PyTorch中nn.Linear浅析

查看源码

Linear 的初始化部分：

class Linear(Module):
	...
	__constants__ = ['bias']
	
	def __init__(self, in_features, out_features, bias=True):
	    super(Linear, self).__init__()
	    self.in_features = in_features
	    self.out_features = out_features
	    self.weight = Parameter(torch.Tensor(out_features, in_features))
	    if bias:
	        self.bias = Parameter(torch.Tensor(out_features))
	    else:
	        self.register_parameter('bias', None)
	    self.reset_parameters()
	...

需要实现的内容：
$$y=x{A}^T+b$$
计算步骤：

@weak_script_method
    def forward(self, input):
        return F.linear(input, self.weight, self.bias)

返回的是：input * weight + bias

对于 weight

weight: the learnable weights of the module of shape
    :math:`(\text{out\_features}, \text{in\_features})`. The values are
    initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`, where
    :math:`k = \frac{1}{\text{in\_features}}`

对于 bias

bias:   the learnable bias of the module of shape :math:`(\text{out\_features})`.
        If :attr:`bias` is ``True``, the values are initialized from
        :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})` where
        :math:`k = \frac{1}{\text{in\_features}}`

---

实例展示

举个例子：

>>> import torch
>>> nn1 = torch.nn.Linear(100, 50)
>>> input1 = torch.randn(140, 100)
>>> output1 = nn1(input1)
>>> output1.size()
torch.Size([140, 50])

张量的大小由 140 x 100 变成了 140 x 50

执行的操作是：
$$[140,100]\times [100,50]=[140,50]$$