這一篇我們來分析一下將 multi-scale deformable attention 取代self-attention的transformer的構(gòu)造。

首先來看一下編碼器部分Encoder

class DeformableTransformerEncoderLayer(nn.Module):
    def __init__(self,
                 d_model=256, d_ffn=1024,
                 dropout=0.1, activation="relu",
                 n_levels=4, n_heads=8, n_points=4):
        super().__init__()

        # self attention
        self.self_attn = MSDeformAttn(d_model, n_levels, n_heads, n_points)
        self.dropout1 = nn.Dropout(dropout)
        self.norm1 = nn.LayerNorm(d_model)

        # ffn
        self.linear1 = nn.Linear(d_model, d_ffn)
        self.activation = _get_activation_fn(activation)
        self.dropout2 = nn.Dropout(dropout)
        self.linear2 = nn.Linear(d_ffn, d_model)
        self.dropout3 = nn.Dropout(dropout)
        self.norm2 = nn.LayerNorm(d_model)

    @staticmethod
    def with_pos_embed(tensor, pos):
        return tensor if pos is None else tensor + pos

    def forward_ffn(self, src):
        src2 = self.linear2(self.dropout2(self.activation(self.linear1(src))))
        src = src + self.dropout3(src2)
        src = self.norm2(src)
        return src

    def forward(self, src, pos, reference_points, spatial_shapes, level_start_index, padding_mask=None):
        # self attention
        src2 = self.self_attn(self.with_pos_embed(src, pos), reference_points, src, spatial_shapes, level_start_index, padding_mask)
        src = src + self.dropout1(src2)
        src = self.norm1(src)

        # ffn
        src = self.forward_ffn(src)

        return src

實(shí)現(xiàn)過程如下圖所示。multi-head self-attention使用MSDeformAttn構(gòu)造，然后兩個(gè)線性層定義了FFN模塊， Norm是nn.LayerNorm， Add表示跨層鏈接， 中間使用了多層dropout層。
self_attn即MSDeformAttn得輸入為：

1. query 每個(gè)query的特征，在encoder里是每一個(gè)level中每個(gè)位置點(diǎn)的特征
2. reference_points batch_size x query個(gè)數(shù) x level個(gè)數(shù) x 2 ，每個(gè)query每個(gè)level的位置點(diǎn)，歸一化之后的點(diǎn)，encoder里是每個(gè)level的位置點(diǎn)歸一化之后的位置
3. src backbone的輸出，可能是多個(gè)stage，是cat之后再flatten的結(jié)果
4. spatial_shapes 每個(gè)level的featmap尺寸
5. level_start_index 每個(gè)level在flatten的特征向量集上的起始索引
6. padding_mask 考慮所有l(wèi)evel，每個(gè)位置是否mask的標(biāo)志。

Encoder

上面定義的是每一個(gè)encoder layer的實(shí)現(xiàn)， transformer中的Encoder是多個(gè)相同結(jié)構(gòu)的Encode layer的串聯(lián)。所以Encoder定義如下：

class DeformableTransformerEncoder(nn.Module):
    def __init__(self, encoder_layer, num_layers):
        super().__init__()
        self.layers = _get_clones(encoder_layer, num_layers)  
        self.num_layers = num_layers  # 堆疊的個(gè)數(shù)

    @staticmethod
    def get_reference_points(spatial_shapes, valid_ratios, device):
        reference_points_list = []
        for lvl, (H_, W_) in enumerate(spatial_shapes):

            ref_y, ref_x = torch.meshgrid(torch.linspace(0.5, H_ - 0.5, H_, dtype=torch.float32, device=device),
                                          torch.linspace(0.5, W_ - 0.5, W_, dtype=torch.float32, device=device))
            ref_y = ref_y.reshape(-1)[None] / (valid_ratios[:, None, lvl, 1] * H_)
            ref_x = ref_x.reshape(-1)[None] / (valid_ratios[:, None, lvl, 0] * W_)
            ref = torch.stack((ref_x, ref_y), -1)
            reference_points_list.append(ref)
        reference_points = torch.cat(reference_points_list, 1)
        reference_points = reference_points[:, :, None] * valid_ratios[:, None]
        return reference_points

