(CVPR 2023)路由注意力机制.py

from typing import Tuple, Optional

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


# Github地址：https://github.com/rayleizhu/BiFormer
# 论文地址：https://arxiv.org/pdf/2303.08810

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, n_win=7, num_heads=8, 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=True):
        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
        """
        x = rearrange(x, "n c h w -> n h w c")
        # 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 rearrange(out, "n h w c -> n c h w")


class Attention(nn.Module):
    """
    vanilla attention
    """

    def __init__(self, dim, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0.):
        super().__init__()
        self.num_heads = num_heads
        head_dim = dim // num_heads
        # NOTE scale factor was wrong in my original version, can set manually to be compat with prev weights
        self.scale = qk_scale or head_dim ** -0.5

        self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)

    def forward(self, x):
        """
        args:
            x: NCHW tensor
        return:
            NCHW tensor
        """
        _, _, H, W = x.size()
        x = rearrange(x, 'n c h w -> n (h w) c')

        #######################################
        B, N, C = x.shape
        qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)

        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)
        #######################################

        x = rearrange(x, 'n (h w) c -> n c h w', h=H, w=W)
        return x


class AttentionLePE(nn.Module):
    """
    vanilla attention
    """

    def __init__(self, dim, num_heads=8, qkv_bias=False, qk_scale=None, attn_drop=0., proj_drop=0., side_dwconv=5):
        super().__init__()
        self.num_heads = num_heads
        head_dim = dim // num_heads
        # NOTE scale factor was wrong in my original version, can set manually to be compat with prev weights
        self.scale = qk_scale or head_dim ** -0.5

        self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
        self.attn_drop = nn.Dropout(attn_drop)
        self.proj = nn.Linear(dim, dim)
        self.proj_drop = nn.Dropout(proj_drop)
        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)

    def forward(self, x):
        """
        args:
            x: NCHW tensor
        return:
            NCHW tensor
        """
        _, _, H, W = x.size()
        x = rearrange(x, 'n c h w -> n (h w) c')

        #######################################
        B, N, C = x.shape
        qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, C // self.num_heads).permute(2, 0, 3, 1, 4)
        q, k, v = qkv[0], qkv[1], qkv[2]  # make torchscript happy (cannot use tensor as tuple)

        lepe = self.lepe(rearrange(x, 'n (h w) c -> n c h w', h=H, w=W))
        lepe = rearrange(lepe, 'n c h w -> n (h w) c')

        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 = x + lepe

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

        x = rearrange(x, 'n (h w) c -> n c h w', h=H, w=W)
        return x


def _grid2seq(x: Tensor, region_size: Tuple[int], num_heads: int):
    """
    Args:
        x: BCHW tensor
        region size: int
        num_heads: number of attention heads
    Return:
        out: rearranged x, has a shape of (bs, nhead, nregion, reg_size, head_dim)
        region_h, region_w: number of regions per col/row
    """
    B, C, H, W = x.size()
    region_h, region_w = H // region_size[0], W // region_size[1]
    x = x.view(B, num_heads, C // num_heads, region_h, region_size[0], region_w, region_size[1])
    x = torch.einsum('bmdhpwq->bmhwpqd', x).flatten(2, 3).flatten(-3, -2)  # (bs, nhead, nregion, reg_size, head_dim)
    return x, region_h, region_w


def _seq2grid(x: Tensor, region_h: int, region_w: int, region_size: Tuple[int]):
    """
    Args:
        x: (bs, nhead, nregion, reg_size^2, head_dim)
    Return:
        x: (bs, C, H, W)
    """
    bs, nhead, nregion, reg_size_square, head_dim = x.size()
    x = x.view(bs, nhead, region_h, region_w, region_size[0], region_size[1], head_dim)
    x = torch.einsum('bmhwpqd->bmdhpwq', x).reshape(bs, nhead * head_dim,
                                                    region_h * region_size[0], region_w * region_size[1])
    return x


