Transformer实现以及Pytorch源码解读（五）-多头注意力机制MultiheadAttention
介绍
接前序的四篇Transformer解读博客，补充说明第四次博客中MltiheadAttention类的数据源码处理。
Transformer实现以及Pytorch源码解读（四）-Encoder层
涉及到的源文件
\site-packages\torch\nn\modules\activation.py
\site-packages\torch\nn\functional.py
涉及到的函数
用到\site-packages\torch\nn\modules\activation.py的类：
MultiheadAttention类：
\site-packages\torch\nn\functional.py：
_in_projection_packed函数
_scaled_dot_product_attention函数
multi_head_attention_forward函数
数据流动过程
第一步：
根据以下的参数将MultiheadAttention类初始化。主要接受的参数，词向量维度，和头的数量
def __init__(self, embed_dim, num_heads, dropout=0., bias=True, add_bias_kv=False, add_zero_attn=False,
kdim=None, vdim=None, batch_first=False, device=None, dtype=None) -> None:
factory_kwargs = {'device': device, 'dtype': dtype}
super(MultiheadAttention, self).__init__()
self.embed_dim = embed_dim
self.kdim = kdim if kdim is not None else embed_dim
self.vdim = vdim if vdim is not None else embed_dim
#是一个binary变量，表示k,q,v的维度是否一样
self._qkv_same_embed_dim = self.kdim == embed_dim and self.vdim == embed_dim
# print("=========================_qkv_same_embed_dim=:",self._qkv_same_embed_dim)
self.num_heads = num_heads
self.dropout = dropout
self.batch_first = batch_first
self.head_dim = embed_dim // num_heads
assert self.head_dim * num_heads == self.embed_dim, "embed_dim must be divisible by num_heads"
if self._qkv_same_embed_dim is False:
self.q_proj_weight = Parameter(torch.empty((embed_dim, embed_dim), **factory_kwargs))
self.k_proj_weight = Parameter(torch.empty((embed_dim, self.kdim), **factory_kwargs))
self.v_proj_weight = Parameter(torch.empty((embed_dim, self.vdim), **factory_kwargs))
self.register_parameter('in_proj_weight', None)
else:
self.in_proj_weight = Parameter(torch.empty((3 * embed_dim, embed_dim), **factory_kwargs))
# print(self.in_proj_weight.shape)
self.register_parameter('q_proj_weight', None)
self.register_parameter('k_proj_weight', None)
self.register_parameter('v_proj_weight', None)
if bias:
self.in_proj_bias = Parameter(torch.empty(3 * embed_dim, **factory_kwargs))
else:
self.register_parameter('in_proj_bias', None)
self.out_proj = NonDynamicallyQuantizableLinear(embed_dim, embed_dim, bias=bias, **factory_kwargs)
if add_bias_kv:
self.bias_k = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
self.bias_v = Parameter(torch.empty((1, 1, embed_dim), **factory_kwargs))
else:
self.bias_k = self.bias_v = None
self.add_zero_attn = add_zero_attn
self._reset_parameters()
其中in_proj_weight和in_proj_bias为初始化的权重和偏置项。通过参数_qkv_same_embed_dim判断是否为自注意力，如果是自注意力的话将q进行扩充3倍处理。
第二步
初始化权重和偏置项：
在_reset_parameters()函数中进行初始化，给权重和偏置项中的每个位置随机填充-a到a之间的一个数字,a的计算用到的以下的公式：
a = gain × 6 fan_in + fan_out a = \text{gain} \times \sqrt{\frac{6}{\text{fan\_in} + \text{fan\_out}}} a=gain×fan_in+fan_out6
以上公式的实现如下
def xavier_uniform_(tensor: Tensor, gain: float = 1.) -> Tensor:
r"""Fills the input `Tensor` with values according to the method
described in `Understanding the difficulty of training deep feedforward
neural networks` - Glorot, X. & Bengio, Y. (2010), using a uniform
distribution. The resulting tensor will have values sampled from
:math:`\mathcal{U}(-a, a)` where
.. math::
a = \text{gain} \times \sqrt{\frac{6}{\text{fan\_in} + \text{fan\_out}}}
Also known as Glorot initialization.
Args:
tensor: an n-dimensional `torch.Tensor`
gain: an optional scaling factor
Examples:
>>> w = torch.empty(3, 5)
>>> nn.init.xavier_uniform_(w, gain=nn.init.calculate_gain('relu'))
"""
fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor)
std = gain * math.sqrt(2.0 / float(fan_in + fan_out))
a = math.sqrt(3.0) * std # Calculate uniform bounds from standard deviation
return _no_grad_uniform_(tensor, -a, a)
fan_in 和fan_out的计算是根据输入tensor的维度确定的：
def _calculate_fan_in_and_fan_out(tensor):
dimensions = tensor.dim()
if dimensions < 2:
raise ValueError("Fan in and fan out can not be computed for tensor with fewer than 2 dimensions")
num_input_fmaps = tensor.size(1)
num_output_fmaps = tensor.size(0)
receptive_field_size = 1
if tensor.dim() > 2:
# math.prod is not always available, accumulate the product manually
# we could use functools.reduce but that is not supported by TorchScript
for s in tensor.shape[2:]:
receptive_field_size *= s
fan_in = num_input_fmaps * receptive_field_size
fan_out = num_output_fmaps * receptive_field_size
return fan_in, fan_out
第三步
在MultiheadAttention类的forward中进行每个batch的计算。
简化来看进行的是如下的操作：
（1）三个参数分别经过一个全连接层
if not use_separate_proj_weight:
#三个参数与in_porj_weight相乘。
q, k, v = _in_projection_packed(query, key, value, in_proj_weight, in_proj_bias)
def _in_projection_packed(
q: Tensor,
k: Tensor,
v: Tensor,
w: Tensor,
b: Optional[Tensor] = None,
) -> List[Tensor]:
r"""
Performs the in-projection step of the attention operation, using packed weights.