    def forward(self, src, spatial_shapes, level_start_index, valid_ratios, pos=None, padding_mask=None):
        output = src
        reference_points = self.get_reference_points(spatial_shapes, valid_ratios, device=src.device)
        for _, layer in enumerate(self.layers):
            output = layer(output, pos, reference_points, spatial_shapes, level_start_index, padding_mask)

        return output

這里的_get_clones()函數(shù)時(shí)結(jié)構(gòu)的深度復(fù)制，即參數(shù)是不同的。

def _get_clones(module, N):
    return nn.ModuleList([copy.deepcopy(module) for i in range(N)])

forward里面即順序執(zhí)行的過程，主要要理解的是reference_points的定義。其實(shí)就是計(jì)算每個(gè)level中每個(gè)網(wǎng)格點(diǎn)的位置，這里的位置采用的是網(wǎng)格的中心點(diǎn)。這里有一個(gè)變量valid_ratios需要解釋一下，query的個(gè)數(shù)是所有的像素位置，包括不同的level， 那么每個(gè)query都需要在不同的level上采點(diǎn)，所以需要每個(gè)reference_point在每個(gè)level上映射后的點(diǎn)，所以這里的valid_ratios在計(jì)算時(shí)就是公式2里的函數(shù)。于是reference_points的size為，總共有個(gè)queries。

接下來是編碼器部分Decoder

class DeformableTransformerDecoderLayer(nn.Module):
    def __init__(self, d_model=256, d_ffn=1024,
                 dropout=0.1, activation="relu",
                 n_levels=4, n_heads=8, n_points=4):
        super().__init__()

        # cross attention
        self.cross_attn = MSDeformAttn(d_model, n_levels, n_heads, n_points)
        self.dropout1 = nn.Dropout(dropout)
        self.norm1 = nn.LayerNorm(d_model)

        # self attention
        self.self_attn = nn.MultiheadAttention(d_model, n_heads, dropout=dropout)
        self.dropout2 = nn.Dropout(dropout)
        self.norm2 = nn.LayerNorm(d_model)

        # ffn
        self.linear1 = nn.Linear(d_model, d_ffn)
        self.activation = _get_activation_fn(activation)
        self.dropout3 = nn.Dropout(dropout)
        self.linear2 = nn.Linear(d_ffn, d_model)
        self.dropout4 = nn.Dropout(dropout)
        self.norm3 = nn.LayerNorm(d_model)

    @staticmethod
    def with_pos_embed(tensor, pos):
        return tensor if pos is None else tensor + pos

    def forward_ffn(self, tgt):
        tgt2 = self.linear2(self.dropout3(self.activation(self.linear1(tgt))))
        tgt = tgt + self.dropout4(tgt2)
        tgt = self.norm3(tgt)
        return tgt

    def forward(self, tgt, query_pos, reference_points, src, src_spatial_shapes, level_start_index, src_padding_mask=None):
        # self attention
        q = k = self.with_pos_embed(tgt, query_pos)
        tgt2 = self.self_attn(q.transpose(0, 1), k.transpose(0, 1), tgt.transpose(0, 1))[0].transpose(0, 1)
        tgt = tgt + self.dropout2(tgt2)
        tgt = self.norm2(tgt)

        # cross attention
        tgt2 = self.cross_attn(self.with_pos_embed(tgt, query_pos),
                               reference_points,
                               src, src_spatial_shapes, level_start_index, src_padding_mask)
        tgt = tgt + self.dropout1(tgt2)
        tgt = self.norm1(tgt)

        # ffn
        tgt = self.forward_ffn(tgt)

        return tgt

編碼部分如下圖所示，每個(gè)layer中包含兩個(gè)部分，即query之間的self-attention，以及query與key之間的cross-attention.
self-attention由nn.MultiheadAttention實(shí)現(xiàn)，這里的pos表示的是query之間的位置編碼。cross-attention調(diào)用的MSDeformAttn， 其輸入的query不再是所有的像素位置，而src，src_spatial_shapes依然是所有的level。

decoder

class DeformableTransformerDecoder(nn.Module):
    def __init__(self, decoder_layer, num_layers, return_intermediate=False):
        super().__init__()
        self.layers = _get_clones(decoder_layer, num_layers)
        self.num_layers = num_layers
        self.return_intermediate = return_intermediate
        # hack implementation for iterative bounding box refinement and two-stage Deformable DETR
        self.bbox_embed = None
        self.class_embed = None

