Pytorch中的torch.nn.Linear()方法用法解读
作者：拥抱晨曦之温暖
这篇文章主要介绍了Pytorch中的torch.nn.Linear()方法用法,具有很好的参考价值,希望对大家有所帮助,如有错误或未考虑完全的地方,望不吝赐教
Pytorch torch.nn.Linear()方法
torch.nn.Linear()作为深度学习中最简单的线性变换方法，其主要作用是对输入数据应用线性转换
看一下官方的解释及介绍
class Linear(Module):
r"""Applies a linear transformation to the incoming data: :math:`y = xA^T + b`
This module supports :ref:`TensorFloat32<tf32_on_ampere>`.
Args:
in_features: size of each input sample
out_features: size of each output sample
bias: If set to ``False``, the layer will not learn an additive bias.
Default: ``True``
Shape:
- Input: :math:`(N, *, H_{in})` where :math:`*` means any number of
additional dimensions and :math:`H_{in} = \text{in\_features}`
- Output: :math:`(N, *, H_{out})` where all but the last dimension
are the same shape as the input and :math:`H_{out} = \text{out\_features}`.
Attributes:
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}}`
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}}`
Examples::
>>> m = nn.Linear(20, 30)
>>> input = torch.randn(128, 20)
>>> output = m(input)
>>> print(output.size())
torch.Size([128, 30])
"""
__constants__ = ['in_features', 'out_features']
in_features: int
out_features: int
weight: Tensor
def __init__(self, in_features: int, out_features: int, bias: bool = True) -> None:
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()
def reset_parameters(self) -> None:
init.kaiming_uniform_(self.weight, a=math.sqrt(5))
if self.bias is not None:
fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in)
init.uniform_(self.bias, -bound, bound)
def forward(self, input: Tensor) -> Tensor:
return F.linear(input, self.weight, self.bias)
def extra_repr(self) -> str:
return 'in_features={}, out_features={}, bias={}'.format(
self.in_features, self.out_features, self.bias is not None
)
# This class exists solely for Transformer; it has an annotation stating
# that bias is never None, which appeases TorchScript这里我们主要看__init__()方法，很容易知道，当我们使用这个方法时一般需要传入2~3个参数，分别是in_features: int, out_features: int, bias: bool = True，第三个参数是说是否加偏置(bias)，简单来讲，这个函数其实就是一个'一次函数':y = xA^T + b,(T表示张量A的转置),首先super(Linear, self).__init__()就是老生常谈的方法，之后初始化in_features和out_features，接下来就是比较重要的weight的设置，我们可以很清晰的看到weight的shape是(out_features,in_features)的，而我们在做xA^T时，并不是x和A^T相乘的，而是x和A.weight^T相乘的，这里需要大大留意，也就是说先对A做转置得到A.weight，然后在丢入y = xA^T + b中，得出结果。
接下来奉上一个小例子来实践一下：
import torch
# 随机初始化一个shape为(128,20)的Tensor
x = torch.randn(128,20)
# 构造线性变换函数y = xA^T + b,且参数(20,30)指的是A的shape,则A.weight的shape就是(30,20)了
y= torch.nn.Linear(20,30)
output = y(x)
# 按照以上逻辑使用torch中的简单乘法函数进行检验，结果很显然与上述符合
# 下面的y.weight可以理解为一个shape为(30,20)的一个可学习的矩阵，.t()表示转置
# y.bias若为TRUE，则bias是一个Tensor，且其shape为out_features,在该程序中应为30
# 更加细致的表达一下y = (128 * 20) * (30 * 20)^T + (if bias (1,30) ,else: 0)
ans = torch.mm(x,y.weight.t())+y.bias
print('ans.shape:\n',ans.shape)
print(torch.equal(ans,output))对torch.nn.Linear的理解
torch.nn.Linear是pytorch的线性变换层
定义如下：
Linear(in_features: int, out_features: int, bias: bool = True, device: Any | None = None, dtype: Any | None = None)
全连接层 Fully Connect 一般就就用这个函数来实现。
因此在潜意识里，变换的输入张量的 shape 为 (batchsize, in_features)，输出张量的 shape 为 (batchsize, out_features)。
当然这是常用的方式，但是 Linear 的输入张量的维度其实并不需要必须为上述的二维，多维也是完全可以的，Linear 仅是对输入的最后一维做线性变换，不影响其他维。
可以看下官网的解释
Linear — PyTorch 1.11.0 documentation
一个例子
如下：
import torch input = torch.randn(30, 20, 10) # [30, 20, 10] linear = torch.nn.Linear(10, 15) # (*, 10) --> (*, 15) output = linear(input) print(output.size()) # 输出 [30, 20, 15]
总结
以上为个人经验，希望能给大家一个参考，也希望大家多多支持脚本之家。