本文介绍Agent Attention注意力机制，Transformer中的Attention模块可以提取全局语义信息，但是计算量太大，Agent Attention是一种计算非常有效的Attention模块。

论文：Agent Attention: On the Integration of Softmax and Linear Attention

代码：https://github.comA/leaplabthu/agent-attention

一、模块结构

Softmax Attention，Linear Attention， Agent Attention结构如下图：

Softmax Attention先进行Q和K的矩阵乘法，然后经过softmax并与V相乘，计算量大。

Linear Attention先进行K和V的矩阵乘法，然后再与Q相乘，降低了计算量。

Agent Attention引入了agent token A，A的维度为（n,d），n远小于N，通过与A的矩阵乘法降低了Q,K的维度，进而降低计算量。

二、推理公式

传统Attention的计算如下（x是输入，W是权重）：

Softmax Attention就是将上式中的Sim（Q，K）变成了下式：

而Linear Attention的Sim（Q,K）如下：

为了简单起见，可以将Softmax Attention和Linear Attention写成下式：

那么Agent Attention可以写成：

等价于下式（A是引入的Agent token）：

下图是Agent Attention的示意图（可以看到与最上面的图和上式很相似）：

三、代码

Agent Attention可以放入各种Transformer模块中，这里展示PVT中使用Agent Attention的代码（就是将PVT原有的Attention模块替换成Agent Attention）：

# -----------------------------------------------------------------------
# Agent Attention: On the Integration of Softmax and Linear Attention
# Modified by Dongchen Han
# -----------------------------------------------------------------------


import torch
import torch.nn as nn
import torch.nn.functional as F
from functools import partial

from timm.models.layers import DropPath, to_2tuple, trunc_normal_
from timm.models.registry import register_model
from timm.models.vision_transformer import _cfg

__all__ = [
    'agent_pvt_tiny', 'agent_pvt_small', 'agent_pvt_medium', 'agent_pvt_large'
]


class Mlp(nn.Module):
    def __init__(self, in_features, hidden_features=None, out_features=None, act_layer=nn.GELU, drop=0.):
        super().__init__()
        out_features = out_features or in_features
        hidden_features = hidden_features or in_features
        self.fc1 = nn.Linear(in_features, hidden_features)
        self.act = act_layer()
        self.fc2 = nn.Linear(hidden_features, out_features)
        self.drop = nn.Dropout(drop)

    def forward(self, x):
        x = self.fc1(x)
        x = self.act(x)
        x = self.drop(x)
        x = self.fc2(x)
        x = self.drop(x)
        return x


class Attention(nn.Module):
    def __init__(self, dim, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0., sr_ratio=1):
        super().__init__()
        assert dim % num_heads == 0, f"dim {dim} should be divided by num_heads {num_heads}."

        self.dim = dim
        self.num_heads = num_heads
        head_dim = dim // num_heads
        self.scale = qk_scale or head_dim ** -0.5

        self.q = nn.Linear(dim, dim, bias=qkv_bias)
        self.kv = nn.Linear(dim, dim * 2, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)

        self.sr_ratio = sr_ratio
        if sr_ratio > 1:
            self.sr = nn.Conv2d(dim, dim, kernel_size=sr_ratio, stride=sr_ratio)
            self.norm = nn.LayerNorm(dim)

    def forward(self, x, H, W):
        B, N, C = x.shape
        q = self.q(x).reshape(B, N, self.num_heads, C // self.num_heads).permute(0, 2, 1, 3)

        if self.sr_ratio > 1:
            x_ = x.permute(0, 2, 1).reshape(B, C, H, W)
            x_ = self.sr(x_).reshape(B, C, -1).permute(0, 2, 1)
            x_ = self.norm(x_)
            kv = self.kv(x_).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        else:
            kv = self.kv(x).reshape(B, -1, 2, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        k, v = kv[0], kv[1]

        attn = (q @ k.transpose(-2, -1)) * self.scale
        attn = attn.softmax(dim=-1)
        attn = self.attn_drop(attn)

        x = (attn @ v).transpose(1, 2).reshape(B, N, C)
        x = self.proj(x)
        x = self.proj_drop(x)

        return x


class AgentAttention(nn.Module):
    def __init__(self, dim, num_patches, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0.,
                 sr_ratio=1, agent_num=49, **kwargs):
        super().__init__()
        assert dim % num_heads == 0, f"dim {dim} should be divided by num_heads {num_heads}."