    def forward(self, tgt, reference_points, src, src_spatial_shapes, src_level_start_index, src_valid_ratios,
                query_pos=None, src_padding_mask=None):
        output = tgt

        intermediate = []
        intermediate_reference_points = []
        for lid, layer in enumerate(self.layers):
            if reference_points.shape[-1] == 4:
                reference_points_input = reference_points[:, :, None] \
                                         * torch.cat([src_valid_ratios, src_valid_ratios], -1)[:, None]
            else:
                assert reference_points.shape[-1] == 2
                reference_points_input = reference_points[:, :, None] * src_valid_ratios[:, None]
            output = layer(output, query_pos, reference_points_input, src, src_spatial_shapes, src_level_start_index, src_padding_mask)

            # hack implementation for iterative bounding box refinement
            if self.bbox_embed is not None:
                tmp = self.bbox_embed[lid](output)
                if reference_points.shape[-1] == 4:
                    new_reference_points = tmp + inverse_sigmoid(reference_points)
                    new_reference_points = new_reference_points.sigmoid()
                else:
                    assert reference_points.shape[-1] == 2
                    new_reference_points = tmp
                    new_reference_points[..., :2] = tmp[..., :2] + inverse_sigmoid(reference_points)
                    new_reference_points = new_reference_points.sigmoid()
                reference_points = new_reference_points.detach()

            if self.return_intermediate:
                intermediate.append(output)
                intermediate_reference_points.append(reference_points)

        if self.return_intermediate:
            return torch.stack(intermediate), torch.stack(intermediate_reference_points)

        return output, reference_points

用decoderLayer搭建decoder的過程即順序執(zhí)行的過程，每次cross-attention的key和value都來自于相同的量，即encoder的多個(gè)level的輸出。這里還定義了兩個(gè)改進(jìn)的接口，即box迭代細(xì)化和兩階段DETR。

Transformer

這部分是最終把Encoder和Decoder組裝起來的過程。

class DeformableTransformer(nn.Module):
    def __init__(self, d_model=256, nhead=8,
                 num_encoder_layers=6, num_decoder_layers=6, dim_feedforward=1024, dropout=0.1,
                 activation="relu", return_intermediate_dec=False,
                 num_feature_levels=4, dec_n_points=4,  enc_n_points=4,
                 two_stage=False, two_stage_num_proposals=300):
        super().__init__()

        self.d_model = d_model
        self.nhead = nhead
        self.two_stage = two_stage
        self.two_stage_num_proposals = two_stage_num_proposals

        encoder_layer = DeformableTransformerEncoderLayer(d_model, dim_feedforward,
                                                          dropout, activation,
                                                          num_feature_levels, nhead, enc_n_points)
        self.encoder = DeformableTransformerEncoder(encoder_layer, num_encoder_layers)

        decoder_layer = DeformableTransformerDecoderLayer(d_model, dim_feedforward,
                                                          dropout, activation,
                                                          num_feature_levels, nhead, dec_n_points)
        self.decoder = DeformableTransformerDecoder(decoder_layer, num_decoder_layers, return_intermediate_dec)

        self.level_embed = nn.Parameter(torch.Tensor(num_feature_levels, d_model))

        if two_stage:
            self.enc_output = nn.Linear(d_model, d_model)
            self.enc_output_norm = nn.LayerNorm(d_model)
            self.pos_trans = nn.Linear(d_model * 2, d_model * 2)
            self.pos_trans_norm = nn.LayerNorm(d_model * 2)
        else:
            self.reference_points = nn.Linear(d_model, 2)
        self._reset_parameters()

這里出現(xiàn)了幾個(gè)變量two_stage, two_stage_num_proposals, 'level_embed', reference_points以及two_stage的提取proposal過程。

看看其在forward中的作用：

def forward(self, srcs, masks, pos_embeds, query_embed=None):
        assert self.two_stage or query_embed is not None

