注意力增强卷积网络.
传统的卷积操作是一个固定的滤波器在图片上扫过，对于$(i,j)$点，只能关注到滤波器大小的邻域中的内容，即使进行多次卷积，感受野依旧较小，丢失了全局信息。自注意力机制能够捕获长距离交互，得到$(i,j)$这个点在全局的语义特征。本文使用self-attention机制来增强卷积算子，将强调局部性的convolutional feature maps与能够捕获长距离依赖性的self-attention feature maps concat到一起。
对于自注意力机制，作者引入了multi head形式。对于每一个head，注意力计算如下：
\[O_h = \text{Softmax} \left( \frac{(XW_q)(XW_k)^T}{\sqrt{d_k^h}} \right) (XW_v)\]然后将多个single head结果进行拼接，然后进行线性变换得到最终结果：
\[MHA(X) = Concat[O_1,...,O_{Nh}]W^O\]作者进一步引入相对位置编码，通过独立添加相关高度信息与相关宽度信息实现二维relative self-attention，能够在满足非排列等变的情况下实现平移等变性。
\[O_h = \text{Softmax} \left( \frac{(XW_q)(XW_k+R_H + R_W)^T}{\sqrt{d_k^h}} \right) (XW_v)\]最后将卷积特征映射与self-attention特征映射concat到一起：
\[AAConv(X) = Concat[Conv(X), MHA(X)]\]class AugmentedConv(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size, dk, dv, Nh, shape=0, relative=False, stride=1):
super(AugmentedConv, self).__init__()
self.in_channels = in_channels
self.out_channels = out_channels
self.kernel_size = kernel_size
self.dk = dk
self.dv = dv
self.Nh = Nh
self.shape = shape
self.relative = relative
self.stride = stride
self.padding = (self.kernel_size - 1) // 2
assert self.Nh != 0, "integer division or modulo by zero, Nh >= 1"
assert self.dk % self.Nh == 0, "dk should be divided by Nh. (example: out_channels: 20, dk: 40, Nh: 4)"
assert self.dv % self.Nh == 0, "dv should be divided by Nh. (example: out_channels: 20, dv: 4, Nh: 4)"
assert stride in [1, 2], str(stride) + " Up to 2 strides are allowed."
self.conv_out = nn.Conv2d(self.in_channels, self.out_channels - self.dv, self.kernel_size, stride=stride, padding=self.padding)
self.qkv_conv = nn.Conv2d(self.in_channels, 2 * self.dk + self.dv, kernel_size=self.kernel_size, stride=stride, padding=self.padding)
self.attn_out = nn.Conv2d(self.dv, self.dv, kernel_size=1, stride=1)
if self.relative:
self.key_rel_w = nn.Parameter(torch.randn((2 * self.shape - 1, dk // Nh), requires_grad=True))
self.key_rel_h = nn.Parameter(torch.randn((2 * self.shape - 1, dk // Nh), requires_grad=True))
def forward(self, x):
# Input x
# (batch_size, channels, height, width)
# batch, _, height, width = x.size()
# conv_out
# (batch_size, out_channels, height, width)
conv_out = self.conv_out(x)
batch, _, height, width = conv_out.size()
# flat_q, flat_k, flat_v
# (batch_size, Nh, height * width, dvh or dkh)
# dvh = dv / Nh, dkh = dk / Nh
# q, k, v
# (batch_size, Nh, height, width, dv or dk)
flat_q, flat_k, flat_v, q, k, v = self.compute_flat_qkv(x, self.dk, self.dv, self.Nh)
logits = torch.matmul(flat_q.transpose(2, 3), flat_k)
if self.relative:
h_rel_logits, w_rel_logits = self.relative_logits(q)
logits += h_rel_logits
logits += w_rel_logits
weights = F.softmax(logits, dim=-1)
# attn_out
# (batch, Nh, height * width, dvh)
attn_out = torch.matmul(weights, flat_v.transpose(2, 3))
attn_out = torch.reshape(attn_out, (batch, self.Nh, self.dv // self.Nh, height, width))