        self.dim = dim
        self.num_patches = num_patches
        window_size = (int(num_patches ** 0.5), int(num_patches ** 0.5))
        self.window_size = window_size
        self.num_heads = num_heads
        head_dim = dim // num_heads
        self.scale = head_dim ** -0.5

        self.q = nn.Linear(dim, dim, bias=qkv_bias)
        self.kv = nn.Linear(dim, dim * 2, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)

        self.sr_ratio = sr_ratio
        if sr_ratio > 1:
            self.sr = nn.Conv2d(dim, dim, kernel_size=sr_ratio, stride=sr_ratio)
            self.norm = nn.LayerNorm(dim)

        self.agent_num = agent_num
        self.dwc = nn.Conv2d(in_channels=dim, out_channels=dim, kernel_size=(3, 3), padding=1, groups=dim)
        self.an_bias = nn.Parameter(torch.zeros(num_heads, agent_num, 7, 7))
        self.na_bias = nn.Parameter(torch.zeros(num_heads, agent_num, 7, 7))
        self.ah_bias = nn.Parameter(torch.zeros(1, num_heads, agent_num, window_size[0] // sr_ratio, 1))
        self.aw_bias = nn.Parameter(torch.zeros(1, num_heads, agent_num, 1, window_size[1] // sr_ratio))
        self.ha_bias = nn.Parameter(torch.zeros(1, num_heads, window_size[0], 1, agent_num))
        self.wa_bias = nn.Parameter(torch.zeros(1, num_heads, 1, window_size[1], agent_num))
        trunc_normal_(self.an_bias, std=.02)
        trunc_normal_(self.na_bias, std=.02)
        trunc_normal_(self.ah_bias, std=.02)
        trunc_normal_(self.aw_bias, std=.02)
        trunc_normal_(self.ha_bias, std=.02)
        trunc_normal_(self.wa_bias, std=.02)
        pool_size = int(agent_num ** 0.5)
        self.pool = nn.AdaptiveAvgPool2d(output_size=(pool_size, pool_size))
        self.softmax = nn.Softmax(dim=-1)

    def forward(self, x, H, W):
        b, n, c = x.shape
        num_heads = self.num_heads
        head_dim = c // num_heads
        q = self.q(x)

        if self.sr_ratio > 1:
            x_ = x.permute(0, 2, 1).reshape(b, c, H, W)
            x_ = self.sr(x_).reshape(b, c, -1).permute(0, 2, 1)
            x_ = self.norm(x_)
            kv = self.kv(x_).reshape(b, -1, 2, c).permute(2, 0, 1, 3)
        else:
            kv = self.kv(x).reshape(b, -1, 2, c).permute(2, 0, 1, 3)
        k, v = kv[0], kv[1]

        agent_tokens = self.pool(q.reshape(b, H, W, c).permute(0, 3, 1, 2)).reshape(b, c, -1).permute(0, 2, 1)
        q = q.reshape(b, n, num_heads, head_dim).permute(0, 2, 1, 3)
        k = k.reshape(b, n, num_heads, head_dim).permute(0, 2, 1, 3)
        v = v.reshape(b, n, num_heads, head_dim).permute(0, 2, 1, 3)
        agent_tokens = agent_tokens.reshape(b, self.agent_num, num_heads, head_dim).permute(0, 2, 1, 3)

        kv_size = (self.window_size[0] // self.sr_ratio, self.window_size[1] // self.sr_ratio)
        position_bias1 = nn.functional.interpolate(self.an_bias, size=kv_size, mode='bilinear')
        position_bias1 = position_bias1.reshape(1, num_heads, self.agent_num, -1).repeat(b, 1, 1, 1)
        position_bias2 = (self.ah_bias + self.aw_bias).reshape(1, num_heads, self.agent_num, -1).repeat(b, 1, 1, 1)
        position_bias = position_bias1 + position_bias2
        agent_attn = self.softmax((agent_tokens * self.scale) @ k.transpose(-2, -1) + position_bias)
        agent_attn = self.attn_drop(agent_attn)
        agent_v = agent_attn @ v

        agent_bias1 = nn.functional.interpolate(self.na_bias, size=self.window_size, mode='bilinear')
        agent_bias1 = agent_bias1.reshape(1, num_heads, self.agent_num, -1).permute(0, 1, 3, 2).repeat(b, 1, 1, 1)
        agent_bias2 = (self.ha_bias + self.wa_bias).reshape(1, num_heads, -1, self.agent_num).repeat(b, 1, 1, 1)
        agent_bias = agent_bias1 + agent_bias2
        q_attn = self.softmax((q * self.scale) @ agent_tokens.transpose(-2, -1) + agent_bias)
        q_attn = self.attn_drop(q_attn)
        x = q_attn @ agent_v