        # prepare input for encoder
        src_flatten = []
        mask_flatten = []
        lvl_pos_embed_flatten = []
        spatial_shapes = []
        for lvl, (src, mask, pos_embed) in enumerate(zip(srcs, masks, pos_embeds)):
            bs, c, h, w = src.shape
            spatial_shape = (h, w)
            spatial_shapes.append(spatial_shape)
            src = src.flatten(2).transpose(1, 2)        # bs x c x h x w -> bs x c x hw -> bs x hw x c
            mask = mask.flatten(1)                      # bs x hw
            pos_embed = pos_embed.flatten(2).transpose(1, 2) # bs x c x h x w -> bs x c x hw -> bs x hw x c
            lvl_pos_embed = pos_embed + self.level_embed[lvl].view(1, 1, -1) # bs x hw x c + 1 x 1 x c, 每一level提供一個(gè)可學(xué)習(xí)的編碼
            lvl_pos_embed_flatten.append(lvl_pos_embed)     # 分別flatten之后append，方便encoder調(diào)用，即所有的keys
            src_flatten.append(src)
            mask_flatten.append(mask)
        src_flatten = torch.cat(src_flatten, 1)
        mask_flatten = torch.cat(mask_flatten, 1)
        lvl_pos_embed_flatten = torch.cat(lvl_pos_embed_flatten, 1)
        spatial_shapes = torch.as_tensor(spatial_shapes, dtype=torch.long, device=src_flatten.device)
        level_start_index = torch.cat((spatial_shapes.new_zeros((1, )), spatial_shapes.prod(1).cumsum(0)[:-1]))
        valid_ratios = torch.stack([self.get_valid_ratio(m) for m in masks], 1) # bs x num_level x 2

        # encoder
        memory = self.encoder(src_flatten, spatial_shapes, level_start_index, valid_ratios, lvl_pos_embed_flatten, mask_flatten)

        # prepare input for decoder
        bs, _, c = memory.shape
        if self.two_stage:
            output_memory, output_proposals = self.gen_encoder_output_proposals(memory, mask_flatten, spatial_shapes)

            # hack implementation for two-stage Deformable DETR
            enc_outputs_class = self.decoder.class_embed[self.decoder.num_layers](output_memory)  # 預(yù)測(cè)輸出的score
            enc_outputs_coord_unact = self.decoder.bbox_embed[self.decoder.num_layers](output_memory) + output_proposals  # 編碼后的anchor+相對(duì)偏差

            topk = self.two_stage_num_proposals
            topk_proposals = torch.topk(enc_outputs_class[..., 0], topk, dim=1)[1]  # 選擇最大的topk的proposal
            topk_coords_unact = torch.gather(enc_outputs_coord_unact, 1, topk_proposals.unsqueeze(-1).repeat(1, 1, 4))  # 選擇對(duì)應(yīng)topl score的編碼后的框
            topk_coords_unact = topk_coords_unact.detach()
            reference_points = topk_coords_unact.sigmoid()  # 相當(dāng)于對(duì)proposal的微調(diào)
            init_reference_out = reference_points
            pos_trans_out = self.pos_trans_norm(self.pos_trans(self.get_proposal_pos_embed(topk_coords_unact)))
            query_embed, tgt = torch.split(pos_trans_out, c, dim=2)
        else:
            query_embed, tgt = torch.split(query_embed, c, dim=1)       # Lq x d_model
            query_embed = query_embed.unsqueeze(0).expand(bs, -1, -1)   # bs x Lq x d_model     每個(gè)sample的query相同，參考位置也相同
            tgt = tgt.unsqueeze(0).expand(bs, -1, -1)                   # 初始的query
            reference_points = self.reference_points(query_embed).sigmoid()     # 每個(gè)query是學(xué)習(xí)到不同的參考位置
            init_reference_out = reference_points

        # decoder
        hs, inter_references = self.decoder(tgt, reference_points, memory,
                                            spatial_shapes, level_start_index, valid_ratios, query_embed, mask_flatten)

        inter_references_out = inter_references
        if self.two_stage:
            return hs, init_reference_out, inter_references_out, enc_outputs_class, enc_outputs_coord_unact
        return hs, init_reference_out, inter_references_out, None, None

可以發(fā)現(xiàn) level_embed始終可學(xué)習(xí)的對(duì)于不同level進(jìn)行額外位置編碼的作用。

不考慮two_stage的情況中query_embed是大小的向量組，2d_model的長(zhǎng)度包含query的可學(xué)習(xí)特征以及初始化的pos編碼， reference_points對(duì)pos編碼特征進(jìn)行線性變換以得到初始可能的reference點(diǎn)。（這里有點(diǎn)值得思考的問題，相當(dāng)于query_embed中包含了兩類，一類是表觀特征，一類是位置編碼，那么我們是不是可以理解為表觀特征作為模板在編碼位置臨近進(jìn)行模板匹配呢？這樣我們可以直接提供模板特征和侯選位置。）