Output is a triple containing projection tensors for query, key and value.
Args:
q, k, v: query, key and value tensors to be projected. For self-attention,
these are typically the same tensor; for encoder-decoder attention,
k and v are typically the same tensor. (We take advantage of these
identities for performance if they are present.) Regardless, q, k and v
must share a common embedding dimension; otherwise their shapes may vary.
w: projection weights for q, k and v, packed into a single tensor. Weights
are packed along dimension 0, in q, k, v order.
b: optional projection biases for q, k and v, packed into a single tensor
in q, k, v order.
Shape:
Inputs:
- q: :math:`(..., E)` where E is the embedding dimension
- k: :math:`(..., E)` where E is the embedding dimension
- v: :math:`(..., E)` where E is the embedding dimension
- w: :math:`(E * 3, E)` where E is the embedding dimension
- b: :math:`E * 3` where E is the embedding dimension
Output:
- in output list :math:`[q', k', v']`, each output tensor will have the
same shape as the corresponding input tensor.
"""
E = q.size(-1)
if k is v:
if q is k:
# print("=========q:",q.shape)
# print("=========w:",w.shape)
return linear(q, w, b).chunk(3, dim=-1)
else:
# encoder-decoder attention
w_q, w_kv = w.split([E, E * 2])
if b is None:
b_q = b_kv = None
else:
b_q, b_kv = b.split([E, E * 2])
return (linear(q, w_q, b_q),) + linear(k, w_kv, b_kv).chunk(2, dim=-1)
else:
w_q, w_k, w_v = w.chunk(3)
if b is None:
b_q = b_k = b_v = None
else:
b_q, b_k, b_v = b.chunk(3)
return linear(q, w_q, b_q), linear(k, w_k, b_k), linear(v, w_v, b_v)
（2）三参数在bachsize维度根据头数扩充
多头就是在这里进行工作的
q = q.contiguous().view(tgt_len, bsz * num_heads, head_dim).transpose(0, 1)
k = k.contiguous().view(k.shape[0], bsz * num_heads, head_dim).transpose(0, 1)
v = v.contiguous().view(v.shape[0], bsz * num_heads, head_dim).transpose(0, 1)
（3）三参数顺序列相乘
获得注意力向量和最终结果。注意这里torch.bmm的使用。
def _scaled_dot_product_attention(
q: Tensor,
k: Tensor,
v: Tensor,
attn_mask: Optional[Tensor] = None,
dropout_p: float = 0.0,
) -> Tuple[Tensor, Tensor]:
r"""
Computes scaled dot product attention on query, key and value tensors, using
an optional attention mask if passed, and applying dropout if a probability
greater than 0.0 is specified.
Returns a tensor pair containing attended values and attention weights.
Args:
q, k, v: query, key and value tensors. See Shape section for shape details.
attn_mask: optional tensor containing mask values to be added to calculated
attention. May be 2D or 3D; see Shape section for details.
dropout_p: dropout probability. If greater than 0.0, dropout is applied.
Shape:
- q: :math:`(B, Nt, E)` where B is batch size, Nt is the target sequence length,
and E is embedding dimension.
- key: :math:`(B, Ns, E)` where B is batch size, Ns is the source sequence length,
and E is embedding dimension.
- value: :math:`(B, Ns, E)` where B is batch size, Ns is the source sequence length,
and E is embedding dimension.
- attn_mask: either a 3D tensor of shape :math:`(B, Nt, Ns)` or a 2D tensor of
shape :math:`(Nt, Ns)`.
- Output: attention values have shape :math:`(B, Nt, E)`; attention weights
have shape :math:`(B, Nt, Ns)`
"""
B, Nt, E = q.shape
q = q / math.sqrt(E)
# (B, Nt, E) x (B, E, Ns) -> (B, Nt, Ns)
attn = torch.bmm(q, k.transpose(-2, -1))
if attn_mask is not None:
attn += attn_mask
attn = softmax(attn, dim=-1)
if dropout_p > 0.0:
attn = dropout(attn, p=dropout_p)
# (B, Nt, Ns) x (B, Ns, E) -> (B, Nt, E)
output = torch.bmm(attn, v)
return output, attn
总结
源码总对于num_head的处理有代码冗余的情况。