论文地址：BiFormer: Vision Transformer with Bi-Level Routing Attention

代码地址：https://github.com/rayleizhu/BiFormer

vision transformer中Attention是极其重要的模块，但是它有着非常大的缺点：计算量太大。

BiFormer提出了Bi-Level Routing Attention，在Attention计算时，只关注最重要的token，由此来降低计算量。

一、Bi-Level Routing Attention

下图是多个不同的Attention模块关注的区域，（a）是原始的attention，其他的都是稀疏的Attention结构。Bi-Level Routing Attention如下图（f）所示。

与其他的稀疏Attention结构有所不同，Bi-Level Routing Attention首先将特征图分为不同的区域（区域大小是SxS），每个区域经过线性映射，得到QKV，然后QK在每个SxS的窗口内取平均作为该区域的token（可参考代码），得到（r表示region，即SxS的窗口）,通过的矩阵运算得到，如下式：

得到了邻接矩阵后，取其相关性最高的k个token索引，这样就知道每个窗口与哪k个窗口相关性更高了。

得到了后，用gather运算得到和：

最后计算Attention：

Bi-Level Routing Attention的计算过程如下图所示，其中的k就是计算相关性索引时设置的参数。

二、代码

Bi-Level Routing Attention的代码如下：

"""
Core of BiFormer, Bi-Level Routing Attention.

To be refactored.

author: ZHU Lei
github: https://github.com/rayleizhu
email: ray.leizhu@outlook.com

This source code is licensed under the license found in the
LICENSE file in the root directory of this source tree.
"""
from typing import Tuple

import torch
import torch.nn as nn
import torch.nn.functional as F
from einops import rearrange
from torch import Tensor


class TopkRouting(nn.Module):
    """
    differentiable topk routing with scaling
    Args:
        qk_dim: int, feature dimension of query and key
        topk: int, the 'topk'
        qk_scale: int or None, temperature (multiply) of softmax activation
        with_param: bool, wether inorporate learnable params in routing unit
        diff_routing: bool, wether make routing differentiable
        soft_routing: bool, wether make output value multiplied by routing weights
    """
    def __init__(self, qk_dim, topk=4, qk_scale=None, param_routing=False, diff_routing=False):
        super().__init__()
        self.topk = topk
        self.qk_dim = qk_dim
        self.scale = qk_scale or qk_dim ** -0.5
        self.diff_routing = diff_routing
        # TODO: norm layer before/after linear?
        self.emb = nn.Linear(qk_dim, qk_dim) if param_routing else nn.Identity()
        # routing activation
        self.routing_act = nn.Softmax(dim=-1)
    
    def forward(self, query:Tensor, key:Tensor)->Tuple[Tensor]:
        """
        Args:
            q, k: (n, p^2, c) tensor
        Return:
            r_weight, topk_index: (n, p^2, topk) tensor
        """
        if not self.diff_routing:
            query, key = query.detach(), key.detach()
        query_hat, key_hat = self.emb(query), self.emb(key) # per-window pooling -> (n, p^2, c) 
        attn_logit = (query_hat*self.scale) @ key_hat.transpose(-2, -1) # (n, p^2, p^2)
        topk_attn_logit, topk_index = torch.topk(attn_logit, k=self.topk, dim=-1) # (n, p^2, k), (n, p^2, k)
        r_weight = self.routing_act(topk_attn_logit) # (n, p^2, k)
        
        return r_weight, topk_index
        

class KVGather(nn.Module):
    def __init__(self, mul_weight='none'):
        super().__init__()
        assert mul_weight in ['none', 'soft', 'hard']
        self.mul_weight = mul_weight

    def forward(self, r_idx:Tensor, r_weight:Tensor, kv:Tensor):
        """
        r_idx: (n, p^2, topk) tensor
        r_weight: (n, p^2, topk) tensor
        kv: (n, p^2, w^2, c_kq+c_v)

