【pytorch】torch.nn.Linear详解 |
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在学习transformer时，遇到过非常频繁的nn.Linear()函数，这里对nn.Linear进行一个详解。 参考：https://pytorch.org/docs/stable/_modules/torch/nn/modules/linear.html 概要 1. nn.Linear的原理:2. nn.Linear的使用:3. nn.Linear的源码定义:4. nn.Linear的官方源码: 1. nn.Linear的原理:从名称就可以看出来，nn.Linear表示的是线性变换，原型就是初级数学里学到的线性函数：y=kx+b 不过在深度学习中，变量都是多维张量，乘法就是矩阵乘法，加法就是矩阵加法，因此nn.Linear()运行的真正的计算就是： output = weight @ input + bias@: 在python中代表矩阵乘法 input: 表示输入的Tensor，可以有多个维度 weights: 表示可学习的权重，shape=(output_feature,in_feature) bias: 表示科学习的偏置，shape=(output_feature) in_feature： nn.Linear 初始化的第一个参数，即输入Tensor最后一维的通道数 out_feature： nn.Linear 初始化的第二个参数，即返回Tensor最后一维的通道数 output: 表示输入的Tensor，可以有多个维度 2. nn.Linear的使用:常用头文件：import torch.nn as nn nn.Linear()的初始化： nn.Linear(in_feature,out_feature,bias)in_feature： int型, 在forward中输入Tensor最后一维的通道数 out_feature： int型, 在forward中输出Tensor最后一维的通道数 bias: bool型， Linear线性变换中是否添加bias偏置 nn.Linear()的执行：（即执行forward函数） out=nn.Linear(input)input: 表示输入的Tensor，可以有多个维度 output: 表示输入的Tensor，可以有多个维度 举例： 2维 Tensor m = nn.Linear(20, 40) input = torch.randn(128, 20) output = m(input) print(output.size()) # [(128，40])4维 Tensor: m = nn.Linear(128, 64) input = torch.randn(512, 3,128,128) output = m(input) print(output.size()) # [(512, 3,128,64)) 3. nn.Linear的源码定义: import math import torch import torch.nn as nn from torch import Tensor from torch.nn.parameter import Parameter, UninitializedParameter from torch.nn import functional as F from torch.nn import init # from .lazy import LazyModuleMixin class myLinear(nn.Module): r"""Applies a linear transformation to the incoming data: :math:`y = xA^T + b` This module supports :ref:`TensorFloat32`. 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:`(*, H_{in})` where :math:`*` means any number of dimensions including none and :math:`H_{in} = \text{in\_features}`. - Output: :math:`(*, 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, device=None, dtype=None) -> None: factory_kwargs = {'device': device, 'dtype': dtype} super(myLinear, self).__init__() self.in_features = in_features self.out_features = out_features self.weight = Parameter(torch.empty((out_features, in_features), **factory_kwargs)) if bias: self.bias = Parameter(torch.empty(out_features, **factory_kwargs)) else: self.register_parameter('bias', None) self.reset_parameters() def reset_parameters(self) -> None: # Setting a=sqrt(5) in kaiming_uniform is the same as initializing with # uniform(-1/sqrt(in_features), 1/sqrt(in_features)). For details, see # https://github.com/pytorch/pytorch/issues/57109 print("333") 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) if fan_in > 0 else 0 init.uniform_(self.bias, -bound, bound) def forward(self, input: Tensor) -> Tensor: print("111") print("self.weight.shape=(", ) return F.linear(input, self.weight, self.bias) def extra_repr(self) -> str: print("www") return 'in_features={}, out_features={}, bias={}'.format( self.in_features, self.out_features, self.bias is not None ) # m = myLinear(20, 40) # input = torch.randn(128, 40, 20) # output = m(input) # print(output.size()) m = myLinear(128, 64) input = torch.randn(512, 3,128,128) output = m(input) print(output.size()) # [(512, 3,128,64)) 4. nn.Linear的官方源码: import math import torch from torch import Tensor from torch.nn.parameter import Parameter, UninitializedParameter from .. import functional as F from .. import init from .module import Module from .lazy import LazyModuleMixin class Identity(Module): r"""A placeholder identity operator that is argument-insensitive. Args: args: any argument (unused) kwargs: any keyword argument (unused) Shape: - Input: :math:`(*)`, where :math:`*` means any number of dimensions. - Output: :math:`(*)`, same shape as the input. Examples:: >>> m = nn.Identity(54, unused_argument1=0.1, unused_argument2=False) >>> input = torch.randn(128, 20) >>> output = m(input) >>> print(output.size()) torch.Size([128, 20]) """ def __init__(self, *args, **kwargs): super(Identity, self).__init__() def forward(self, input: Tensor) -> Tensor: return input class Linear(Module): r"""Applies a linear transformation to the incoming data: :math:`y = xA^T + b` This module supports :ref:`TensorFloat32`. 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:`(*, H_{in})` where :math:`*` means any number of dimensions including none and :math:`H_{in} = \text{in\_features}`. - Output: :math:`(*, 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, device=None, dtype=None) -> None: factory_kwargs = {'device': device, 'dtype': dtype} super(Linear, self).