def regional_routing_attention_torch(
        query: Tensor, key: Tensor, value: Tensor, scale: float,
        region_graph: LongTensor, region_size: Tuple[int],
        kv_region_size: Optional[Tuple[int]] = None,
        auto_pad=True) -> Tensor:
    """
    Args:
        query, key, value: (B, C, H, W) tensor
        scale: the scale/temperature for dot product attention
        region_graph: (B, nhead, h_q*w_q, topk) tensor, topk <= h_k*w_k
        region_size: region/window size for queries, (rh, rw)
        key_region_size: optional, if None, key_region_size=region_size
        auto_pad: required to be true if the input sizes are not divisible by the region_size
    Return:
        output: (B, C, H, W) tensor
        attn: (bs, nhead, q_nregion, reg_size, topk*kv_region_size) attention matrix
    """
    kv_region_size = kv_region_size or region_size
    bs, nhead, q_nregion, topk = region_graph.size()

    # Auto pad to deal with any input size
    q_pad_b, q_pad_r, kv_pad_b, kv_pad_r = 0, 0, 0, 0
    if auto_pad:
        _, _, Hq, Wq = query.size()
        q_pad_b = (region_size[0] - Hq % region_size[0]) % region_size[0]
        q_pad_r = (region_size[1] - Wq % region_size[1]) % region_size[1]
        if (q_pad_b > 0 or q_pad_r > 0):
            query = F.pad(query, (0, q_pad_r, 0, q_pad_b))  # zero padding

        _, _, Hk, Wk = key.size()
        kv_pad_b = (kv_region_size[0] - Hk % kv_region_size[0]) % kv_region_size[0]
        kv_pad_r = (kv_region_size[1] - Wk % kv_region_size[1]) % kv_region_size[1]
        if (kv_pad_r > 0 or kv_pad_b > 0):
            key = F.pad(key, (0, kv_pad_r, 0, kv_pad_b))  # zero padding
            value = F.pad(value, (0, kv_pad_r, 0, kv_pad_b))  # zero padding

    # to sequence format, i.e. (bs, nhead, nregion, reg_size, head_dim)
    query, q_region_h, q_region_w = _grid2seq(query, region_size=region_size, num_heads=nhead)
    key, _, _ = _grid2seq(key, region_size=kv_region_size, num_heads=nhead)
    value, _, _ = _grid2seq(value, region_size=kv_region_size, num_heads=nhead)

    # gather key and values.
    # TODO: is seperate gathering slower than fused one (our old version) ?
    # torch.gather does not support broadcasting, hence we do it manually
    bs, nhead, kv_nregion, kv_region_size, head_dim = key.size()
    broadcasted_region_graph = region_graph.view(bs, nhead, q_nregion, topk, 1, 1). \
        expand(-1, -1, -1, -1, kv_region_size, head_dim)
    key_g = torch.gather(key.view(bs, nhead, 1, kv_nregion, kv_region_size, head_dim). \
                         expand(-1, -1, query.size(2), -1, -1, -1), dim=3,
                         index=broadcasted_region_graph)  # (bs, nhead, q_nregion, topk, kv_region_size, head_dim)
    value_g = torch.gather(value.view(bs, nhead, 1, kv_nregion, kv_region_size, head_dim). \
                           expand(-1, -1, query.size(2), -1, -1, -1), dim=3,
                           index=broadcasted_region_graph)  # (bs, nhead, q_nregion, topk, kv_region_size, head_dim)

    # token-to-token attention
    # (bs, nhead, q_nregion, reg_size, head_dim) @ (bs, nhead, q_nregion, head_dim, topk*kv_region_size)
    # -> (bs, nhead, q_nregion, reg_size, topk*kv_region_size)
    # TODO: mask padding region
    attn = (query * scale) @ key_g.flatten(-3, -2).transpose(-1, -2)
    attn = torch.softmax(attn, dim=-1)
    # (bs, nhead, q_nregion, reg_size, topk*kv_region_size) @ (bs, nhead, q_nregion, topk*kv_region_size, head_dim)
    # -> (bs, nhead, q_nregion, reg_size, head_dim)
    output = attn @ value_g.flatten(-3, -2)