        x = x.transpose(1, 2).reshape(b, n, c)
        v = v.transpose(1, 2).reshape(b, H, W, c).permute(0, 3, 1, 2)
        x = x + self.dwc(v).permute(0, 2, 3, 1).reshape(b, n, c)

        x = self.proj(x)
        x = self.proj_drop(x)
        return x


class Block(nn.Module):

    def __init__(self, dim, num_patches, num_heads, mlp_ratio=4., qkv_bias=False, qk_scale=None, drop=0., attn_drop=0.,
                 drop_path=0., act_layer=nn.GELU, norm_layer=nn.LayerNorm, sr_ratio=1,
                 agent_num=49, attn_type='A'):
        super().__init__()
        self.norm1 = norm_layer(dim)
        assert attn_type in ['A', 'B']
        if attn_type == 'A':
            self.attn = AgentAttention(
                dim, num_patches,
                num_heads=num_heads, qkv_bias=qkv_bias, qk_scale=qk_scale,
                attn_drop=attn_drop, proj_drop=drop, sr_ratio=sr_ratio,
                agent_num=agent_num)
        else:
            self.attn = Attention(
                dim,
                num_heads=num_heads, qkv_bias=qkv_bias, qk_scale=qk_scale,
                attn_drop=attn_drop, proj_drop=drop, sr_ratio=sr_ratio)
        # NOTE: drop path for stochastic depth, we shall see if this is better than dropout here
        self.drop_path = DropPath(drop_path) if drop_path > 0. else nn.Identity()
        self.norm2 = norm_layer(dim)
        mlp_hidden_dim = int(dim * mlp_ratio)
        self.mlp = Mlp(in_features=dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop=drop)

    def forward(self, x, H, W):
        x = x + self.drop_path(self.attn(self.norm1(x), H, W))
        x = x + self.drop_path(self.mlp(self.norm2(x)))

        return x


class PatchEmbed(nn.Module):
    """ Image to Patch Embedding
    """

    def __init__(self, img_size=224, patch_size=16, in_chans=3, embed_dim=768):
        super().__init__()
        img_size = to_2tuple(img_size)
        patch_size = to_2tuple(patch_size)

        self.img_size = img_size
        self.patch_size = patch_size
        # assert img_size[0] % patch_size[0] == 0 and img_size[1] % patch_size[1] == 0, \
        #     f"img_size {img_size} should be divided by patch_size {patch_size}."
        self.H, self.W = img_size[0] // patch_size[0], img_size[1] // patch_size[1]
        self.num_patches = self.H * self.W
        self.proj = nn.Conv2d(in_chans, embed_dim, kernel_size=patch_size, stride=patch_size)
        self.norm = nn.LayerNorm(embed_dim)

    def forward(self, x):
        B, C, H, W = x.shape

        x = self.proj(x).flatten(2).transpose(1, 2)
        x = self.norm(x)
        H, W = H // self.patch_size[0], W // self.patch_size[1]

        return x, (H, W)


class PyramidVisionTransformer(nn.Module):
    def __init__(self, img_size=224, patch_size=16, in_chans=3, num_classes=1000, embed_dims=[64, 128, 256, 512],
                 num_heads=[1, 2, 4, 8], mlp_ratios=[4, 4, 4, 4], qkv_bias=False, qk_scale=None, drop_rate=0.,
                 attn_drop_rate=0., drop_path_rate=0., norm_layer=nn.LayerNorm,
                 depths=[3, 4, 6, 3], sr_ratios=[8, 4, 2, 1], agent_sr_ratios='1111', num_stages=4,
                 agent_num=[9, 16, 49, 49], attn_type='AAAA', **kwargs):
        super().__init__()
        self.num_classes = num_classes
        self.depths = depths
        self.num_stages = num_stages

        dpr = [x.item() for x in torch.linspace(0, drop_path_rate, sum(depths))]  # stochastic depth decay rule
        cur = 0

        attn_type = 'AAAA' if attn_type is None else attn_type
        for i in range(num_stages):
            patch_embed = PatchEmbed(img_size=img_size if i == 0 else img_size // (2 ** (i - 1) * patch_size),
                                     patch_size=patch_size if i == 0 else 2,
                                     in_chans=in_chans if i == 0 else embed_dims[i - 1],
                                     embed_dim=embed_dims[i])
            num_patches = patch_embed.num_patches
            pos_embed = nn.Parameter(torch.zeros(1, num_patches, embed_dims[i]))
            pos_drop = nn.Dropout(p=drop_rate)

            block = nn.ModuleList([Block(
                dim=embed_dims[i], num_patches=num_patches, num_heads=num_heads[i], mlp_ratio=mlp_ratios[i], qkv_bias=qkv_bias,
                qk_scale=qk_scale, drop=drop_rate, attn_drop=attn_drop_rate, drop_path=dpr[cur + j],
                norm_layer=norm_layer, sr_ratio=sr_ratios[i] if attn_type[i] == 'B' else int(agent_sr_ratios[i]),
                agent_num=int(agent_num[i]), attn_type=attn_type[i])
                for j in range(depths[i])])
            cur += depths[i]

            setattr(self, f"patch_embed{i + 1}", patch_embed)
            setattr(self, f"pos_embed{i + 1}", pos_embed)
            setattr(self, f"pos_drop{i + 1}", pos_drop)
            setattr(self, f"block{i + 1}", block)