__init__() self.in_features = in_features self.out_features = out_features self.weight = Parameter(torch.empty((out_features, in_features), **factory_kwargs)) if bias: self.bias = Parameter(torch.empty(out_features, **factory_kwargs)) else: self.register_parameter('bias', None) self.reset_parameters() def reset_parameters(self) -> None: # Setting a=sqrt(5) in kaiming_uniform is the same as initializing with # uniform(-1/sqrt(in_features), 1/sqrt(in_features)). For details, see # https://github.com/pytorch/pytorch/issues/57109 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) if fan_in > 0 else 0 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 to avoid triggering an obscure error when scripting # an improperly quantized attention layer. See this issue for details: # https://github.com/pytorch/pytorch/issues/58969 # TODO: fail fast on quantization API usage error, then remove this class # and replace uses of it with plain Linear class NonDynamicallyQuantizableLinear(Linear): def __init__(self, in_features: int, out_features: int, bias: bool = True, device=None, dtype=None) -> None: super().__init__(in_features, out_features, bias=bias, device=device, dtype=dtype) [docs]class Bilinear(Module): r"""Applies a bilinear transformation to the incoming data: :math:`y = x_1^T A x_2 + b` Args: in1_features: size of each first input sample in2_features: size of each second 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: - Input1: :math:`(*, H_{in1})` where :math:`H_{in1}=\text{in1\_features}` and :math:`*` means any number of additional dimensions including none. All but the last dimension of the inputs should be the same. - Input2: :math:`(*, H_{in2})` where :math:`H_{in2}=\text{in2\_features}`. - Output: :math:`(*, H_{out})` where :math:`H_{out}=\text{out\_features}` and all but the last dimension are the same shape as the input. Attributes: weight: the learnable weights of the module of shape :math:`(\text{out\_features}, \text{in1\_features}, \text{in2\_features})`. The values are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`, where :math:`k = \frac{1}{\text{in1\_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{in1\_features}}` Examples:: >>> m = nn.Bilinear(20, 30, 40) >>> input1 = torch.randn(128, 20) >>> input2 = torch.randn(128, 30) >>> output = m(input1, input2) >>> print(output.size()) torch.Size([128, 40]) """ __constants__ = ['in1_features', 'in2_features', 'out_features'] in1_features: int in2_features: int out_features: int weight: Tensor def __init__(self, in1_features: int, in2_features: int, out_features: int, bias: bool = True, device=None, dtype=None) -> None: factory_kwargs = {'device': device, 'dtype': dtype} super(Bilinear, self).__init__() self.in1_features = in1_features self.in2_features = in2_features self.out_features = out_features self.weight = Parameter(torch.empty((out_features, in1_features, in2_features), **factory_kwargs)) if bias: self.bias = Parameter(torch.empty(out_features, **factory_kwargs)) else: self.register_parameter('bias', None) self.reset_parameters() def reset_parameters(self) -> None: bound = 1 / math.sqrt(self.weight.size(1)) init.uniform_(self.weight, -bound, bound) if self.bias is not None: init.uniform_(self.bias, -bound, bound) def forward(self, input1: Tensor, input2: Tensor) -> Tensor: return F.bilinear(input1, input2, self.weight, self.bias) def extra_repr(self) -> str: return 'in1_features={}, in2_features={}, out_features={}, bias={}'.format( self.in1_features, self.in2_features, self.out_features, self.bias is not None ) class LazyLinear(LazyModuleMixin, Linear): r"""A :class:`torch.nn.Linear` module where `in_features` is inferred. In this module, the `weight` and `bias` are of :class:`torch.nn.UninitializedParameter` class. They will be initialized after the first call to ``forward`` is done and the module will become a regular :class:`torch.nn.Linear` module. The ``in_features`` argument of the :class:`Linear` is inferred from the ``input.shape[-1]``. Check the :class:`torch.nn.modules.lazy.LazyModuleMixin` for further documentation on lazy modules and their limitations. Args: out_features: size of each output sample bias: If set to ``False``, the layer will not learn an additive bias. Default: ``True`` 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}}` """ cls_to_become = Linear # type: ignore[assignment] weight: UninitializedParameter bias: UninitializedParameter # type: ignore[assignment] def __init__(self, out_features: int, bias: bool = True, device=None, dtype=None) -> None: factory_kwargs = {'device': device, 'dtype': dtype} # bias is hardcoded to False to avoid creating tensor # that will soon be overwritten. super().__init__(0, 0, False) self.weight = UninitializedParameter(**factory_kwargs) self.out_features = out_features if bias: self.bias = UninitializedParameter(**factory_kwargs) def reset_parameters(self) -> None: if not self.has_uninitialized_params() and self.in_features != 0: super().reset_parameters() def initialize_parameters(self, input) -> None: # type: ignore[override] if self.has_uninitialized_params(): with torch.no_grad(): self.in_features = input.shape[-1] self.weight.materialize((self.out_features, self.in_features)) if self.bias is not None: self.bias.materialize((self.out_features,)) self.reset_parameters() # TODO: PartialLinear - maybe in sparse? |
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