# combine_heads_2d
# (batch, out_channels, height, width)
attn_out = self.combine_heads_2d(attn_out)
attn_out = self.attn_out(attn_out)
return torch.cat((conv_out, attn_out), dim=1)
def compute_flat_qkv(self, x, dk, dv, Nh):
qkv = self.qkv_conv(x)
N, _, H, W = qkv.size()
q, k, v = torch.split(qkv, [dk, dk, dv], dim=1)
q = self.split_heads_2d(q, Nh)
k = self.split_heads_2d(k, Nh)
v = self.split_heads_2d(v, Nh)
dkh = dk // Nh
q *= dkh ** -0.5
flat_q = torch.reshape(q, (N, Nh, dk // Nh, H * W))
flat_k = torch.reshape(k, (N, Nh, dk // Nh, H * W))
flat_v = torch.reshape(v, (N, Nh, dv // Nh, H * W))
return flat_q, flat_k, flat_v, q, k, v
def split_heads_2d(self, x, Nh):
batch, channels, height, width = x.size()
ret_shape = (batch, Nh, channels // Nh, height, width)
split = torch.reshape(x, ret_shape)
return split
def combine_heads_2d(self, x):
batch, Nh, dv, H, W = x.size()
ret_shape = (batch, Nh * dv, H, W)
return torch.reshape(x, ret_shape)
def relative_logits(self, q):
B, Nh, dk, H, W = q.size()
q = torch.transpose(q, 2, 4).transpose(2, 3) # [B, Nh, H, W, dk]
rel_logits_w = self.relative_logits_1d(q, self.key_rel_w, H, W, Nh, "w")
rel_logits_h = self.relative_logits_1d(torch.transpose(q, 2, 3), self.key_rel_h, W, H, Nh, "h")
return rel_logits_h, rel_logits_w
def relative_logits_1d(self, q, rel_k, H, W, Nh, case):
rel_logits = torch.einsum('bhxyd,md->bhxym', q, rel_k)
rel_logits = torch.reshape(rel_logits, (-1, Nh * H, W, 2 * W - 1))
rel_logits = self.rel_to_abs(rel_logits)
rel_logits = torch.reshape(rel_logits, (-1, Nh, H, W, W))
rel_logits = torch.unsqueeze(rel_logits, dim=3)
rel_logits = rel_logits.repeat((1, 1, 1, H, 1, 1))
if case == "w":
rel_logits = torch.transpose(rel_logits, 3, 4)
elif case == "h":
rel_logits = torch.transpose(rel_logits, 2, 4).transpose(4, 5).transpose(3, 5)
rel_logits = torch.reshape(rel_logits, (-1, Nh, H * W, H * W))
return rel_logits
def rel_to_abs(self, x):
B, Nh, L, _ = x.size()
col_pad = torch.zeros((B, Nh, L, 1)).to(x)
x = torch.cat((x, col_pad), dim=3)
flat_x = torch.reshape(x, (B, Nh, L * 2 * L))
flat_pad = torch.zeros((B, Nh, L - 1)).to(x)
flat_x_padded = torch.cat((flat_x, flat_pad), dim=2)
final_x = torch.reshape(flat_x_padded, (B, Nh, L + 1, 2 * L - 1))
final_x = final_x[:, :, :L, L - 1:]
return
# Example Code
# tmp = torch.randn((16, 3, 32, 32)).to(device)
# augmented_conv1 = AugmentedConv(in_channels=3, out_channels=20, kernel_size=3, dk=40, dv=4, Nh=4, relative=True, padding=1, stride=2, shape=16).to(device)
# conv_out1 = augmented_conv1(tmp)
# print(conv_out1.shape)
#
# for name, param in augmented_conv1.named_parameters():
# print('parameter name: ', name)
#
# augmented_conv2 = AugmentedConv(in_channels=3, out_channels=20, kernel_size=3, dk=40, dv=4, Nh=4, relative=True, padding=1, stride=1, shape=32).to(device)
# conv_out2 = augmented_conv2(tmp)
# print(conv_out2.shape)