    # to BCHW format
    output = _seq2grid(output, region_h=q_region_h, region_w=q_region_w, region_size=region_size)

    # remove paddings if needed
    if auto_pad and (q_pad_b > 0 or q_pad_r > 0):
        output = output[:, :, :Hq, :Wq]

    return output, attn


class BiLevelRoutingAttention_nchw(nn.Module):
    """Bi-Level Routing Attention that takes nchw input

    Compared to legacy version, this implementation:
    * removes unused args and components
    * uses nchw input format to avoid frequent permutation

    When the size of inputs is not divisible by the region size, there is also a numerical difference
    than legacy implementation, due to:
    * different way to pad the input feature map (padding after linear projection)
    * different pooling behavior (count_include_pad=False)

    Current implementation is more reasonable, hence we do not keep backward numerical compatiability
    """

    def __init__(self, dim, num_heads=8, n_win=7, qk_scale=None, topk=4, side_dwconv=3, auto_pad=False,
                 attn_backend='torch'):
        super().__init__()
        # local attention setting
        self.dim = dim
        self.num_heads = num_heads
        assert self.dim % num_heads == 0, 'dim must be divisible by num_heads!'
        self.head_dim = self.dim // self.num_heads
        self.scale = qk_scale or self.dim ** -0.5  # NOTE: to be consistent with old models.

        ################side_dwconv (i.e. LCE in Shunted Transformer)###########
        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)

        ################ regional routing setting #################
        self.topk = topk
        self.n_win = n_win  # number of windows per row/col

        ##########################################

        self.qkv_linear = nn.Conv2d(self.dim, 3 * self.dim, kernel_size=1)
        self.output_linear = nn.Conv2d(self.dim, self.dim, kernel_size=1)

        if attn_backend == 'torch':
            self.attn_fn = regional_routing_attention_torch
        else:
            raise ValueError('CUDA implementation is not available yet. Please stay tuned.')

    def forward(self, x: Tensor, ret_attn_mask=False):
        """
        Args:
            x: NCHW tensor, better to be channel_last (https://pytorch.org/tutorials/intermediate/memory_format_tutorial.html)
        Return:
            NCHW tensor
        """
        N, C, H, W = x.size()
        region_size = (H // self.n_win, W // self.n_win)

        # STEP 1: linear projection
        qkv = self.qkv_linear.forward(x)  # ncHW
        q, k, v = qkv.chunk(3, dim=1)  # ncHW

        # STEP 2: region-to-region routing
        # NOTE: ceil_mode=True, count_include_pad=False = auto padding
        # NOTE: gradients backward through token-to-token attention. See Appendix A for the intuition.
        q_r = F.avg_pool2d(q.detach(), kernel_size=region_size, ceil_mode=True, count_include_pad=False)
        k_r = F.avg_pool2d(k.detach(), kernel_size=region_size, ceil_mode=True, count_include_pad=False)  # nchw
        q_r: Tensor = q_r.permute(0, 2, 3, 1).flatten(1, 2)  # n(hw)c
        k_r: Tensor = k_r.flatten(2, 3)  # nc(hw)
        a_r = q_r @ k_r  # n(hw)(hw), adj matrix of regional graph
        _, idx_r = torch.topk(a_r, k=self.topk, dim=-1)  # n(hw)k long tensor
        idx_r: LongTensor = idx_r.unsqueeze_(1).expand(-1, self.num_heads, -1, -1)

        # STEP 3: token to token attention (non-parametric function)
        output, attn_mat = self.attn_fn(query=q, key=k, value=v, scale=self.scale,
                                        region_graph=idx_r, region_size=region_size
                                        )

        output = output + self.lepe(v)  # ncHW
        output = self.output_linear(output)  # ncHW

        if ret_attn_mask:
            return output, attn_mat

        return output


# 输入 N C HW,  输出 N C H W
if __name__ == '__main__':
    block = BiLevelRoutingAttention_nchw(64).cuda()
    input = torch.rand(1, 64, 64, 64).cuda() # 输入 B C H W
    output = block(input)
    print(input.size(), output.size())