        Return:
            (n, p^2, topk, w^2, c_kq+c_v) tensor
        """
        # select kv according to routing index
        n, p2, w2, c_kv = kv.size()
        topk = r_idx.size(-1)
        # print(r_idx.size(), r_weight.size())
        # FIXME: gather consumes much memory (topk times redundancy), write cuda kernel? 
        topk_kv = torch.gather(kv.view(n, 1, p2, w2, c_kv).expand(-1, p2, -1, -1, -1), # (n, p^2, p^2, w^2, c_kv) without mem cpy
                                dim=2,
                                index=r_idx.view(n, p2, topk, 1, 1).expand(-1, -1, -1, w2, c_kv) # (n, p^2, k, w^2, c_kv)
                               )

        if self.mul_weight == 'soft':
            topk_kv = r_weight.view(n, p2, topk, 1, 1) * topk_kv # (n, p^2, k, w^2, c_kv)
        elif self.mul_weight == 'hard':
            raise NotImplementedError('differentiable hard routing TBA')
        # else: #'none'
        #     topk_kv = topk_kv # do nothing

        return topk_kv

class QKVLinear(nn.Module):
    def __init__(self, dim, qk_dim, bias=True):
        super().__init__()
        self.dim = dim
        self.qk_dim = qk_dim
        self.qkv = nn.Linear(dim, qk_dim + qk_dim + dim, bias=bias)
    
    def forward(self, x):
        q, kv = self.qkv(x).split([self.qk_dim, self.qk_dim+self.dim], dim=-1)
        return q, kv
        # q, k, v = self.qkv(x).split([self.qk_dim, self.qk_dim, self.dim], dim=-1)
        # return q, k, v

class BiLevelRoutingAttention(nn.Module):
    """
    n_win: number of windows in one side (so the actual number of windows is n_win*n_win)
    kv_per_win: for kv_downsample_mode='ada_xxxpool' only, number of key/values per window. Similar to n_win, the actual number is kv_per_win*kv_per_win.
    topk: topk for window filtering
    param_attention: 'qkvo'-linear for q,k,v and o, 'none': param free attention
    param_routing: extra linear for routing
    diff_routing: wether to set routing differentiable
    soft_routing: wether to multiply soft routing weights 
    """
    def __init__(self, dim, num_heads=8, n_win=7, qk_dim=None, qk_scale=None,
                 kv_per_win=4, kv_downsample_ratio=4, kv_downsample_kernel=None, kv_downsample_mode='identity',
                 topk=4, param_attention="qkvo", param_routing=False, diff_routing=False, soft_routing=False, side_dwconv=3,
                 auto_pad=False):
        super().__init__()
        # local attention setting
        self.dim = dim
        self.n_win = n_win  # Wh, Ww
        self.num_heads = num_heads
        self.qk_dim = qk_dim or dim
        assert self.qk_dim % num_heads == 0 and self.dim % num_heads==0, 'qk_dim and dim must be divisible by num_heads!'
        self.scale = qk_scale or self.qk_dim ** -0.5


        ################side_dwconv (i.e. LCE in ShuntedTransformer)###########
        self.lepe = nn.Conv2d(dim, dim, kernel_size=side_dwconv, stride=1, padding=side_dwconv//2, groups=dim) if side_dwconv > 0 else \
                    lambda x: torch.zeros_like(x)
        
        ################ global routing setting #################
        self.topk = topk
        self.param_routing = param_routing
        self.diff_routing = diff_routing
        self.soft_routing = soft_routing
        # router
        assert not (self.param_routing and not self.diff_routing) # cannot be with_param=True and diff_routing=False
        self.router = TopkRouting(qk_dim=self.qk_dim,
                                  qk_scale=self.scale,
                                  topk=self.topk,
                                  diff_routing=self.diff_routing,
                                  param_routing=self.param_routing)
        if self.soft_routing: # soft routing, always diffrentiable (if no detach)
            mul_weight = 'soft'
        elif self.diff_routing: # hard differentiable routing
            mul_weight = 'hard'
        else:  # hard non-differentiable routing
            mul_weight = 'none'
        self.kv_gather = KVGather(mul_weight=mul_weight)

