对于神经网络（火炬）中的每一层，应该有多少偏差？

Question

我在pytorch中有一个简单的模型。

model = Network()

详细信息是：

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)
)

总共有3个神经元层。 1个输入（786个神经元），1个隐藏（256个神经元）和1个输出（10个神经元）。 因此，将有两个重量层。 所以两个权重层都必须有两个偏差（仅两个浮点数），对吗？ （纠正我，如果我错了）。

现在，在初始化我的网络后，我对这两个偏差值感到好奇。 所以我想检查隐藏层的偏差值，所以我写道：

model.hidden.bias

结果是我没有想到的！ 我实际上期望一个值！ 这就是我真正得到的：

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)

有人可以向我解释这种行为吗？ 为什么我得到256个值而不是一个？

编辑1：

这是我对各层的理解：对于整个神经元层，偏差只是一个值。 我对吗？ 但是我看到的输出是256个值？ 为什么呢？ pytorch假设我对每个神经元都有偏见吗？ 这样可以吗？

Answer 1

因此，首先重要的是要意识到这些层之一内部正在发生的事情。 当你写：

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

您正在建模输入和输出之间的线性关系 。 您可能对基本数学很熟悉：

Y = MX + B

但是，您具有权重矩阵和偏差项，而不是“斜率”和“ y截距”。 这仍然是线性关系，但是矩阵是我们的输入和输出。

Y是我们的输出，M是我们的权重矩阵，X是我们的输入，B是我们的偏差。 您定义输入为（N x 784）矩阵，而我们的输出为（N x 256）矩阵（N为样本数）。

如果您熟悉矩阵乘法，则意味着我们的权重矩阵为（784 X 256）。 MX的输出将是一个（N x 256）矩阵，因此我们的偏差项也必须是（N x 256）才能计算出MX +B。

通常，偏差项中值的数量将与out_features的数量相同。

Answer 2

看一下这个：

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

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

这将为您提供一个庞大的清单，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

您将知道所有参数并获得了基础， 但是，如果打印模型，您将得到：

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)
)

偏倚设置为True或False ，表示是否将实际使用它们。 您也可以通过修改第一段代码来检查最后一个，但是希望这会有所帮助。