线性层的源码及原理

class Linear(Module):
    r"""Applies a linear transformation to the incoming data: :math:`y = xA^T + b`

    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__ = ['bias', 'in_features', 'out_features']

    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()

    def reset_parameters(self):
        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):
        return F.linear(input, self.weight, self.bias)

    def extra_repr(self):
        return 'in_features={}, out_features={}, bias={}'.format(
            self.in_features, self.out_features, self.bias is not None
        )




def linear(input, weight, bias=None):
    # type: (Tensor, Tensor, Optional[Tensor]) -> Tensor
    r"""
    Applies a linear transformation to the incoming data: :math:`y = xA^T + b`.

    Shape:

        - Input: :math:`(N, *, in\_features)` where `*` means any number of
          additional dimensions
        - Weight: :math:`(out\_features, in\_features)`
        - Bias: :math:`(out\_features)`
        - Output: :math:`(N, *, out\_features)`
    """
    if input.dim() == 2 and bias is not None:
        # fused op is marginally faster
        ret = torch.addmm(bias, input, weight.t())
    else:
        output = input.matmul(weight.t())
        if bias is not None:
            output += bias
        ret = output
    return ret

参考博客 ：torch.matmul()用法介绍-优快云博客

 

# 定义输入张量input，形状为(2, 3, 4)，对应批次大小为2，序列长度为3，每个时间步有4个输入特征
input = torch.tensor([[[1., 2., 3., 4.],
                       [5., 6., 7., 8.],
                       [9., 10., 11., 12.]],
                      [[13., 14., 15., 16.],
                       [17., 18., 19., 20.],
                       [21., 22., 23., 24.]]])

# 定义权重张量weight，形状为(2, 4)，用于将4个输入特征线性组合为2个输出特征
weight = torch.tensor([[0.1, 0.2, 0.3, 0.4],
                       [0.5, 0.6, 0.7, 0.8]])

 每一行有4个特征，3个时间步

经过相乘

每一行有两个特征，3个时间步