        # qkv mapping (shared by both global routing and local attention)
        self.param_attention = param_attention
        if self.param_attention == 'qkvo':
            self.qkv = QKVLinear(self.dim, self.qk_dim)
            self.wo = nn.Linear(dim, dim)
        elif self.param_attention == 'qkv':
            self.qkv = QKVLinear(self.dim, self.qk_dim)
            self.wo = nn.Identity()
        else:
            raise ValueError(f'param_attention mode {self.param_attention} is not surpported!')
        
        self.kv_downsample_mode = kv_downsample_mode
        self.kv_per_win = kv_per_win
        self.kv_downsample_ratio = kv_downsample_ratio
        self.kv_downsample_kenel = kv_downsample_kernel
        if self.kv_downsample_mode == 'ada_avgpool':
            assert self.kv_per_win is not None
            self.kv_down = nn.AdaptiveAvgPool2d(self.kv_per_win)
        elif self.kv_downsample_mode == 'ada_maxpool':
            assert self.kv_per_win is not None
            self.kv_down = nn.AdaptiveMaxPool2d(self.kv_per_win)
        elif self.kv_downsample_mode == 'maxpool':
            assert self.kv_downsample_ratio is not None
            self.kv_down = nn.MaxPool2d(self.kv_downsample_ratio) if self.kv_downsample_ratio > 1 else nn.Identity()
        elif self.kv_downsample_mode == 'avgpool':
            assert self.kv_downsample_ratio is not None
            self.kv_down = nn.AvgPool2d(self.kv_downsample_ratio) if self.kv_downsample_ratio > 1 else nn.Identity()
        elif self.kv_downsample_mode == 'identity': # no kv downsampling
            self.kv_down = nn.Identity()
        elif self.kv_downsample_mode == 'fracpool':
            # assert self.kv_downsample_ratio is not None
            # assert self.kv_downsample_kenel is not None
            # TODO: fracpool
            # 1. kernel size should be input size dependent
            # 2. there is a random factor, need to avoid independent sampling for k and v 
            raise NotImplementedError('fracpool policy is not implemented yet!')
        elif kv_downsample_mode == 'conv':
            # TODO: need to consider the case where k != v so that need two downsample modules
            raise NotImplementedError('conv policy is not implemented yet!')
        else:
            raise ValueError(f'kv_down_sample_mode {self.kv_downsaple_mode} is not surpported!')

        # softmax for local attention
        self.attn_act = nn.Softmax(dim=-1)

        self.auto_pad=auto_pad

    def forward(self, x, ret_attn_mask=False):
        """
        x: NHWC tensor

        Return:
            NHWC tensor
        """
         # NOTE: use padding for semantic segmentation
        ###################################################
        if self.auto_pad:
            N, H_in, W_in, C = x.size()

            pad_l = pad_t = 0
            pad_r = (self.n_win - W_in % self.n_win) % self.n_win
            pad_b = (self.n_win - H_in % self.n_win) % self.n_win
            x = F.pad(x, (0, 0, # dim=-1
                          pad_l, pad_r, # dim=-2
                          pad_t, pad_b)) # dim=-3
            _, H, W, _ = x.size() # padded size
        else:
            N, H, W, C = x.size()
            assert H%self.n_win == 0 and W%self.n_win == 0 #
        ###################################################


        # patchify, (n, p^2, w, w, c), keep 2d window as we need 2d pooling to reduce kv size
        x = rearrange(x, "n (j h) (i w) c -> n (j i) h w c", j=self.n_win, i=self.n_win)