        # classification head
        self.head = nn.Linear(embed_dims[3], num_classes) if num_classes > 0 else nn.Identity()

        # init weights
        for i in range(num_stages):
            pos_embed = getattr(self, f"pos_embed{i + 1}")
            trunc_normal_(pos_embed, std=.02)
        # trunc_normal_(self.cls_token, std=.02)
        self.apply(self._init_weights)

    def _init_weights(self, m):
        if isinstance(m, nn.Linear):
            trunc_normal_(m.weight, std=.02)
            if isinstance(m, nn.Linear) and m.bias is not None:
                nn.init.constant_(m.bias, 0)
        elif isinstance(m, nn.LayerNorm):
            nn.init.constant_(m.bias, 0)
            nn.init.constant_(m.weight, 1.0)

    @torch.jit.ignore
    def no_weight_decay(self):
        # return {'pos_embed', 'cls_token'} # has pos_embed may be better
        return {'cls_token'}

    def get_classifier(self):
        return self.head

    def reset_classifier(self, num_classes, global_pool=''):
        self.num_classes = num_classes
        self.head = nn.Linear(self.embed_dim, num_classes) if num_classes > 0 else nn.Identity()

    def _get_pos_embed(self, pos_embed, patch_embed, H, W):
        if H * W == self.patch_embed1.num_patches:
            return pos_embed
        else:
            return F.interpolate(
                pos_embed.reshape(1, patch_embed.H, patch_embed.W, -1).permute(0, 3, 1, 2),
                size=(H, W), mode="bilinear").reshape(1, -1, H * W).permute(0, 2, 1)

    def forward_features(self, x):
        B = x.shape[0]

        for i in range(self.num_stages):
            patch_embed = getattr(self, f"patch_embed{i + 1}")
            pos_embed = getattr(self, f"pos_embed{i + 1}")
            pos_drop = getattr(self, f"pos_drop{i + 1}")
            block = getattr(self, f"block{i + 1}")
            x, (H, W) = patch_embed(x)

            pos_embed = self._get_pos_embed(pos_embed, patch_embed, H, W)

            x = pos_drop(x + pos_embed)
            for blk in block:
                x = blk(x, H, W)
            if i != self.num_stages - 1:
                x = x.reshape(B, H, W, -1).permute(0, 3, 1, 2).contiguous()

        return x.mean(dim=1)

    def forward(self, x):
        x = self.forward_features(x)
        x = self.head(x)

        return x


def _conv_filter(state_dict, patch_size=16):
    """ convert patch embedding weight from manual patchify + linear proj to conv"""
    out_dict = {}
    for k, v in state_dict.items():
        if 'patch_embed.proj.weight' in k:
            v = v.reshape((v.shape[0], 3, patch_size, patch_size))
        out_dict[k] = v

    return out_dict


def agent_pvt_tiny(pretrained=False, **kwargs):
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[2, 2, 2, 2], sr_ratios=[8, 4, 2, 1],
        **kwargs)
    model.default_cfg = _cfg()

    return model


def agent_pvt_small(pretrained=False, **kwargs):
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[3, 4, 6, 3], sr_ratios=[8, 4, 2, 1], **kwargs)
    model.default_cfg = _cfg()

    return model


def agent_pvt_medium(pretrained=False, **kwargs):
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[3, 4, 18, 3], sr_ratios=[8, 4, 2, 1],
        **kwargs)
    model.default_cfg = _cfg()

    return model


def agent_pvt_large(pretrained=False, **kwargs):
    model = PyramidVisionTransformer(
        patch_size=4, embed_dims=[64, 128, 320, 512], num_heads=[1, 2, 5, 8], mlp_ratios=[8, 8, 4, 4], qkv_bias=True,
        norm_layer=partial(nn.LayerNorm, eps=1e-6), depths=[3, 8, 27, 3], sr_ratios=[8, 4, 2, 1],
        **kwargs)
    model.default_cfg = _cfg()

    return model