nn.Linear

torch.nn.Linear(in_features, out_features, bias=True, device=None, dtype=None)
这个函数主要是进行空间的线性映射

• in_features：输入数据的数据维度
• out_features：输出数据的数据维度

函数执行过程：

假设我们有一批数据$x$，$x$的维度为20维，这一批数据一共有128个，我们要将20维的$x$映射到30维空间的$y$中，下面是计算过程，其中$w$是Linear函数的weight权重

$$y=x{W}^T+b$$

其中$x={\left(\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1,20}\\ x_{21}& x_{22}& ...& x_{2,20}\\ ...& ...& ...& ...\\ x_{128,1}& x_{128,2}& ...& x_{128,20}\end{array}\right)}_{128\times 20}$ $w={\left(\begin{array}{cccc}{w}_{11}& w_{12}& ...& w_{1,20}\\ w_{21}& w_{22}& ...& w_{2,20}\\ ...& ...& ...& ...\\ w_{30,1}& w_{30,2}& ...& w_{30,20}\end{array}\right)}_{30\times 20}$

$${\left(\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1,20}\\ x_{21}& x_{22}& ...& x_{2,20}\\ ...& ...& ...& ...\\ x_{128,1}& x_{128,2}& ...& x_{128,20}\end{array}\right)}_{128\times 20}{\left(\begin{array}{cccc}{w}_{11}& w_{21}& ...& w_{30,1}\\ w_{12}& w_{22}& ...& w_{30,2}\\ ...& ...& ...& ...\\ w_{1,20}& w_{2,20}& ...& w_{30,20}\end{array}\right)}_{20\times 30}={\left(\begin{array}{cccc}{y}_{11}& y_{12}& ...& y_{1,30}\\ y_{12}& y_{22}& ...& y_{2,30}\\ ...& ...& ...& ...\\ y_{128,1}& y_{128,2}& ...& y_{128,30}\end{array}\right)}_{128\times 30}$$

一个简单的例子

import torch


x = torch.randn(128, 20)  # 输入的维度是（128，20）
linear = torch.nn.Linear(20, 30)  # 20, 30是指维度
output = linear(x)

print('linear.weight.shape:   ', linear.weight.shape)
print('linear.bias.shape:     ', linear.bias.shape)
print('output.shape:          ', output.shape)

# ans = torch.mm(input,torch.t(m.weight))+m.bias 等价于下面的
# .t就是w转置之后的部分
ans = torch.mm(x, linear.weight.t()) + linear.bias
print('ans.shape:             ', ans.shape)
print(torch.equal(ans, output))


'''output:
linear.weight.shape:    torch.Size([30, 20])
linear.bias.shape:      torch.Size([30])
output.shape:           torch.Size([128, 30])
ans.shape:              torch.Size([128, 30])
True
'''