        #################qkv projection###################
        # q: (n, p^2, w, w, c_qk)
        # kv: (n, p^2, w, w, c_qk+c_v)
        # NOTE: separte kv if there were memory leak issue caused by gather
        q, kv = self.qkv(x) 

        # pixel-wise qkv
        # q_pix: (n, p^2, w^2, c_qk)
        # kv_pix: (n, p^2, h_kv*w_kv, c_qk+c_v)
        q_pix = rearrange(q, 'n p2 h w c -> n p2 (h w) c')
        kv_pix = self.kv_down(rearrange(kv, 'n p2 h w c -> (n p2) c h w'))
        kv_pix = rearrange(kv_pix, '(n j i) c h w -> n (j i) (h w) c', j=self.n_win, i=self.n_win)

        q_win, k_win = q.mean([2, 3]), kv[..., 0:self.qk_dim].mean([2, 3]) # window-wise qk, (n, p^2, c_qk), (n, p^2, c_qk)

        ##################side_dwconv(lepe)##################
        # NOTE: call contiguous to avoid gradient warning when using ddp
        lepe = self.lepe(rearrange(kv[..., self.qk_dim:], 'n (j i) h w c -> n c (j h) (i w)', j=self.n_win, i=self.n_win).contiguous())
        lepe = rearrange(lepe, 'n c (j h) (i w) -> n (j h) (i w) c', j=self.n_win, i=self.n_win)

        ############ gather q dependent k/v #################

        r_weight, r_idx = self.router(q_win, k_win) # both are (n, p^2, topk) tensors

        kv_pix_sel = self.kv_gather(r_idx=r_idx, r_weight=r_weight, kv=kv_pix) #(n, p^2, topk, h_kv*w_kv, c_qk+c_v)
        k_pix_sel, v_pix_sel = kv_pix_sel.split([self.qk_dim, self.dim], dim=-1)
        # kv_pix_sel: (n, p^2, topk, h_kv*w_kv, c_qk)
        # v_pix_sel: (n, p^2, topk, h_kv*w_kv, c_v)
        
        ######### do attention as normal ####################
        k_pix_sel = rearrange(k_pix_sel, 'n p2 k w2 (m c) -> (n p2) m c (k w2)', m=self.num_heads) # flatten to BMLC, (n*p^2, m, topk*h_kv*w_kv, c_kq//m) transpose here?
        v_pix_sel = rearrange(v_pix_sel, 'n p2 k w2 (m c) -> (n p2) m (k w2) c', m=self.num_heads) # flatten to BMLC, (n*p^2, m, topk*h_kv*w_kv, c_v//m)
        q_pix = rearrange(q_pix, 'n p2 w2 (m c) -> (n p2) m w2 c', m=self.num_heads) # to BMLC tensor (n*p^2, m, w^2, c_qk//m)

        # param-free multihead attention
        attn_weight = (q_pix * self.scale) @ k_pix_sel # (n*p^2, m, w^2, c) @ (n*p^2, m, c, topk*h_kv*w_kv) -> (n*p^2, m, w^2, topk*h_kv*w_kv)
        attn_weight = self.attn_act(attn_weight)
        out = attn_weight @ v_pix_sel # (n*p^2, m, w^2, topk*h_kv*w_kv) @ (n*p^2, m, topk*h_kv*w_kv, c) -> (n*p^2, m, w^2, c)
        out = rearrange(out, '(n j i) m (h w) c -> n (j h) (i w) (m c)', j=self.n_win, i=self.n_win,
                        h=H//self.n_win, w=W//self.n_win)

        out = out + lepe
        # output linear
        out = self.wo(out)

        # NOTE: use padding for semantic segmentation
        # crop padded region
        if self.auto_pad and (pad_r > 0 or pad_b > 0):
            out = out[:, :H_in, :W_in, :].contiguous()

        if ret_attn_mask:
            return out, r_weight, r_idx, attn_weight
        else:
            return out