考慮two_stage的情況，相當(dāng)于先利用encoder進(jìn)行proposals的粗選，即更具score篩選topk個(gè)候選位置。那么我看一看怎么由encoder提取proposals：

def gen_encoder_output_proposals(self, memory, memory_padding_mask, spatial_shapes):
        N_, S_, C_ = memory.shape
        base_scale = 4.0
        proposals = []
        _cur = 0
        for lvl, (H_, W_) in enumerate(spatial_shapes):
            mask_flatten_ = memory_padding_mask[:, _cur:(_cur + H_ * W_)].view(N_, H_, W_, 1)
            valid_H = torch.sum(~mask_flatten_[:, :, 0, 0], 1)
            valid_W = torch.sum(~mask_flatten_[:, 0, :, 0], 1)

            grid_y, grid_x = torch.meshgrid(torch.linspace(0, H_ - 1, H_, dtype=torch.float32, device=memory.device),
                                            torch.linspace(0, W_ - 1, W_, dtype=torch.float32, device=memory.device))
            grid = torch.cat([grid_x.unsqueeze(-1), grid_y.unsqueeze(-1)], -1)  # H x W x 2 

            scale = torch.cat([valid_W.unsqueeze(-1), valid_H.unsqueeze(-1)], 1).view(N_, 1, 1, 2) # 每個(gè)sample的有效尺寸
            grid = (grid.unsqueeze(0).expand(N_, -1, -1, -1) + 0.5) / scale  # 歸一化
            wh = torch.ones_like(grid) * 0.05 * (2.0 ** lvl) #  方形的候選框，其實(shí)等價(jià)于anchor
            proposal = torch.cat((grid, wh), -1).view(N_, -1, 4)
            proposals.append(proposal)
            _cur += (H_ * W_)  # 每個(gè)level的起始索引
        output_proposals = torch.cat(proposals, 1)  # bs x key_num x 4
        output_proposals_valid = ((output_proposals > 0.01) & (output_proposals < 0.99)).all(-1, keepdim=True)  
        # 篩選有效的proposal，將靠近邊界的點(diǎn)舍棄
        output_proposals = torch.log(output_proposals / (1 - output_proposals))
        output_proposals = output_proposals.masked_fill(memory_padding_mask.unsqueeze(-1), float('inf'))
        output_proposals = output_proposals.masked_fill(~output_proposals_valid, float('inf'))

        output_memory = memory
        output_memory = output_memory.masked_fill(memory_padding_mask.unsqueeze(-1), float(0))
        output_memory = output_memory.masked_fill(~output_proposals_valid, float(0))
        output_memory = self.enc_output_norm(self.enc_output(output_memory))
        return output_memory, output_proposals

for循環(huán)里是對(duì)不同level的所有格點(diǎn)創(chuàng)建不同尺寸的anchor框，scale其實(shí)是對(duì)有效區(qū)域的處理，后續(xù)對(duì)output_proposals的處理是篩選掉邊界附近的候選，輸出是對(duì)應(yīng)位置的特征和編碼后的proposal， 對(duì)應(yīng)位置的特征用于映射proposal的類別score以及校正偏差。值得注意的是proposal并沒有直接使用原始坐標(biāo)，而是進(jìn)行了log的編碼
， 在forward中的two_stage情況提取reference_points是使用sigmoid函數(shù)進(jìn)行了解碼，我們假設(shè)偏置量為0，可以發(fā)現(xiàn)：

以上就是整個(gè)transformer的實(shí)現(xiàn)過程，不考慮two-stage的情形就是encoder和decoder的調(diào)用，而ecoderlayer和decoderlayer主要是deformAttn的調(diào)用。
下一篇我們來看整個(gè)deformable DETR的實(shí)現(xiàn)，即backbone + transformer以及FFN過程， transformer提供了每個(gè)query變換后的embedding和學(xué)習(xí)到的reference_points, FFN則將其轉(zhuǎn)換為bbox和score。