  6.5880e-03, -3.3803e-02,  2.3790e-02, -5.5061e-03,
         2.9413e-02,  1.2290e-02, -1.0958e-02,  1.2680e-03,  1.3343e-02,
         6.6689e-03, -2.2975e-03, -1.2068e-02,  1.6523e-02, -3.1612e-02,
        -1.7529e-02, -2.2220e-02, -1.4723e-02, -1.3495e-02, -5.1805e-03,
        -2.9620e-02,  3.0571e-02, -3.0999e-02,  3.3681e-03,  1.3579e-02,
         1.4837e-02,  1.5694e-02, -1.1178e-02,  4.6233e-03, -2.2583e-02,
        -3.5281e-03,  3.0918e-02,  2.6407e-02,  1.5822e-04, -3.0181e-03,
         8.6989e-03,  2.8998e-02, -1.5975e-02, -3.1574e-02, -1.5609e-02,
         1.0472e-02,  5.8976e-03,  7.0131e-03, -3.2047e-02,  2.6045e-02,
        -2.8882e-02, -2.2121e-02, -3.2960e-02,  1.8268e-02,  3.0984e-02,
         1.4824e-02,  3.0010e-02, -5.7523e-03, -2.0017e-02,  4.8700e-03,
         1.4997e-02, -1.4898e-02,  6.8572e-03,  9.7713e-03,  1.3410e-02,
         4.9619e-03,  3.1016e-02,  3.1240e-02, -3.0203e-02,  2.1435e-02,
         2.7331e-02], requires_grad=True)

有人可以向我解釋這種行為嗎？ 為什么我得到256個值而不是一個？

編輯1：

這是我對各層的理解：對於整個神經元層，偏差只是一個值。 我對嗎？ 但是我看到的輸出是256個值？ 為什么呢？ pytorch假設我對每個神經元都有偏見嗎？ 這樣可以嗎？

Answer 1

因此，首先重要的是要意識到這些層之一內部正在發生的事情。 當你寫：

Linear(in_features=784, out_features=256, bias=True)

您正在建模輸入和輸出之間的線性關系 。 您可能對基本數學很熟悉：

Y = MX + B

但是，您具有權重矩陣和偏差項，而不是“斜率”和“ y截距”。 這仍然是線性關系，但是矩陣是我們的輸入和輸出。

Y是我們的輸出，M是我們的權重矩陣，X是我們的輸入，B是我們的偏差。 您定義輸入為（N x 784）矩陣，而我們的輸出為（N x 256）矩陣（N為樣本數）。

如果您熟悉矩陣乘法，則意味着我們的權重矩陣為（784 X 256）。 MX的輸出將是一個（N x 256）矩陣，因此我們的偏差項也必須是（N x 256）才能計算出MX +B。

通常，偏差項中值的數量將與out_features的數量相同。

Answer 2

看一下這個：

from torchvision.models import resnet18
model = resnet18(pretrained=False)    

for name, param in model.named_parameters():
    if param.requires_grad:
        print (name)

這將為您提供一個龐大的清單，如下所示：

conv1.weight
bn1.weight
bn1.bias
layer1.0.conv1.weight
layer1.0.bn1.weight
layer1.0.bn1.bias
layer1.0.conv2.weight
layer1.0.bn2.weight
layer1.0.bn2.bias
layer1.1.conv1.weight
layer1.1.bn1.weight
layer1.1.bn1.bias
layer1.1.conv2.weight
layer1.1.bn2.weight
layer1.1.bn2.bias
layer2.0.conv1.weight
layer2.0.bn1.weight
layer2.0.bn1.bias
layer2.0.conv2.weight
layer2.0.bn2.weight
layer2.0.bn2.bias
layer2.0.downsample.0.weight
layer2.0.downsample.1.weight
layer2.0.downsample.1.bias
layer2.1.conv1.weight
layer2.1.bn1.weight
layer2.1.bn1.bias
layer2.1.conv2.weight
layer2.1.bn2.weight
layer2.1.bn2.bias
layer3.0.conv1.weight
layer3.0.bn1.weight
layer3.0.bn1.bias
layer3.0.conv2.weight
layer3.0.bn2.weight
layer3.0.bn2.bias
layer3.0.downsample.0.weight
layer3.0.downsample.1.weight
layer3.0.downsample.1.bias
layer3.1.conv1.weight
layer3.1.bn1.weight
layer3.1.bn1.bias
layer3.1.conv2.weight
layer3.1.bn2.weight
layer3.1.bn2.bias
layer4.0.conv1.weight
layer4.0.bn1.weight
layer4.0.bn1.bias
layer4.0.conv2.weight
layer4.0.bn2.weight
layer4.0.bn2.bias
layer4.0.downsample.0.weight
layer4.0.downsample.1.weight
layer4.0.downsample.1.bias
layer4.1.conv1.weight
layer4.1.bn1.weight
layer4.1.bn1.bias
layer4.1.conv2.weight
layer4.1.bn2.weight
layer4.1.bn2.bias
fc.weight
fc.bias

您將知道所有參數並獲得了基礎， 但是，如果打印模型，您將得到：

ResNet(
  (conv1): Conv2d(3, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False)
  (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
  (relu): ReLU(inplace)
  (maxpool): MaxPool2d(kernel_size=3, stride=2, padding=1, dilation=1, ceil_mode=False)
  (layer1): Sequential(
    (0): BasicBlock(
      (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (1): BasicBlock(
      (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
  )
  (layer2): Sequential(
    (0): BasicBlock(
      (conv1): Conv2d(64, 128, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (downsample): Sequential(
        (0): Conv2d(64, 128, kernel_size=(1, 1), stride=(2, 2), bias=False)
        (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (1): BasicBlock(
      (conv1): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
  )
  (layer3): Sequential(
    (0): BasicBlock(
      (conv1): Conv2d(128, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (downsample): Sequential(
        (0): Conv2d(128, 256, kernel_size=(1, 1), stride=(2, 2), bias=False)
        (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (1): BasicBlock(
      (conv1): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
  )
  (layer4): Sequential(
    (0): BasicBlock(
      (conv1): Conv2d(256, 512, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (downsample): Sequential(
        (0): Conv2d(256, 512, kernel_size=(1, 1), stride=(2, 2), bias=False)
        (1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (1): BasicBlock(
      (conv1): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      (relu): ReLU(inplace)
      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
  )
  (avgpool): AdaptiveAvgPool2d(output_size=(1, 1))
  (fc): Linear(in_features=512, out_features=1000, bias=True)
)

偏倚設置為True或False ，表示是否將實際使用它們。 您也可以通過修改第一段代碼來檢查最后一個，但是希望這會有所幫助。